Lab 8: Conservation of Energy Equipment: Data collection system . Dynamics track angle indicator Motion sensor . Rod stand (to elevate track) Dynamics track Balance . Dynamics track end stop . Pivot clamp Dynamics cart with plunger . Mass Hanger and Mass Set . Mass Bars and heavy mass hangers Pasco Super Pulley with table clamp Objective: Measure the spring constant for the spring in the dynamics cart. Calculate the spring potential energy using the spring constant and determine how much of that energy is transformed into kinetic energy and potential energy. For the cart on an incline, determine how much kinetic energy is transformed into gravitational potential energy. Theory: The potential energy of a spring compressed a distance x, with k being the spring constant, from equilibrium is given by: SPE = 7 The force exerted by a spring on an object is a conservative force given by Hooke's Law: F = -kx The spring constant can be experimentally determined by applying different forces to stretch the spring at different distances. The spring constant is the slope of the force vs. distance graph. Gravitational potential energy GPE, or energy of position, is defined by the equation: GPE = mgh For an object on Earth, the mass, m, and the acceleration due to gravity, g, remain constant. Hence, only the change in height h influences any change in gravitational potential energy. For kinetic energy KE or energy of motion, the equation is: KE = = mvz For this same object of constant mass, any change in the kinetic energy is due to a change in velocity v.For a closed system, the total energy TE is defined to be the sum of the different types of energy: TE = KE + GPE+ SPE+ Heat + Light... We will create our closed system and limit the forms of energy changing to kinetic and potential to observe how they change and relate to the system's total energy. TE = KE+GPE+SPE Procedures: Part 1: Determining the Spring Constant 1. Level the track by setting the cart on it to see which way it rolls. Adjust the leveling screw at the end of the track to raise or lower that end until the cart placed at rest on the track will not move. 2. Place the spring plunger against the stopping block at one end of the track. Record the cart's position in Table 1 with zero hanging mass. Use a ruler to aid in reading the scale on the track. Attach a string to the cart and attach the other end to a mass hanger, passing the string over the pulley. 3. Add enough mass to the mass hanger for the cart to compress the spring enough for measurement. Record the new position in Table 1. The displacement is the initial position minus the new position. Repeat this for five different masses. Calculate the displacement for each position and record it in Table 1. 4. Plot the hanging force (mg) vs. displacement. The slope is the spring constant. Record the spring constant below data Table 1. (Make sure to attach the graph with the lab) Part 2: Conservation of Energy 1. Start a new experiment on the data collection system. 2. Connect the end stop to the end of the dynamics track. Then, attach the track to the rod stand near the other end using the rod clamp. 3. Connect the motion sensor to the end of the track with the face of the sensor pointed toward the end stop. Be sure the switch on the sensor is in the cart position. 4. Use the balance to determine the mass of your cart and record the mass in Table 2. 5. Connect the motion sensor to the data collection system. 6. Display Position on the y-axis of a graph with Time on the x-axis. 7. Display Velocity on the y-axis of a graph with Time on the x-axis. 8. Make sure that the sampling rate of your data collection system is at least 20 samples per second.9. Place the cart on the track against the end stop. 10. Record a data run that shows the initial position of the cart relative to the motion sensor and record this value in Table 2. 11. Place the cart, with the plunger extended, on the track against the end stop. 12. Record a data run that shows the second position of the cart relative to the motion sensor and record this value in Table 2. 13. Cock the plunger and then gently tap the release button to launch the cart. Be sure you use the same plunger position throughout this part of the lab. 14. Observe the cart's motion, ensuring the cart never gets closer than 15 cm to the motion sensor. 15. Use your angle indicator to record the angle of the track in Table 2. 16. Cock the plunger and place the cart in position on the track with the plunger against the bumper. 17. Start data recording and tap the release button to launch the cart. 18. Allow the cart to bounce once or twice before stopping data recording. 19. Record a data run that shows the closest position (third position) of the cart relative to the motion sensor and record this value in Table 2. 20. Use the data collection system to determine the distance x and the distance traveled d. 21. Record the distance x and d you measured in Table 2.Data: Part 1: Determining the Spring Constant Data Table 1: Determine the Spring Constant (Plot Force vs. Displacement). Cart's initial position: 39 em Hanging Mass Position Displacement from Hanging Force (mg) (kg (m Equilibrium (m) (N 0.25 0.0371 0. 002 2045 0. 45 0 , 084 0 10 05 4 -41 1. 65 0 031 0 - 0 0 8 6 - 37 0. 85 2. 0 29 8.33 0 . q 0. 027 0 . 012 8 . 82 k (spring constant) = 980 m'n Part 2: Conservation of Energy Data Table 2: Energy of the system. Parameter Values Mass of cart (kg) 0. 4 95 Initial position (m) 1.05 Second position (m) 1. 033 Third position (m) 0 481 Track angle 0 (degrees) 50 Spring maximum compression x (m) 0.019 Distance traveled d (m) 0. 571 Maximum height h (m) 0.0 479 Maximum gravitational potential energy ()) 0 . 2 41 Maximum spring potential energy (]) D. 151 Maximum velocity (m/s) 0 . 71 Maximum kinetic energy ()) 0 , 125Show your work for Table 2: 14 - x9 = 1. 05 - 1033 = 0.017 m d= X1 - xg = 1 05 - 0.481 7 0.569 1. Calculate the % difference between the maximum gravitational potential energy and maximum spring potential energy: 2. Calculate the total energy when the kinetic energy is maximum: 3. Calculate the % difference between the total energy and maximum spring potential energy:Post Lab Questions: 1. In Part 1, did you get the expected relationship between spring force and the displacement of the spring on your graph? Explain. 2. In Part 2, which is larger the spring potential energy or the gravitational potential energy? If one is larger than the other where did this lost energy go? Why would it not make any sense if GPE is larger than SPE? Would this violate any law of nature? 3. In part 2, can you say, based on your data, that mechanical energy is conserved? Explain