Purpose of the experiment

Transcription

1 Work and Energy Theorem PES 116 Advanced Physics Lab I Purpose of the experiment What is Work and how is it related to energy? Learn about different forms of energy. Learn how to use the Conservation of Energy to solve complicated dynamics problems. FYI FYI The early bird gets the worm, but the second mouse gets the cheese. Work and Energy - 1

2 Table of Contents Background Work and Energy 3 Types of Energy 4 Lab Procedure 7 Equipment List LabPro Interface Motion Sensor Force Sensor Rotary Motion Sensor Part A Work by constant force Long string 200 g mass Ring stand (small) Clamp Ring stand clamp Steel rod Part B Work by variable force Spring Mass set Part C Work / Energy Dynamics track Dynamics cart Super pulley 100 g mass Long string Force Sensor adaptor Work and Energy - 2

3 Background Work and Energy Work is a measure of energy transfer. When work is done on an object, there will be an increase in its kinetic or potential energy. In order to do work on an object, it is necessary to apply a force along or against the direction of the object s motion. If the force is constant and parallel to the object s path, work can be calculated using: Work = Force times the Distance traveled W = F x where F is the constant force and x the displacement of the object. If the force is not constant, we can still calculate the work using a graphical technique. If we divide the overall displacement into short segments, x, the force is nearly constant during each segment. The work done during that segment can be calculated using the previous expression. The total work for the overall displacement is the sum of the work done over each individual segment: W = F( x) x This sum can be determined graphically as the area under the plot of force vs. distance. From calculus, you should recognize this sum as leading to the integral: s final W = F( x) dx s initial These equations for work can be easily evaluated using a Force Sensor and a Motion Detector or Rotary Motion Sensor. In either case, the work-energy theorem relates the work done to the change in energy as: W = U + K where W is the work done, U is the change in potential energy, and K the change in kinetic energy, K = 2 mv 2 mv O. In this experiment you will investigate the relationship between work, potential energy, and kinetic energy. Work and Energy - 3

4 What is energy? what it is. Energy is one of those things that everyone talks about but no one knows exactly When asked, What is energy? The reply, I don t know! A direct quote from Scott Rehorst UCCS Physics Lab Coordinator My mom did not raise no dummy! I do know something about physics and this is not such an unreasonable reply to this question. No one really knows what energy is! We know that it exists and we can see how it affects objects. A car speeding down the highway has a precise amount of kinetic energy. A skydiver has a certain amount of potential energy. I can keep listing off examples all day long, but I will not. Something else we know about energy is that within an isolated system (no interactions with anything outside of the system) energy is conserved. Energy is free to change forms, but the total amount of energy must remain constant. We do know that energy can neither be created, nor destroyed. Energy can only be shifted around from one form to another. Types of energy Kinetic Energy (KE) This form of energy is associated with the motion of an object. Kinetic energy is defined mathematically as: KE = 1 2 m v2. Potential Energy (PE) This is a measure of the energy stored in an object due to either its physical properties or its position. Potential energy depends on the situation: For gravity PE = mgh, where h is the distance from the PE =0 point. An object that is suspended above the ground has the potential to drop to the ground when released. Work and Energy - 4

5 For a spring PE = 1 2 kx2, where x is the distance the spring is stretched. Energy Losses (E) Energy can be robbed from a system by several mechanisms. Heat is a form of energy. If there is friction between two objects, heat will be present when they rub against each other. If you have ever warmed your hands by rubbing them together then you know what I am talking about. Since energy is conserved, the energy that goes into heat has to come from a loss in another form of energy. If an object is moving it has kinetic energy. If there is friction between the ground and the object, the object will slow down. This loss in kinetic energy will be taken up as an increase in thermal energy so the total energy will remain constant. This may not sound like it would contribute much to the total energy, but it can be a noticeable amount. It also takes energy to create sound. Sound energy will rob the system of still more energy. There are still more examples of energy loss that I will not go into here and not all can be measured in today s lab. Therefore, be aware of the fact that some of your energy will be lost Work and Energy - 5

6 The Lab The goal of this lab is to investigate the relationships between work and energy. Part A: Work Done by a Constant Force In this part you will measure the work needed to lift an object straight upward at constant speed. The force you apply will balance the weight of the object, and so is constant. The work can be calculated using the displacement and the average force, and also by finding the area under the force vs. distance graph. 1. Connect the Rotary Motion Sensor to DIG/SONIC 1 of the LabPro Interface. Connect the Vernier Force Sensor to Channel 1. Set the range switch to 10 N. 2. Start Logger Pro. Open the file PES 116/Work and Energy/Constant Force.cmbl. Three graphs will appear on the screen: distance vs. time, force vs. time, and force vs. distance. Data will be collected for 5 s. 3. Calibrate the Force Sensor. 4. Hold the Force Sensor with the hook pointing upward, with nothing pushing or pulling on the hook. Click and then to set the Force Sensor to zero. 5. Weigh the 200-g mass on the scale to determine its exact mass. Record the mass in the data table in your lab notebook. 6. Hang the Rotary Motion Sensor from the mounting rod on the ring stand. Then hang the 200-g mass and the Force Sensor from a string that passes over the Rotary Motion Sensor s largest pulley. (Do NOT use any of the smaller pulleys on the Rotary Motion Sensor. Your data will not work out.) Work and Energy - 6

7 Figure 1: Setup for Part A. 7. Pull the Force Sensor downward just enough to bring the 200-g mass completely off the floor and then hold it still. Click to begin data collection. Wait about 1.0 s after data collection starts, and then slowly pull the Force Sensor straight downward with its hook pointed straight up to raise the mass about 0.2 to 0.3 m upward. Lift so that the slope of the distance vs. time graph is constant. Continue lifting the mass straight up until after the data collection stops at 5 s. Be sure to get clean data. 8. Examine the distance vs. time and force vs. time graphs by clicking the Examine button,. Identify when the weight started to move upward at a constant speed. Record this starting time and height in the data table. 9. Examine the distance vs. time and force vs. time graphs and identify where the 200-g mass was when the data collection stopped. Record this stopping time (should be 5 s) and height in the data table. 10. Determine the average force exerted while you were lifting the mass. Do this by selecting the portion of the force vs. time graph corresponding to the time you were Work and Energy - 7

8 lifting. Use the exact times you determined in Steps 8 and 9 to do this. Do not include the brief period before the upward motion started. Click the Statistics button,, to calculate the average force. Record the value in your data table under Average Force. 11. On the force vs. distance graph select the region corresponding to the upward motion of the weight. Click and hold the mouse button at the starting distance, then drag the mouse to the stopping distance and release the button. Click the Integrate button,, to determine the area under the force vs. distance curve during the lift. Again, use the exact distances you determined in Steps 8 and 9. Record this area in the data table under Integral 12. Print the graphs. 13. The work you did lifting the mass did not change its kinetic energy. The work then had to change the potential energy of the mass. Calculate the increase in gravitational potential energy using the following equation: U = mg h where h is the distance the mass was raised (see Prelab 3). Compare this to both the average work, and to the area under the force vs. distance graph with percent difference calculations. % difference = 1 2 value1 value 2 100% ( value1+ value 2) Record your values in the data table. Does the work done on the mass correspond to the change in gravitational potential energy? Should it? Work and Energy - 8

9 Part B: Work Done by a Variable Force In Part B you will measure the work needed to stretch a spring. Unlike the work needed to lift a mass, the work done in stretching a spring is not a constant. However, the work can still be calculated using the area under the force vs. distance graph. 1. Start Logger Pro. Open the experiment file PES 116/Work and Energy/Variable Force.mbl. Three graphs will appear on the screen: distance vs. time, force vs. time, and force vs. distance. Data will be collected for 5 seconds. Connect the Force Sensor to Channel 1 and the Rotary Motion Sensor to DIG/SONIC 1. Be sure the Force Probe is set to the 10 N range and recalibrate the Force Probe as you did in Part A, Step Attach one end of the spring to the shaft of the ring stand. Attach the Force Sensor hook to the other end, as shown in the diagram below: Figure 2: Setup for Part B. Tie a string to the support screw of the Force Sensor, and tie the other end of the string to a 20-g mass. Hang the string over the Rotary Motion Sensor s largest pulley as shown in the diagram above such that as the mass descends, the Rotary Motion Sensor s pulley rotates clockwise as viewed from the pulley side. (If you Work and Energy - 9

10 Force Sensor need to, turn the Rotary Motion Sensor around so that the pulley side faces away from you.) Clamp both of the ring stands to the table top. 3. Very slightly pull on the Force Sensor until the coils of the spring just barely start to separate. Using tape, mark the position of the leading edge of the Force Sensor on the table where this occurs. This marks the starting point where the spring is in a relaxed state. Hold the end of the Force Sensor that is nearest the Rotary Motion Sensor as shown in the figure below. Figure 3: Data collection for Part B. The Rotary Motion Sensor will measure the distance the spring is stretched. With the leading edge of the Force Sensor at the tape mark, click. On the dialog box that appears, click. Logger Pro will now use a coordinate system that is positive towards the Rotary Motion Sensor with the origin at the Force Sensor. 4. Click to begin data collection. Within the limits of the spring (Do NOT overextend the spring), move the Force Sensor and slowly stretch the spring about 20 cm over several seconds. Make sure the spring, Force Sensor, and string are all horizontal and lined up with the pulley as shown in Figure 2 for the duration of the motion. Continue stretching the spring until data collection stops. Be sure to get clean data. 5. Examine the distance vs. time and force vs. time graphs by clicking the Examine button,. Identify the time when you started to pull on the spring. Record this starting time and distance in the data table. Work and Energy - 10

11 6. Examine the distance vs. time and force vs. time graphs and identify how far you stretched the spring when data collection stopped. Record this stopping time should be 5 s) and distance in the table. 8.) Click the force vs. distance graph, then click the Linear Regression button,, to determine the slope of the force vs. distance graph. The slope is the spring constant, k. Record the slope in the data table. 9.) The area under the force vs. distance graph is the work done to stretch the spring. How does the work depend on the amount of stretch? On the force vs. distance graph select the region corresponding to the first 10 cm stretch of the spring. (Click and hold the mouse button at the starting distance, then drag the mouse to 10 cm and release the button. You need to base your starting value on the exact distance you recorded in step 6. Your ending value is the starting value plus 10 cm.) Click the Integrate button,, to determine the area under the force vs. distance curve during the stretch. Record this area in the data table. 10.) Now select the portion of the graph corresponding to the first 15 cm of stretch. Find the work done to stretch the spring 15 cm. (Again, base your starting value on the exact distance you recorded in step 6. Your ending value is the starting value plus 15 cm.) Record the value in the data table. 11.) Select the portion of the graph corresponding to the maximum stretch you achieved. Find the work done to stretch the spring this far. (Your starting value is the distance you recorded in step 6, the ending value is the distance you recorded in step 7.) Record the value of the work in the data table. 12.) Print the graphs. Work and Energy - 11

12 Part C The Work-Energy Theorem In Part C, you will pull on the cart with a hanging mass, causing the cart to accelerate. The Motion Detector allows you to measure the initial and final velocities; along with the Force Sensor, you can measure the work done on the cart to accelerate it. 1. Start Logger Pro. Open the file PES 116/Work and Energy/Work Energy Theorem. cmbl. Four graphs will appear on the screen: distance vs. time, velocity vs. time, force vs. time, and force vs. distance. Data will be collected for 5 s. 2. Mount the Force Sensor on the back of the cart using the cart adapter bracket as shown in Figure 4. Determine the total mass of the cart, Force Sensor and cart adapter bracket. Record the total mass in the data table in your lab notebook. 3. Connect the Force Probe to Channel 1 of the LabPro and the Motion Detector to DIG/SONIC 1. Recalibrate the Force Probe. Be sure the Force Probe is set to the 10 N range, and the Motion Detector s switch is on the Track setting. 4. Using the level provided, level the dynamics track by adjusting the leveling foot. 5. Set up the following apparatus: ~25 cm ~100 g Figure 4: Apparatus for Part C. Place the cart with Force Sensor at rest about 25 cm from the Motion Detector, ready to roll away from the detector. The hanging mass should be about 100 g and the horizontal portion of the string should be parallel to the track. Additionally, the string should be long enough that the 100 g mass will hit the ground before the cart reaches the pulley. Work and Energy - 12

13 6. At a point half-way between the pulley and the cart, hold the string down with your finger against the dynamics track: Push here No tension Figure 5: Zeroing the sensors. The portion of the string between your finger and the cart should just barely have any tension in it. Click. On the dialog box that appears, click. Logger Pro will now use a coordinate system that is positive away from the Motion Detector with the origin at the cart. 7. Make sure the 100-g mass is not spinning or swinging, click to begin data collection. After you hear the Motion Detector begin clicking, quickly lift your finger and allow the cart to roll away from the detector under the influence of the hanging 100 g mass. Make sure the Force Probe s cord doesn t interfere with the motion by taping it out of the way if necessary. Let the cart roll toward the super pulley, but catch it before it strikes the pulley. As always, be certain to get clean data. 8. Examine the distance, velocity and force vs. time graphs by clicking the Examine button,. Identify when you let the cart go. Record this time and distance in the data table. 9. Examine the distance, velocity and force vs. time graphs and identify when the 100 g mass reached the floor. Record this time and distance in the data table. Work and Energy - 13

14 10. Determine the velocity of the cart just after the 100 g mass reached the floor. Using the cursor on the velocity vs. time graph, drag out the selection bars to select a short segment of the graph just after the mass reaches the floor, as shown in the diagram below: v Select this part of the graph. t Use the Statistics button,, to get this velocity. In the statistics information box that pops up, record the average value of the velocity for the section of the graph you selected. Record the velocity under Final velocity in the data table in your lab notebook. 11. From the force vs. distance graph, determine the work done to accelerate the cart. To do this, select only the region corresponding to the cart s acceleration using the distances you determined in Steps 8 and 9. Click the Integrate button,, to measure the area under the curve. Record the value in the data table in your lab notebook. 12. Repeat the procedure for a total of three trials. 13. Print a copy of the graphs from one of the trials. 14. The hanging mass did work to accelerate the cart. In this case, the work went to changing the kinetic energy of the cart. The cart moved along a level surface, there is no change in potential energy of the system. How does the work done compare to the change in kinetic energy? Here, since the initial velocity is zero, 2 K = 1 2 mv where m is the total mass of the cart and Force Probe, and v is the final velocity. Record your values in the data table. Work and Energy - 14