Aquinas College Physics Practical Endorsement Qualification Record Book Practical Endorsement Module 3 P a g e | 1 Module 3 Practical Endorsement Record Book Name: ………………….………..………. Teacher: ……………...…….……...……. Physics Group: ………………………….

Aquinas College Physics Practical Endorsement Qualification Record Book Practical Endorsement Module 3 P a g e | 2 Contents List of practicals in module 3........................................................................................................................ 2 PAG overview.............................................................................................................................................. 3 3.1: Finding g: overview ........................................................................................................................ 5 3.1(i): Finding g: timer ball ....................................................................................................................... 6 3.1(ii): Finding g: trolley & ramp............................................................................................................... 9 3.1(iii): Finding g: card & light gates ...................................................................................................... 13 3.1(iv):Finding g: picket fence & light gate............................................................................................. 16 3.1:Finding g: summary......................................................................................................................... 17 3.5: Investigating terminal velocity..................................................................................................... 19 3.6: Hooke’s law & combinations of springs...................................................................................... 31 3.6: Young modulus & breaking stress of copper............................................................................. 36 3.6: Loading & unloading elastic bands............................................................................................. 46 Spare pages & extra graph paper.............................................................................................................. 52 List of practicals in module 3 Module PAG group Practical Date Completed 3.1 1 Different methods for finding a value for g 3.5 1 Investigating terminal velocity 3.6 2 Hooke’s law & combinations of springs 3.6 2 Young modulus & breaking stress of copper 3.6 2 Loading & unloading elastic bands

Aquinas College Physics Practical Endorsement Qualification Record Book Practical Endorsement Module 3 P a g e | 3 PAG overview In order to pass the Practical Endorsement Qualification (expected for any Science- or Engineering-related degree and also for many apprenticeship opportunities) you need to show competency in a number of different practical skills across twelve different practical activity groups (PAGs; see outline below). For the experiments we undertake in module 3, you will mainly be fulfilling the criteria of practical activity groups (PAGs) 1 and 2 (see above). PAGs 3-6 will be completed in module 4 and PAGs 7-11 will be completed in the second year. During the summer term you will undertake an independent research project, which will involve you writing a report on a physics topic of your choice to fulfill the criteria for PAG 12. We have designed a series of practicals which will allow you to both demonstrate competency across all 12 PAGs and fulfil all the criteria set out by the exam board. Records for these will be kept in this and two other booklets. As well as allowing you to pass the practical endorsement, completion of these practicals will enable you to succeed in the final exams, where a large component of the written assessment will be addressing your knowledge of each practical, the techniques used, and the way that data is processed to enable you to draw conclusions from the experiments.

Aquinas College Physics Practical Endorsement Qualification Record Book Practical Endorsement Module 3 P a g e | 4 To pass the practical endorsement qualification you need to: ● Keep accurate records of each practical activity you complete on the main records page (page 2) of this booklet, including the date each experiment was carried out. ● Complete all parts of each practical activity including any data processing. If you process your data using computer software (Excel etc.), you will need to print out any data tables and graphs and insert them between the relevant pages in this booklet. ● Answer all questions associated with each practical activity in the space provided on the instruction sheets. For each practical carried out you will need to ensure that you are fully aware of the competencies being assessed. Although you will often work as one of a pair (and sometimes even in a group of three), each member of the group needs to be seen to be using the equipment, making the measurements and taking a full part in the practical to pass each competency skill.

c where y and x represent the dependent and independent variables respectively. • As in all science experiments, we must be mindful of the uncertainty inherent in each measurement that we take, and the uncertainty of every measurement should be quantified (see Appendix 3). • From the uncertainty bars plotted in each experiment you will be expected to determine whether your value of g may be considered to be accurate compared to the accepted value of 9.81 m s-2 . General instructions Complete the experiments in the order instructed by your teacher. 1. Download the results table spreadsheet available at http://bit.ly/31-GravityExpts (also available at www.aquinasphysics.com) and go to the correct tab for the experiment you are completing. 2. Complete the data table as you make your measurements. 3. Save the spreadsheet and share with all members in your group. 4. Each person should then print out the results table and graph for each experiment, annotate as instructed and add them to their practical folder. PAG 1 date completed …………………………………. ..

. If a graph is plotted with time squared t 2 on the y-axis against displacement s on the x-axis it should yield a straight line (through the origin) with a gradient equal in value to . Method 1. Open the spreadsheet (http://bit.ly/31-GravityExpts) and go to the correct worksheet (red tab) 2. Press and hold the button on the timer ball screen to zero the timer. Releasing the button starts the clock. Enter the resolution of the timer ball into the appropriate cell of the spreadsheet. 3. Drop the ball (releasing the button) so that it falls onto a flat horizontal surface. 4. Record the height and the time taken to fall, with absolute uncertainty (±U) for each of the two measurements. When deciding upon a value for the uncertainty, you may wish to think about how certain you are that: a. the base of the ball is perfectly in line with the appropriate marking on the ruler; b. the ruler is exactly vertical; c. you are perfectly steady in holding and releasing the ball from your stated height. 5. Drop the ball from the same height twice more and record your results. Ensure that each member of your group undertakes each role in this experiment. The absolute (±) uncertainty in the time measurements can be found from either: a. The resolution of the timer ball (the smallest possible change in measurement that can be made) b. The spread of the three values ( = 2 ); whichever is larger.

PAG 1 3.1: Finding g P a g e | 7 6. Change the height by about 20 cm and repeat steps 2-5 to gain three more measurements of time at the new height. You should aim to have results for ten different heights ranging between approximately 0.2 to 2.0 m. Enter the results into the spreadsheet (red tab). 7. Print out your table of results with the graph and add them into your practical folder. 8. Using the uncertainty bars on the graph, draw two lines of worst fit (LOWF) representing the steepest and shallowest possible gradients that reflect the uncertainty values you obtained in your experiment. 9. Calculate the gradient for the line of best fit and for the two lines of worst fit (annotate your graphs clearly to show how you have done this) and record your gradient values in the table below. Use these to calculate best, minimum and maximum values for g from your experiment and record in the table below. Answer the questions that follow. Results Line of Best Fit Shallowest LOWF Steepest LOWF gradient = gradient = gradient = value of g = value of g = value of g = Analysis 10. Why was the timer ball method better than using a normal ball and stopwatch? ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. 11. How could the precision of this experiment be improved? ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. .............................................................................................................................................................

PAG 1 3.1: Finding g P a g e | 8 *Please staple or stick the print-out of your table of results and graph to this page in your booklet

PAG 1 3.1: Finding g P a g e | 9 3.1(ii): Finding g: trolley & ramp Theory When a trolley rolls down a slope, gravitational potential energy is transferred to kinetic energy. Assuming no other forms of energy are involved, the law of conservation of energy states that: gravitational potential energy lost = kinetic energy gained giving ∆ = cancelling the mass ∆ = re-arranging gives: = ∆ Plotting a graph of final velocity squared v 2 on the y-axis and change in height of the trolley h on the xaxis should therefore give a straight line graph through the origin with a gradient of 2g. Method 1. Open the spreadsheet (http://bit.ly/31-GravityExpts) and go to the correct worksheet (blue tab) 2. Set up the equipment as shown above. Measure the angle of the slope using a large protractor and record its value in the appropriate cell on the spreadsheet. Include an estimate for the absolute uncertainty (±U) for the angle measured. 3. Start with the trolley ~30 cm along the ramp up from the light gate. Measure the distance x along the ramp between the light gate and the centre of the trolley and record its value in the spreadsheet. Also estimate and record a value for the absolute uncertainty (±U) in x. *Make sure the light gate and data logger are set to record velocity and the settings are preset correctly for the length of card passing through the light beam. 4. Release the trolley and record the value for the speed v of the trolley when it passes through the light gate. Repeat a further two times to obtain three values for the speed. 5. The spreadsheet uses a trigonometric equation to calculate the change in height of the trolley between its starting position and the light gate. State the equation used in terms of distance x and angle . h =

% The spreadsheet contains formulae which combine the percentage uncertainties in and x and adds them together to find percentage and hence absolute uncertainties for all values of h (for simplicity we have assumed the %U in tan , cos or sin is the same as the %U in itself). **On this occasion the spreadsheet is set up to propagate the uncertainties for you; in future practicals you will be expected to do this yourself. 7. Increase the distance you have moved the trolley away from the light gate and record more results, so that you have ten sets of results ranging between ~0.30 m and ~2.0 m for your value for x. 8. Print out your table of results with the graph and add them into your practical folder. 9. Using the uncertainty bars on the graph, draw two lines of worst fit (LOWF) representing the steepest and shallowest possible gradients that reflect the values you obtained in your experiment. 10. Calculate the gradient for the line of best fit and the two lines of worst fit (annotate your graphs clearly to show how you have done this) and record them in the table below. Use these to calculate best, minimum and maximum values for g from your experiment and record them in the table below. Answer the questions that follow. Results Line of Best Fit Shallowest LOWF Steepest LOWF gradient = gradient = gradient = value of g = value of g = value of g = Analysis 11. Where was the greatest source of uncertainty in your experiment? ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. .............................................................................................................................................................

PAG 1 3.1: Finding g P a g e | 11 12. Describe a method by which the angle could be determined to a greater resolution. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. 13. How else could the precision of this experiment be improved? ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. .............................................................................................................................................................

PAG 1 3.1: Finding g P a g e | 12 *Please staple or stick the print-out of your table of results and graph to this page in your booklet

where a = g can be re-arranged to give: ( − ) = Therefore a graph of (v 2 - u 2 ) plotted on the y-axis against displacement s plotted on the x-axis should form a straight line through the origin with a gradient of 2g. Method 1. Open the spreadsheet (http://bit.ly/31-GravityExpts) and select the correct worksheet (yellow tab) 2. Set up the equipment as shown right. Initially arrange the light gates to be separated by a distance s of approximately 10 cm. 3. Measure the length of the card and enter this information into the data logging program. 4. Measure the distance s between the two light gates and assess the absolute uncertainty (±U) values, recording them in the spreadsheet. 5. Drop the card from a small distance above the top light gate. Record the velocity of the card through each of the light gates. Repeat twice so that you have recorded three separate pairs of values for u and v in your spreadsheet. 6. Increase the separation between the two light gates by a few cm. repeat steps 4-5 to obtain three more sets of velocity measurements for a new value of s. 7. Repeat step 6 so that you have ten sets of results ranging between ~0.10 m and ~0.40 m for values of s. 8. Print out your table of results with the your graph and add them into your practical folder. 9. Using the uncertainty bars on the graph, draw two lines of worst fit (LOWF) representing the steepest and shallowest possible gradients that reflect the values you obtained in your experiment. 10. Calculate the gradient for the line of best fit and the two lines of worst fit (annotate your graphs clearly to show how you have done this) and record them in the table below. Use these to calculate best, minimum and maximum values for g from your experiment and record them in the table below. Answer the questions that follow.

PAG 1 Mod 3 Topic 1: Finding g P a g e | 14 Results Line of Best Fit Shallowest LOWF Steepest LOWF gradient = gradient = gradient = value of g = value of g = value of g = Analysis 11. Explain factors that affect the repeatability of your results. What were the values of s for which the values for (v 2 – u 2 ) were most repeatable and what were the values of s which were least repeatable? Why might this be? ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. .............................................................................................................................................................

PAG 1 Mod 3 Topic 1: Finding g P a g e | 15 *Please staple or stick the print-out of your table of results and graph to this page in your booklet

PAG 1 Mod 3 Topic 1: Finding g P a g e | 16 3.1(iv): Finding g: picket fence & light gate Theory When a picket fence card is dropped through a light gate, the data logging software can track the increase in speed of adjacent transparent regions as they pass through the gate. It does this by measuring the time the beam remains unbroken, which should decrease as the picket fence card accelerates. By comparing the different velocities at different time intervals, the data logger is able to calculate the acceleration. Method 1. Set up the equipment as shown. 2. Make sure the correct spacing between dark regions is entered correctly into the settings of the data logging software. 3. Drop the picket fence card from a small distance above the light gate, and using the table function record the average acceleration. 4. Repeat dropping the card from the same height until you have ten results. 5. Record your results below and find the mean value with the absolute uncertainty (±U) in your value of g from the spread of your data ( = 2 ). Results 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Mean value of g / m s-2 : Absolute uncertainty / m s-2 Percentage uncertainty in g

PAG 1 Mod 3 Topic 1: Finding g P a g e | 17 3.1: Finding g: summary Results overview & analysis For each of the experiments, you should have calculated your best, maximum and minimum values for the acceleration due to gravity (or gravitational field strength) g. You now need to assess which practical gave the best method for measuring g. 1. Plot your values of g on the chart below to compare your best, maximum and minimum values as shown on the lowest bar. 2. For each experiment, calculate the percentage uncertainty (%U) in the calculated value of g and record your results in the table below ( = (±) × 100) 3. For each experiment calculate the percentage difference between your mean calculated value of g and the accepted value of g of 9.81 m s-2 ( = & × 100%) 4. Use the values you have just calculated to determine whether or not each experiment was accurate. 4.2.A(i) Timer Ball 4.2.A(ii) Trolley & Ramp 4.2.A(iii) Card & Light Gates 4.2.A(iv) Picket Fence & Light Gate Percentage Uncertainty Percentage Difference Was the experiment accurate? YES / NO YES / NO YES / NO YES / NO

PAG 1 Mod 3 Topic 1: Finding g P a g e | 18 ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. ............................................................................................................................................................. .............................................................................................................................................................

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 19 3.5: Investigating terminal velocity Competencies assessed: 1.2.1(c) follow written instructions · Written instructions followed and practical completed safely & successfully 1.2.1(d) make and record observations and measurements · Measurements taken correctly using a range of measuring equipment · Measurements recorded appropriately, using correct number of significant figures · Measurements recorded with appropriate values for experimental uncertainty 1.2.1(e) keep appropriate records of experimental activities · Data processed and values calculated correctly · Experiment write-up complete (all questions answered to an appropriate standard) 1.2.1(g) use appropriate software and tools to process data, carry out research and report findings · Data logging software used to track processes through time, with choices made on appropriate settings (e.g. variables to measure, sampling frequencies etc.) 1.2.1(j) use a wide range of experimental and practical instruments, equipment and techniques appropriate to the knowledge and understanding included in the specification · All equipment is used safely and correctly 1.2.2(a) Use of appropriate analogue apparatus to record a range of measurements, to include: · length / distance 1.2.2(b) Use of appropriate digital equipment, including digital multimeters to obtain a range of measurements, to include: · time 1.2.2(c) Use of methods to increase accuracy of measurements, such as: · use of a fiducial marker, set square or plumb line Use of specific equipment / techniques 1.2.2(d) use of a stopwatch or light gates for timing 1.2.2(k) use of ICT such as computer modelling, or data logger with a variety of sensors to collect data, or use of software to process data PAG 1 date completed …………………………………. ..

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 20 Background theory When objects fall, they experience a drag force which increases as the speed of falling increases. Eventually, the drag force on an object increases to a point at which it matches the downward weight force and the object is in equilibrium. Here there is no resultant force acting on the falling object and it stops accelerating. The object falls at its terminal velocity (see diagram). The aim of this practical is to measure the terminal velocity of a paper muffin case. We will look at a couple of different methods and finish by investigating whether the drag force Fd follows the relationship given in the drag equation (shown on the right). This practical is split into three separate parts: • Part A looks at a simple way to measure the terminal velocity of a muffin case using a tape measure and stop watch. • Part B is a more sophisticated method using a position sensor and data logger to create a displacement-time graph for the muffin case as it falls. The terminal velocity can be measured from the gradient of the graph. • Part C requires you to investigate the relationship between the terminal velocity and the mass of the muffin cases and then to determine whether your results support the relationship stated above. Part A: Simple measurements of terminal velocity 1. Take a muffin case and drop it from the same height 16 times, allowing it to reach the ground. In the table below, record how long it takes to fall each time. Record your results to the nearest 0.1 s. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 2. Explain why it was unnecessary to record your timing values to a greater precision than 0.1 s. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. = 1 2 2

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 21 3. Display your results as a dot plot using the axes below. 4. Explain how you could identify any outliers from your plot above. Does your data contain any outliers? .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 5. Calculate the mean value and state the absolute uncertainty (±U) and percentage uncertainty (%U) in the time t taken for the muffin cases to fall. 6. Record the value for the distance d fallen by the muffin cases (with a reasonable estimate for the absolute uncertainty (±U) and therefore the percentage uncertainty (%U)). 7. Calculate the average velocity for the falling muffin cases. Use the values for percentage uncertainty in t and d to calculate values for the percentage uncertainty (%U) and absolute uncertainty (±U) in the velocity. t = …………… ± ……………. s ± ………….…. % d = …………… ± ………..…. m ± …..………. % v = …………m s-1 ± ………..…. % ± ……….…. m s-1

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 22 8. Explain, giving reasons, whether this value is likely to be greater or less than the actual terminal velocity of the muffin case. In particular, are there any systematic errors in the method that you should have accounted for? .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. Part B: Terminal velocity using a position sensor & data logger In this part of the experiment you will use a position sensor attached to a data logger to generate a displacement-time graph for the falling muffin case. 9. Explain how the velocity of an object may be determined from a displacement-time graph of its motion. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 10. Set up the equipment as shown in the diagram. 11. Connect a position sensor to your computer and download the file at http://bit.ly/TermVelExpt (also available at www.aquinasphysics.com) and open it using the CAPSTONE software. 12. Hold a muffin case under the position sensor. Press the RECORD button at the bottom left of the display. Release the muffin case, and stop the recording once it hits the floor.

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 23 13. Depending on the quality of the data, some processing may be required before you obtain a value for the terminal velocity. In order to remove any noise or anomalous data points that clearly depart from the trend of your line: • Select the HIGHLIGHTER tool (1) from the top-left of the graph display. A box will appear. Drag the box to cover most of the anomalous data points you wish to remove. You can re-size the box by repositioning its outer edges. • Once these points are highlighted, delete them from the data set by selecting the DELETE DATA (2) tool, middle-right at the top of the graph display. • Highlight any further data points you wish to remove and delete them so that a relatively smooth line remains. 14. Which value of sampling frequency gave the best results for the graph? Describe what happens if you use a higher sampling frequency. Explain why the results are not as good. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. ..............................................................................................................................................................................

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 24 15. To find the line of best fit (LOBF) for the position data: • use the HIGHLIGHTER tool to highlight all data that falls on the straight line portion of the graph. • Next use the LINE OF BEST FIT tool (middle-left of toolbar, see RIGHT) to find the equation for the line that fits through this data. You will have to select a linear relationship from the drop-down menu for this tool. Make sure you are fitting a line of best fit only to the straight-line portion of the data. 16. Record the value of terminal velocity (taken from the gradient of the graph) in the table below. 17. Repeat this process a further five times. Calculate a mean terminal velocity with the absolute uncertainty (±U) and percentage uncertainty also stated. terminal velocity values / m s-1 1. 2. 3. 4. 5. 6. mean terminal velocity / m s-1 absolute uncertainty / m s-1 percentage uncertainty %

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 25 18. Compare the value of mean terminal velocity derived from the position sensor and data-logging software (Part B) with the value for the average terminal velocity obtained in Part A. Which is greater? Which shows the greater % uncertainty? Comment on whether these readings are consistent with your answer from step 7 in Part A. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. ..............................................................................................................................................................................

c, so a graph of v 2 on the yaxis against m on the x axis should plot as a straight line where the gradient is equal to the term you have written inside the dashed box. All of these quantities should be constants. = 1 2 2 2 = × =

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 27 Results 21. Construct a table of results for your data in the space below. Use a ruler to ensure it is neat, think about the different columns you need and the appropriate headings (quantities and units) and don’t forget to collect you data to an appropriate number of significant figures.

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 28 Graph 22. Plot your results on the graph paper below.

PAG 1 Mod 3 Topic 5: Investigating terminal velocity P a g e | 29 Analysis 23. With reference to the graph that you have just plotted, explain whether or not the motion of a muffin case falling under gravity agrees with the drag equation. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. ..............................................................................................................................................................................

PAG 2 Mod 3 Topic 6: Hooke’s law & combinations of springs P a g e | 30

PAG 2 Mod 3 Topic 6: Hooke’s law & combinations of springs P a g e | 31 3.6: Hooke’s law & combinations of springs Competencies assessed: 1.2.1(c) follow written instructions · Written instructions followed and practical completed safely & successfully 1.2.1(d) make and record observations and measurements · Measurements recorded appropriately, using correct number of significant figures · Qualitative observations are recorded with sufficient detail and using appropriate technical terminology 1.2.1(e) keep appropriate records of experimental activities · Data processed and values calculated correctly · Graphs from experiment drawn · Data processed and values calculated correctly · Experiment write-up complete (all questions answered to an appropriate standard) 1.2.1(g) present information and data in a scientific way · Suitable table constructed (title, lines drawn with a ruler, column headings, units) · Suitable graph plotted (title, appropriate axes chosen, suitable scale, data fits in graph appropriately, LOBF drawn correctly) 1.2.1(j) use a wide range of experimental and practical instruments, equipment and techniques appropriate to the knowledge and understanding included in the specification · All equipment is used safely and correctly 1.2.2(a) Use of appropriate analogue apparatus to record a range of measurements, to include: · length / distance 1.2.2(c) Use of methods to increase accuracy of measurements, such as: · use of a fiducial marker, set square or plumb line Outline In this experiment, you will be investigating the relationship between the force F applied and extension x of a single spring compared to the same relationship when springs are combined in series (end-to-end) and in parallel (side-by-side). Your challenge in undertaking this experiment is to answer the following two questions: • How does the spring constant k of two identical springs attached end-to-end relate to the spring constant k for a single spring? • How does the spring constant k of two identical springs placed side-by-side relate to the spring constant k for a single spring. PAG 2 date completed …………………………………. ..

PAG 2 Mod 3 Topic 6: Hooke’s law & combinations of springs P a g e | 32 To do this you will be required to find values for the spring constant from a graph (not from a single measurement). You will be provided with: • the equipment to set up the experiment as shown in the diagram on the right. • Space to make a table (or tables) of results for the different experiments you undertake • A single piece of graph paper on which to plot your results and find your values for k. Results 1. Plot your table of results for each experiment you do in the space below. Think carefully about appropriate headings (quantities & units) and the number of significant figures for your data. Use a ruler to ensure everything is neat and legible.

PAG 2 Mod 3 Topic 6: Hooke’s law & combinations of springs P a g e | 33 Graph 2. Plot graphs of results for all your experiments in the space below (use the same set of axes for ease of comparison between the different combinations of springs)

PAG 2 Mod 3 Topic 6: Hooke’s law & combinations of springs P a g e | 34 Analysis & conclusion 3. Find values for the spring constant k for the different combinations of springs from your graph. You will need to annotate your graph to show how you found these values. single spring 2 springs in series (end-to-end) 2 springs in parallel (side-by-side) k = k = k = 4. What is the relationship between the value of k for a single spring and two springs in series (end-toend)? How can this relationship be explained? .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 5. What is the relationship between the value of k for a single spring and two springs in parallel (side-byside)? How can this relationship be explained? .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 35

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 36 3.6: Young modulus & breaking stress of copper Competencies assessed: 1.2.1(b) safely and correctly use a range of practical equipment and materials · Work carried out in a suitable manner to minimising risks and hazards · Appropriate risk assessment is recorded in notes (identifying the hazards associated with the equipment and techniques, and outlining the steps taken to minimise the risks involved) 1.2.1(c) follow written instructions · Written instructions followed and practical completed safely & successfully 1.2.1(d) make and record observations and measurements · Measurements taken correctly using a range of measuring equipment · Measurements recorded appropriately, using correct number of significant figures · Measurements recorded with appropriate values for experimental uncertainty 1.2.1(e) keep appropriate records of experimental activities · Data processed and values calculated correctly · Graphs from experiment drawn · Data processed and values calculated correctly · Experiment write-up complete (all questions answered to an appropriate standard) 1.2.1(g) present information and data in a scientific way · Suitable table constructed (title, lines drawn with a ruler, column headings, units) · Suitable graph plotted (title, appropriate axes chosen, suitable scale, data fits in graph appropriately, LOBF drawn correctly) 1.2.1(h) use online and offline research skills including websites, textbooks and other printed scientific sources of information · Student consults websites, textbooks or journals for independent research 1.2.1(i) correctly cites sources of information · Accurate and appropriate references are provided to any information that the student has looked up 1.2.1(j) use a wide range of experimental and practical instruments, equipment and techniques appropriate to the knowledge and understanding included in the specification · All equipment is used safely and correctly 1.2.2(a) Use of appropriate analogue apparatus to record a range of measurements, to include: · length / distance 1.2.2(b) Use of appropriate digital equipment, including digital multimeters to obtain a range of measurements, to include: · mass 1.2.2(c) Use of methods to increase accuracy of measurements, such as: · use of a fiducial marker, set square or plumb line Use of specific equipment / techniques 1.2.2(e) use of calipers and micrometers for small distances, using digital or vernier scales PAG 2 date completed …………………………………. ..

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 37 Overview In this experiment, you will be attempting to measure the Young Modulus E of copper by measuring the extension x of a copper wire as the force F on it is increased. You will also be required to consider the quality of the values you measure. To improve the accuracy of some measurements you will need to take repeat readings to find an average, and to give an indication of the UNCERTAINTY in the measurement by using the spread of the values. Background theory The Young Modulus E is a better measure of the stiffness of a material than the spring constant k as it applies to the material as a whole rather than just the sample we are testing. The Young Modulus E can be found by the equation = ⁄ where: • the stress is defined as the force acting per unit cross-sectional area and • the strain is defined as the extension per unit initial length. From these definitions: = ⁄ = ⁄ and therefore = ⁄ = ⁄ where F is the force applied to the wire, A is its cross-sectional area, x is the extension and L is the initial length of the sample of wire. Practice questions 1. Answer the following questions: (a) What is the Young modulus of a 3 m long, 1 mm diameter wire, which extends by 4.5 mm when a force of 20 N is applied? Young Modulus = ................................. (b) A wire has a Young modulus of 3.8 x 1011 N m-2 . What is the stress applied when the strain is 0.02 %? Stress = .................................

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 38 (c) What is the tension in the wire above if it has a diameter of 0.5 mm? Tension = ................................. (d) What extension would you expect from a wire with a Young modulus of 150 GPa if the force applied is 75 N and the wire has a cross-sectional area of 2 mm2 and original length of 3 m? Extension = ................................. 2. State the readings on the screw-gauge micrometers below (assuming no zero-error for the screw-gauge micrometer when it is fully closed)

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 39 Method & Safety 1. Complete the RISK ASSESSMENT form below to identify any potential risks you need to account for whilst undertaking this practical. Please also include information on how you aim to minimise the likelihood of this hazards being problematic. Include any references you have made when researching potential hazards for this experiment. Hazard (identify possible issue) Risk (what could go wrong) Likelihood 1 (unlikely) to 3 (likely) Severity 1 (low) to 3 (high) Precautions taken References:

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 40 3. Set up your equipment as shown in the diagram on the previous page. Note that the diagram is not to scale and the distance between the clamped end and paper marker should be approximately 1.5 m whilst the distance between the paper marker and the pulley should be about 0.7 m. Before loading your wire, you will need to use a screw-gauge micrometer to measure the wire diameter at several different places along the wire length and in several different orientations to find an AVERAGE diameter along with the ABSOULTE UNCERTAINTY (±U) for the diameter from the SPREAD ( 2 ) of your readings. The screw-gauge micrometer has two scales on it: • The scale on the inner stem measures in increments of 0.5 mm • The scale on the outer thimble measures to the nearest 0.01 mm To find the thickness measured, simply add the value of the outer thimble that lines up to the centre line on the inner stem, to the greatest increment that can be seen on the inner stem not covered by the thimble. 4. Record values of the measured diameter d of the wire in the space below. measured diameter / mm average diameter / mm ±U / mm reading 1 reading 2 reading 3 reading 4 reading 5 5. For each measurement that you take, the minimum value of the absolute uncertainty will be set by the resolution of the measuring instrument that you use. State the resolution of the following pieces of equipment: screw-gauge micrometer (used to measure the d) metre rule (used to measure x and L) 6. Measure the initial length L of the wire between the clamped end and the paper marker as it is just pulled taut by the weight hanger (see diagram). Record your value with uncertainties in the table below. To estimate the absolute uncertainty you will need to make a judgement about how close your measurement is likely to be to the true value of L based on the resolution of the instrument and the technique you use. initial length, L / m ± U / m %U 7. You will be adding weights one at a time to the end of the copper wire to increase the force F (tension) in the wire. The weights are nominally 100 g, but in reality there will be a discrepancy from this value. To quantify the absolute uncertainty in the mass m, measure the mass of ten separate 100 g weights using the mass balance provided. Record your answers in the table below. measured mass / g average mass / g ±U / g %U reading 1 reading 2 reading 3 reading 4 reading 5 reading 6 reading 7 reading 8 reading 9 reading 10

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 41 Find the ABSOLUTE UNCERTAINTY (±U) in the value of m from the SPREAD of your data and use this to calculate a PERCENTAGE UNCERTAINTY (%U) in the value of m (and therefore in the force F acting. 8. Add masses 100g at a time and measure the extension by finding the distance from the starting position moved by the paper marker along the metre rule with each mass added. It may be helpful to align the paper marker with the metre rule using a set-square to avoid a parallax error. Record values for force F (tension = weight added = mass x gravitational field strength) and extension x with uncertainties in the table on the next page. You may wish to add 50 g weights when you get to a point where plastic deformation begins and the wire starts to stretch by a few centimetres each time you add another weight on to the stack. Note the following: 1. to find values for mass added, multiply the average mass found above by the number of weights on the mass stack. 2. to find the absolute uncertainty in the mass of n weights, multiply the absolute uncertainty above by n (for a greater number of weights, the absolute uncertainty will increase). 3. to find the absolute uncertainty in the force F, multiply the absolute uncertainty in mass by the gravitational field strength g. 4. Uncertainty values in extension x are down to your own discretion, but cannot be smaller than the resolution of the metre rule. 5. If you add 50 g weights to the mass stack, assume the same %U value as in the 100 g weights (so the ±U value will be half that of the 100 g weights). 9. Continue to add weights until the wire snaps. This may be at a mass of up to about 2 kg total. Record the force Fbreaking at which this occurs. Fbreaking = ………………………….. N 10. Plot a graph of Force F (y-axis) against extension x (x-axis) on the graph paper provided. You may wish to think about the scale of your axes. (You are calculating the Young modulus of the wire from the elastic portion of the graph, which may be very compressed if you choose to include all data points you have collected)

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 42 Results mass m / kg force F / N extension x / × 10-3 m value ±U value ±U value ±U

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 43 Graph

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 44 Analysis 11. Annotate your graph to show regions where the wire undergoes (a) ELASTIC DEFORMATION and (b) PLASTIC DEFORMATION. 12. Using suitable diagrams, explain what is happening to the atomic structure of copper at the transition between the two deformation regimes .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 13. For the elastic portion of your graph, calculate the gradient to determine the stiffness k of the sample of the wire that you investigated. k = ......................... N m-1 14. From the data recorded for the diameter (including uncertainties), calculate the cross-sectional area A of the wire with uncertainties. Calculations: cross-sectional area A / m2 ± U / m2 %U 15. From the equation for the Young Modulus E and using the value of the gradient or stiffness constant k, the initial length of the wire L and the cross-sectional area A, calculate the Young Modulus E of the copper. E =

PAG 2 Mod 3 Topic 6: Young modulus & breaking stress of copper P a g e | 45 16. Look up a value for the accepted value for the Young Modulus of copper. What is the percentage difference between your experimental value and the accepted value? = × 100 % experimental value of E accepted value of E % difference 17. Calculate the BREAKING STRESS breaking for your material. What assumptions have you made in this calculation? Assumptions: .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 18. Looking at the PERCENTAGE UNCERTAINTY in each of your readings, which of your measurements contributed most to the overall uncertainty in your experiment? Outline steps you could take to improve the overall uncertainty in this experiment. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. breaking =

PAG 2 Mod 3 Topic 6: Loading & unloading elastic bands P a g e | 46 3.6: Loading & unloading elastic bands Competencies assessed: 1.2.1(c) follow written instructions · Written instructions followed and practical completed safely & successfully 1.2.1(d) make and record observations and measurements · Measurements recorded appropriately, using correct number of significant figures · Qualitative observations are recorded with sufficient detail and using appropriate technical terminology 1.2.1(e) keep appropriate records of experimental activities · Data processed and values calculated correctly · Graphs from experiment drawn · Data processed and values calculated correctly · Experiment write-up complete (all questions answered to an appropriate standard) 1.2.1(g) present information and data in a scientific way · Suitable table constructed (title, lines drawn with a ruler, column headings, units) · Suitable graph plotted (title, appropriate axes chosen, suitable scale, data fits in graph appropriately, LOBF drawn correctly) 1.2.1(j) use a wide range of experimental and practical instruments, equipment and techniques appropriate to the knowledge and understanding included in the specification · All equipment is used safely and correctly 1.2.2(a) Use of appropriate analogue apparatus to record a range of measurements, to include: · length / distance 1.2.2(c) Use of methods to increase accuracy of measurements, such as: · use of a fiducial marker, set square or plumb line Background In this experiment, you will be looking at the relationship between the force applied, and extension of an elastic material - a rubber band. Rubber is a type of polymer and shows an interesting property on loading and unloading known as ELASTIC HYSTERESIS. 1. Research and make notes on the phenomenon of ELASTIC HYSTERESIS in the space below. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. PAG 2 date completed …………………………………. ..

PAG 2 Mod 3 Topic 6: Loading & unloading elastic bands P a g e | 47 Method 2. Draw a labelled diagram of the experimental set-up you will use in this investigation in the box on the right. Loading 3. Set up the equipment as demonstrated by your teacher and shown in the diagram. 4. Measure the initial length L of the elastic band with just the mass hanger attached. Record the value below. 5. Add one weight to the mass hanger and measure the new length of the elastic band. Calculate the FORCE F (weight) added from the equation F = m g, where m is the total additional mass hanging from the elastic band (in kg) and g is the gravitational field strength (9.81 N kg-1 ). 6. Find the extension x by subtracting the original length L from the new length. Record your results in a table on the following page. Make sure that you think carefully about the headings you will need in your table of results (give quantities and units), and that you record your results to an appropriate number of significant figures. Use a ruler to ensure that your table is neat. 7. Add another weight, record your results, and repeat until approximately 1.0 to 1.5 kg has been added (do not snap the elastic band). Unloading 8. Now remove the weights one at a time, measuring the new length of the elastic band each time you remove a weight. Use this and the value for L recorded above to find values of extension for each weight as you unload the elastic band. Record your results in a table on the following page. 9. Continue until all weights are removed from the mass hanger. experimental set-up L =

PAG 2 Mod 3 Topic 6: Loading & unloading elastic bands P a g e | 48 Results Loading Unloading

PAG 2 Mod 3 Topic 6: Loading & unloading elastic bands P a g e | 49 Graph 10. Plot a graph of FORCE F (y-axis) against EXTENSION x (x-axis) for both the loading and unloading results on the paper below. You will find this easiest if you use different colours for your loading graph and your unloading graph.

PAG 2 Mod 3 Topic 6: Loading & unloading elastic bands P a g e | 50 Analysis & conclusions 11. Calculate the energy stored in stretching the rubber band (area under the loading graph). You can count squares or it may be easier to estimate the area using a number of trapeziums (remember the units on each of the axes). Record your value in the table below. 12. Now calculate the energy released when unloading the spring (area under your unloading graph). Again, record your value in the table. 13. Calculate the difference in the energy stored on loading then returned on unloading and record their values in the table. energy stored on loading / J energy released on unloading / J energy difference / J 14. Explain what has happened to this energy. You may need to do some research. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. ..............................................................................................................................................................................