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Rotational Kinetic EnergyEquipment1Rotary Motion Sensor PS-2120A 1Rotational Accessory CI-6691 1Mass and Hanger Set ME-8979 1Braided String SE-8050 190 cm Rod ME-8738 145 cm Rod ME-8736 1Multi-Clamp ME-9507 1Large Rod Base ME-8735 1No-Bounce Pad SE-7347 Required but not included:1Calipers SE-8710 1Meter Stick SE-8827 1Balance SE-8723 IntroductionThe rotational kinetic energy of a rotating object depends on its rotational inertia, I, and its angular velocity, ω.KE = ? I ω? (1)For a disk of radius, R, and mass M, I = ? M R? (2)This lab investigates the potential energies for a modified Atwood's Machine (see Fig. 1), where a disk has been added to the Rotary Motion Sensor pulley. As the hanging mass (m?) falls, the lighter mass (m?) rises, but the combined gravitational potential energy of the two decreases, and this energy is converted into the kinetic energy of the system. This includes not only the linear kinetic energy of the two hanging masses, but also the rotational kinetic energy of the rotating disk.3286125-615315Figure 1: Modified Atwood’s MachineFigure 1: Modified Atwood’s MachineThe Rotary Motion Sensor measures the rotational velocity of the disk, as well as the tangential (linear) velocity of the string over the Three-step Pulley. SetupUse the large rod base as shown in Figure 1 with the 90 cm rod, the 45 cm rod, and the multi-clamp.Attach the Rotary Motion Sensor to the end of the 45 cm Rod and plug it into the interface.In PASCO Capstone, set the sample rate to 20 Hz. Create a graph of Position vs. Time.Measure the mass and radius of the disk and then fasten the disk to the sensor using the Three-step Pulley.Cut a piece of string about 1 m long. Tie a loop on each end and place the string over the large radius pulley, with a mass hanger at each end.Place the yellow No-Bounce Pad under the hanging masses.Add 50 g to the mass hanger (m?) and add 90 g to the mass hanger (m2). Pull the lighter (m?) mass hanger down to the level of the pad. Click on Record and release the hanger. You should try and stop recording just before the other mass hanger hits the pad.You want the velocity to be positive. If it is not, switch the two masses, or you can change the sign in the properties for the sensor.Pull the lighter (m?) mass hanger down to the level of the pad. Measure the height of m? above the pad. This initial height, h?, will be used in calculating the potential energy of the two masses.In the Capstone calculator, create the following equations:?PE? = m?*g*[Position (m)?]+m?*g*(h?-[Position (m)?])units of J?KElinear? = 0.5*(m?+m?)*[Velocity (m/s)?]?units of J?KErot? = 0.5*I*[Angular Velocity (rad/s)?]?units of J?I? = 0.5*M*R?units of kg m2??Total = [PE (J)?]+[KElinear (J)?]+[KErot (J)?]units of JMake a graph of the PE calculation vs. Time.Procedure: Potential EnergyLine # 6 of the calculator shows the built-in calculation for the potential energy of the two hanging masses. PE=m?gh + m?g(h? -h)The height, h, is measured directly by the sensor. As one moves down, the other moves upwards. Enter your values for m?, m?, and h?, on lines #3 through #5 in the calculator.Create a graph of PE vs. Time.Pull the lighter (m?) mass hanger down to the level of the pad. Click on Record and release the hanger. You should try to stop recording just before the other mass hanger hits the pad. You could also try a Stop Condition on the position to automatically halt the recording.Get a single good run of data.In general, what is happening to the total potential energy of the two hanging masses?What is happening to the potential energy of just mass (m?)? Procedure: Kinetic EnergyLook at line #8 of the calculator. It shows the calculation for the kinetic energy of the two hanging masses.KElinear = ?(m?+m?)v?where v is the tangential (linear) velocity of the string over the pulley, and thus the velocity of the hanging masses.But the rotating disk has kinetic energy, too.KErot = ?Iω?where the angular velocity, ω, is measured directly by the sensor. Enter your values for the disk mass and radius on lines #1 and #2 in the calculator.On the PE graph, click on the vertical axis measurement selector and select Add Similar Measurement and add KElinear and KErot.Display the last run or take a new run of data.Which has more kinetic energy: The hanging masses or the rotating disk? Why? What would you have to change to have it be the opposite? Total EnergyIn general, what is happening to the potential energy of the system compared to the kinetic energy of the system?Look at line #11 of the calculator. It shows the calculation for total energy = PE + KElinear + KErotOn the Energy graph, click on the vertical axis measurement selector and select Add Similar Measurement and add Total. Is energy conserved?If there were no frictional losses, what would the graph show? ................
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