Ch. 4 Lab Conservation of Energy

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Feb 20, 2024

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Phys 151 – College Physics Chapter 4 Lab : Conservation of Energy (Online Simulation) Objectives By the end of this lab, students will be able to… 1. Calculate the maximum speed and displacement of an object using conservation of energy. 2. Determine the work done (energy lost) by friction. Instructions Use this Word document to record your answers to the questions in each section. Please put your answers in blue so that I can grade them easily. You will then turn in this document with your name on it to the lab submission box. Simulation Link This lab uses the Energy Skate Park: Basics simulation from PhET Interactive Simulation at University of Colorado Boulder ( https://phet.colorado.edu ), which is available through the following link: https://phet.colorado.edu/sims/html/energy-skate-park-basics/latest/energy-skate-park- basics_en.html

Theory Energy exists in different forms. When calculating the total mechanical energy ( E ) of an object, we consider both its kinetic energy ( KE ) and any potential energy ( PE ( g ) ) that it has. In this lab, we will only consider the object’s gravitational potential energy ( PE g ) : E = KE + PE (1) KE = 1 2 m v 2 (2) PE g = mgy h (3) In most interactions, energy is converted from one type to another (i.e. from potential to kinetic or vice versa); however, energy is conserved (Eq. 4), and the total energy of the system (Eq. 1) remains the same. E sys,f = E sys,i (4) For an individual object to gain energy, work ( W ) must be done to the object: W = ∆ E (5) E object ,f = E object ,i + W (6) However, this energy has to come from somewhere else, such as the Earth pulling on the object through gravity or some other object acting on it with a force, so energy as a whole is still conserved. Procedure Track #1 (Half-Pipe) 1. Click on the simulation link above and navigate to the “Intro” simulation. Take a few minutes to play around with the simulation and get comfortable with the different settings. 2. When you are ready to begin, hit the “Reset” button in the bottom right of the screen and the “Pause” button at the bottom of the screen. You should see a track shaped like a half-pipe (roughly a “U” shape). 3. The “Bar Graph” and “Speed” boxes at the top right of the screen should be CHECKED. 4. How much energy does the skater have when they are at rest on the ground? Put your answer below in blue. When a skater is at rest on the ground,

their energy is zero because they are not moving. 5. Click and drag the skater to the top of the half-pipe (it doesn’t matter which side you choose). What do you notice about the energy of the skater as you pick them up? Put your answer below in blue When I take the skater and raise it up, I see how the potential and total energy grows, the higher I raise it, the more this energy grows In Step #5., positive work is being done to the skater (by you) when they are lifted to the top of the half-pipe, which adds to the total energy of the skater. In real-life, the skater would do this work themselves by converting stored chemical energy (from food) into mechanical energy when they climb a set of stairs or take a ramp to reach the top of the half-pipe. 6. Now hit the “Play” button. Describe what happens to the different energies being plotted on the bar graph. Which energy is the largest at the top of the half-pipe? at the bottom of the half-pipe? How does the total energy of the skater change? Put your answer below in blue As the skater moves along the half-pipe, their kinetic and potential energies change, and the total mechanical energy remains constant. At the top of the half-pipe, the skater has the most potential energy, and thus the potential energy is the largest value on the graph. At the bottom of the half-pipe, the skater has the most kinetic energy, so the kinetic energy is the largest value on the graph. Without friction to slow down the motion of the skater, conservation of energy states that the total mechanical energy of the skater will remain constant, and this energy will continually be converted from gravitational potential energy to kinetic energy and back again. 7. Now adjust the mass of the skater. How does this affect the energy of the skater? the speed of the skater? Put your answer below in blue Increasing the mass of the skater will increase their potential energy and decrease their kinetic energy at the top of the half-pipe, while decreasing their potential energy and increasing their kinetic energy at the bottom of the half-pipe. This is because the skater's increased mass

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requires more energy to lift them to a higher position, resulting in more potential energy at the top of the half-pipe. At the bottom of the half- pipe, the skater's increased mass also increases their momentum, resulting in a greater kinetic energy. The total mechanical energy of the system (skater and half-pipe) remains constant, so as the skater's potential energy increases, their kinetic energy must decrease in order to keep the total mechanical energy constant. Similarly, as the skater's kinetic energy increases, their potential energy must decrease. The skater's speed will also be affected by changes in their mass. A more massive skater will move more slowly along the half-pipe due to their increased inertia, which requires more force to change their velocity. Conversely, a less massive skater will move more quickly along the half-pipe due to their lower inertia. Track #2 (Ramp) 8. Now switch to the second (middle) track on the right side of the screen. This track looks like a curved ramp to the right. Hit the “Pause” button and place the skater at the top of the ramp. 9. The “Grid” box at the top right of the screen should now be CHECKED. 10. Record the height ( y ) of the skater when he is at the top of the ramp. Put your answer below in blue 6 meters 11.Hit the “Play” button. What happens to the skater’s speed when he leaves the ramp? Put your answer below in blue When the skater is placed at the top of the curved ramp on the second track and the simulation is played, the skater's speed increases as he leaves the ramp. This is because the curved ramp is designed to convert

the skater's potential energy into kinetic energy as they move downhill. As the skater moves down the ramp, their potential energy decreases, and their kinetic energy increases, resulting in an overall increase in speed. 12.On the speed gauge, each large tick mark corresponds to 2 m/s, and each small tick mark corresponds to 1 m/s. In your data sheet, record the final speed of the skater at the bottom of the ramp. Put your answer below in blue 11 m/s 13.Now, use Equations (1) through (4) to calculate and record the final speed of the skater using conservation of energy. Since we are ignoring friction, you may assume that all of the gravitational potential energy is being converted into kinetic energy. Note: The mass of the skater doesn’t matter and should cancel out of your equation(s). How do your calculated values compare to the simulation? Put your answer below in blue Ei=Ef mgh=mv^2/2 gh=v^2/2 v=sqrt(2gh) v=sqrt(2*9.8m/ s^2*6m)=10.844m/s 14.Repeat Steps #10. - 13. for five different starting heights. What do you observe about the total energy and final speed of the skater at different heights? Put your answer below in blue As the starting height increases, so does the total energy of the skater. This is because the skater has more potential energy at higher starting heights, which is then converted into kinetic energy as the skater moves down the ramp. As the starting height increases, so does the final speed of the skater. This is because the skater has more potential energy at higher starting heights, which is converted into kinetic energy as the skater moves down the ramp, resulting in a higher final speed.

Track #3 (W) 15.Now switch to the third track on the right side of the screen. This one should be shaped like a “W”. 16.Pause the simulation and place the skater at the top of the ramp on the LEFT side of the “W”. If friction is still being ignored, do you think the skater will be able to make it to the top of the RIGHT side of the “W”? Why or why not? Put your answer below in blue If the skater is placed at the top of the ramp on the LEFT side of the “W” with friction still being ignored, it is likely that the skater will not be able to make it to the top of the RIGHT side of the “W”. Without friction, the skater would not be able to make it to the top of the ramp on the RIGHT side of the “W” because they would not have enough kinetic energy to overcome the force of gravity acting against them. 17.Now hit the “Play” button. Was your prediction accurate? Put your answer below in blue I was wrong, and skater was be able to make it to the top of the RIGHT side of the “W” 18.Pause the simulation and place the skater back on the LEFT side of the track. Through trial-and-error, can you find a place where he does not reach the RIGHT side of the track? Put your answer below in blue I think that one such location is near the bottom of the ramp, where the slope is shallow. If the skater is placed at this location with enough speed to make it up the ramp on the LEFT side of the track, they may not have enough kinetic energy to make it to the top of the ramp on the RIGHT side of the track due to the loss of kinetic energy from friction. The specific location where the skater will not make it to the top of the ramp on the RIGHT side

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of the track may depend on the initial speed and height of the skater, as well as the amount of friction in the simulation. Without friction, the kinetic energy of the skater at the bottom of the track is converted back into gravitational potential energy as they travel up the track. As long as the track doesn’t exceed their starting height, the skater can continue to travel over each hill on the track. This is how most roller coasters work: a chain pulls the coaster to the top of the biggest hill on the ride, and it proceeds to coast the rest of the way (even loops are possible under conservation of energy, if they are smaller than the original hill). However, in real life, friction takes away some of the coaster’s energy, so it can only travel over progressively smaller hills as it goes. 19.Pause the simulation and place the skater at the top of the track. Record the height of the skater at this point and the height of the hill in the middle of the track. Put your answer below in blue 5m and 2m 20.Now, use conservation of energy to calculate and record the speed of the skater as they pass over the hill in the middle of the track. Note: The skater’s gravitational potential energy AND kinetic energy are both NON-zero at this point (see the energy bar graph). Put your answer below in blue PE=mgh PE=5m*9.8m/s^2=49J v=sqrt(2*9.8m/s^2*3m)=7.668 m/s Therefore, the speed of the skater as they pass over the hill in the middle of the track is approximately 7.668 m/s. 21.Select “Slow Motion” at the bottom of the screen and hit the “Play” button. Record the speed of the skater as they go over the top of the hill. Note: It may be helpful to pause the simulation just before the skater reaches the top of the hill, then use the “advance” button ( ) until the skater is at the top of the hill. Put your answer below in blue Around 7.6 m/s 22. Calculate and record the percent difference between your predicted speed in Step #20. and the simulated speed in Step #21.. Put your answer below in blue

% Difference = (7.668 - 7.6) / ((7.668 + 7.6) / 2) x 100% % Difference = 0.887% This indicates that the predicted value and simulated value are very close to each other. Tracks with Friction 23.At the bottom of the screen, select the “Friction” simulation. You should now be on the half-pipe track. As before, the “Bar Graph”, “Speed”, and “Grid” boxes should be CHECKED. 24.Hit the “Pause” button, then click and drag the skater to a height of 5 m on one side of the half-pipe (it doesn’t matter which side you choose). 25.Now hit the “Play” button. What do you observe about the motion of the skater? How is the energy of the skater affected? Does their total energy change? Put your answer below in blue When the skater is placed at a height of 5 m on one side of the half-pipe and the simulation is played, the skater moves back and forth along the half-pipe. The motion of the skater is affected by friction, which causes the skater to lose kinetic energy as they move up the slope and gain kinetic energy as they move down the slope. Due to the presence of friction, the total energy of the skater is not conserved in this simulation. As the skater moves up the slope, their kinetic energy is converted into potential energy and work done against friction. As the skater moves down the slope, their potential energy is converted into kinetic energy and work done by friction. This results in a loss of energy due to friction and the skater's total energy decreases over time.

26.Reset the skater to the top of the track and hit the “Play” button. Record the maximum height of the skater on the other side of the track. Put your answer below in blue 4.5 Friction generates heat, which is being graphed as thermal energy . You may have observed that thermal energy increases the most when the skater is at the bottom of the ramp. This is because the normal force (and therefore the friction force) is highest at this point. In the bar graph, the total energy remains the same. However, the simulation is considering the energy of the system (skater plus their surroundings) and not just the skater. In reality, the skater will gain some of this thermal energy, but the rest goes into the track, so friction is doing negative work to the skater, causing them to lose energy. Energy is still conserved, but it no longer belongs to only the skater. 27. Calculate and record the energy lost by the skater as a percentage of their initial energy. You can do this by subtracting the potential energy of the skater at the final height from the potential energy at the initial height, divided by the potential energy at the initial height x 100. Put your answer below in blue 9.8 m/s^2 x 6 m=58.8J 9.8 m/s^2 x 4.5m=44.1J (58.8J – 44.1 J) / 58.8 J x 100%=25% Therefore, the energy lost by the skater as a percentage of their initial energy is 25%. 28.Now switch to the second (middle) track on the right side of the screen (the curved ramp). Hit the “Pause” button and place the skater at the top of the ramp. 29.Hit the “Play” button and record the final speed of the skater at the bottom of the ramp. How does this speed compare to what you found in Step #12.? Put your answer below in blue 10 m/s The final speed of the skater with friction on the curved ramp (10 m/s) is less than the final speed without friction on the straight ramp (11 m/s). The final speed of the skater with friction on the curved ramp is less than the final speed without friction on the straight ramp because friction between the skater and the surface of the curved ramp converts some of the skater's kinetic energy into thermal energy, reducing the amount of kinetic energy the skater has at the bottom of

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the ramp. The curved ramp also has a larger radius of curvature, which means the skater has to travel a longer distance to reach the bottom compared to the straight ramp, which also reduces the final speed. 30.Now switch to the third track on the right side of the screen (the “W” track). 31.Pause the simulation and place the skater at the top of the ramp on the LEFT side of the “W”. With friction enabled, do you think the skater will be able to make it to the top of the RIGHT side of the “W”? Why or why not? Consider the height of the skater in Step #26.. Put your answer below in blue No, I don't think the skater will be able to make it to the top of the right side of the "W" with friction enabled. This is because in Step #26, we observed that the skater lost a significant amount of energy due to friction on the curved ramp, resulting in a lower final speed at the bottom. With friction enabled, the skater will lose even more energy, making it more difficult to reach the top of the right side of the "W". 32.Now hit the “Play” button. Was your prediction accurate? Put your answer below in blue Yes, it was 33.Reset the skater to the top of the track and hit the “Play” button. Record the maximum height of the skater on the RIGHT side of the track. How does this compare to your answer from Step #26. Put your answer below in blue The maximum height for “W” is 3.5m This is less than my answer from Step #26 (4.5m) When conservative forces (such as gravity) are acting on an object, energy is conserved , meaning it can be reused later on. The path taken by an object acting under conservative forces is irrelevant . That is why the track layout doesn’t matter when friction is ignored: energy is conserved, and the skater reaches the same height as before. However, non-conservative forces (such as friction) take energy away from objects. These forces depend on the path taken. For example, a longer

path means more contact with the track, so more friction is observed (more thermal energy is generated). In this case, the “W” track has more track between the start and finish points than the half-pipe, so more energy is lost overall (becoming thermal energy), and the skater reaches a lower final height than before. Next Steps 34.Once you have completed all experiments and calculations, submit this document to Moodle in the submission box.

Ch. 4 Lab Conservation of Energy

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