L04 The Work-Kinetic Energy Theorem 1. Pre-Lab Exercises. 1) Describe the Work-Kinetic Energy Theorem in words and summarize with an equation.

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1 L04 The Work-Kinetic Energy Theorem 1 Full Name: Lab Section: Pre-Lab Exercises Hand this in at the beginning of the lab period. The grade for these exercises will be included in your lab grade this week. 1) Describe the Work-Kinetic Energy Theorem in words and summarize with an equation. 2) How can the Work-Kinetic Energy Theorem be used to calculate the amount of work done by a non-conservative force? Show an equation relevant to the context of this lab. 3) Draw a free body diagram for each mass in this setup. 4) Write out equations for Newton s Second Law in the x and y directions for the setup in question 3.

2 L04 The Work-Kinetic Energy Theorem 2 The Work-Kinetic Energy Theorem Full Name: Lab Partners Names: Lab Section: Introduction: When investigating a physical system, it is often useful to determine the energies involved. In this lab we will investigate how the work done on a mass m 2 can change the kinetic energy of m 2. The Work-Kinetic Energy Theorem equates these two quantities. First you will confirm this theorem for the case of a conservative force (namely, gravity applied via tension in a string). Then you will use the theorem to determine the work done by an additional non-conservative force (friction). From this you will determine the coefficient of kinetic friction between a plastic-bottomed friction box and the dynamics track. Equipment: Science Workshop interface Dynamics Track Dynamics Cart String Stop Bracket Force Sensor Bubble Level Hanging and Bar Masses Balance (500 grams +) Motion Sensor Plastic Bottom Friction Box Screwdriver Procedure: 1. Setting up the equipment: 1.1 Open data studio and double click on the Motion Sensor and Force Sensor. Connect them to the science workshop interface. 1.2 Double click on the Force Sensor icon. Under the general tab, make sure the sensor is set to slow force changes (10 Hz). Double click on the Motion Sensor Icon. Under the measurement tab select position and velocity data. Under the motion sensor tab, change the trigger rate to Clamp the track to the table as shown on the next page, using the bubble level to make sure that the track is level across its width and length. 1.4 Attach the pulley to the track using the tightening screw and place the motion sensor on top of the track as shown on next page. Attach the bumper in front of the pulley.

3 L04 The Work-Kinetic Energy Theorem Use the screwdriver to attach the force sensor to the cart, with the hook on the same side as the spring loaded plunger. Tape a white index card, to the back of the cart, making sure that it is not bent in any way. This helps the motion sensor work properly. Attach the string to the hook on the force sensor on one end and the hanging mass holder on the other. Check that the string is level between the cart and the pulley. If it is not, adjust the height of the pulley. 2. Calculating change in kinetic energy: 2.1 Measure the masses of the cart, force sensor, iron bars and hanging masses you will use in this experiment. Click on Calculate in the toolbar to generate an equation for the kinetic energy of the cart. Type in the equation and click on Accept. Click on the arrow next to the m and define m as a constant. Type in your value for the mass of the cart. Define v as a data measurement and select velocity from the menu. Under the Properties button, provide a proper name and units for the Kinetic Energy. Ensure that the precision box has the number three in it. Doing this sets the number of reported decimal places to three. Click accept again. 2.2 Create a kinetic energy vs time graph. Now click on the position data in the data run list on the top left of the screen. Click and drag this onto the x-axis of your graph. Now you should have a kinetic energy vs position graph. 2.3 Create a force vs time graph. Now click and drag the position data onto the x-axis so that you now have a force vs position graph. What force are you measuring?

4 L04 The Work-Kinetic Energy Theorem 4 3. Collecting and analyzing data with no friction: 3.1 Tare the force sensor by pushing the tare button on the side. Make sure that you remove the string from the hook and that there are no forces acting on the force sensor when you tare it. Do this before every data run. 3.2 Take your first data run with an additional 20 g added to the mass hanger. Pull the cart back so that it is about 20 cm away from the front of the motion sensor. Click Start and release the cart. Stop collecting data after the cart has impacted the bumper. The kinetic energy will appear to increase linearly with displacement and the force will appear to be a horizontal line. 3.3 These graphs will make it easy to confirm the Work- Kinetic Energy Theorem To find the work done by the string on the cart, simply find the area between the force and the horizontal axis. You can do this by highlighting the desired data points and then picking area from the Σ button menu. This will give you a value in Nm. Record this value in a table. See the next page for an example To find the change in kinetic energy, you will need to use the smart/xy tool found in the toolbar of the graph window. Select the point that is at the same position as the first point that you analyzed in step Hover the cursor over one of the corners of the tool. You will notice a small triangle appear near the cursor. Click and drag the cursor to the other end of the data you wish to select. Make sure that this point is at the same position as the last point you analyzed in step You should notice that both the difference in position and Kinetic Energy appear parallel to their respective axes (see graph above). Record the change in kinetic energy and the change in position in your table If you have set up the graph correctly and taken accurate measurements of

5 L04 The Work-Kinetic Energy Theorem 5 the masses, then the work and change in kinetic energy should be equal. Accurate mass values are crucial. A level track is a must. Be sure to select only clean data points from the center of the runs. Double check that you are analyzing the same range of positions in steps and Perform this experiment using two different cart masses and three different hanging masses for a total of six trials. Be sure to tare the force sensor before each data run, and update your equation for kinetic energy when you change the mass of the cart. Complete your calculations before leaving lab. You might need to retake some of your data. No more than 15% of the work done by the string should be lost. WT K % difference = 100% WT A number of factors can lead to large energy losses. Try these troubleshooting tips to help reduce your errors Track should be level after clamping to table Measure all masses don t assume what s written on them is correct Make certain the string is level between the pulley and cart Make certain the index card is vertical, not curled nor tilted Make certain your motion sensor is pointing horizontally along the track and not tilted up nor down Make certain your track is clean wipe down with Windex and paper towel. You can tell if the track is dirty or gummy if the friction cart is not sliding smoothly along the whole track. This is mostly a problem for small tensions. Are your cart wheels spinning freely? If not, have lab TA substitute a new cart. Use a total mass ranging between 70 and 150 g Make certain that the cord on the force sensor is moving freely. 3.5 Print one graph that includes kinetic energy vs displacement and force vs displacement. Your selections made with the smart/xy tool and for area should appear in your printout. 3.6 Find the percent of energy lost between the work done by the string and the change in kinetic energy of the cart in each measurement. Decide if there is another force present that you have not accounted for justify your answer. And if so, what is this neglected force? 3.7 Include a data table with your lab report. It should include all measured and calculated quantities, an example is below. Run # M1 (kg) M2 (kg) K2 (J) X2 (m) Work Done By String (J) % Lost % % % % % % 4. Collecting and analyzing data with friction: 4.1 Now, disconnect the force sensor from the cart and fit it onto the friction box. Secure the force sensor to the friction box with tape, with the hooks of the sensor and box aligned on the same side. Tape a white card to the back of the box. Measure the

6 L04 The Work-Kinetic Energy Theorem 6 mass of the sensor-box assembly. Attach the string to the hook on the friction box as you did before. Perform the same experiment you did in section 3, being sure to update the mass in your kinetic energy equation. Note that because there is another non-conservative force present, the work done by the tension in the string and the change in kinetic energy will not be equal. 4.2 Calculate the work done by the non-conservative force. Show an example of your calculation in the report 4.3 Calculate the value of the non-conservative force. Show an example of your calculation in the report. 4.4 Calculate the coefficient of kinetic friction, show an example of your calculation in the report. Record these values in a chart, see table below for an example. 4.5 Print one graph that includes kinetic energy vs displacement and force vs displacement. Your selections made with the smart/xy tool and for area should appear in your printout. 4.6 Is your calculated value for the coefficient of friction the same for all runs? Should it be? Where might there have been error in your experiment? 4.7 Hand in a table like the example below, as well as a table for your experiment without friction, a sample graph from both experiments, and answers to any bold-faced questions. Sample Table for Experiment With Friction: Run # M1 (kg) M2 (kg) K2 (J) X2 (m) Work Done By String (J) % Lost W f = K - W T F f =W f / ( x2cos180) µ = F f /m2g % 0 n/a n/a % %