6-2 Energy of a tossed ball PDF

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6-2 Energy of a tossed ball of Algebra-based Physics I Lab...

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Experiment # 6 Energy of a Tossed Ball

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Pre-lab Questions: For each question, consider the free-fall portion of the motion of a ball tossed straight upward, starting just as the ball is released to just before it is caught. Assume that there is very little air resistance. 1. What form or forms of energy does the ball have while momentarily at rest at the top of the path? -If the ball is momentarily at rest, that means that for that moment, its velocity and therefore its kinetic energy is equal to zero. Since the ball has no kinetic energy at this point, all of the ball's energy is in its gravitational potential energy. 1.

What form or forms of energy does the ball have while in motion near the bottom of the path?

-Near the bottom of the path (if we're assuming this is the point just before the ball hits the table), all of the ball's energy is kinetic energy. If we're getting technical, since the ball has height, it does have some small amount of potential energy. However, at this point in its motion, potential energy would be so small it would be negligible, and nearly all of the ball's energy would be kinetic.

1. Sketch a graph of velocity vs. time for the ball, kinetic energy vs. time for the ball, and potential energy vs. time for the ball. ●

y = -9.2645x + 36.902

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y = -1.4429x + 7.2281

y = 1.9397x - 3.5078

Purpose: ● Measure the change in the kinetic and potential energies as a ball moves in free fall. ● See how the total energy of the ball changes during free fall.

Materials: ● Computer

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● Vernier motion detector ● Logger Pro ● Basketball

Independent variables: ● Time (s), Height (m), Position Dependent variables: ● Velocity (m/s), Potential Energy (J) Control variables: ● mass of the ball

PROCEDURE: 1. Measure and record the mass of the ball you plan to use in this experiment. 2. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. Place the Motion Detector on the floor and protect it by placing a wire basket over it. 3. Hold the ball directly above the Motion Detector. Have your partner click to begin data collection. Toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector catch the ball before it hits the detector. Note: Use two hands, be sure to pull your hands away from the ball after it starts moving so they are not picked up by the Motion Detector. Throw the ball so it moves vertically above the detector. Verify that the position vs. time graph corresponding to the free-fall motion is parabolic in shape, without spikes or flat regions, before you continue. This step may require some practice. If necessary, repeat the toss, until you get a good graph. When you have good data on the screen, proceed to the Analysis section. 4. Click on the Examine button, , and move the mouse across the position or velocity graphs of the motion of the ball to answer these questions. a. Identify the portion of each graph where the ball had just left your hands and was in free fall. Determine the height and velocity of the ball at this time. Enter your values in your data table. (after release) b. Identify the point on each graph where the ball was at the top of its path. Determine the time, height, and velocity of the ball at this point. Enter your values in your data table. (top path) 4

c. Find a time where the ball was moving downward, but a short time before it was caught. Measure and record the height and velocity of the ball at that time. (before catch) d. Collect two more times on the way up and on the way down for a total of seven data points. e. For each of the seven points in your data table, calculate the Gravitational Potential Energy (PE), Kinetic Energy (KE), and Total Energy (TE). Use the position of the Motion Detector as the zero of your gravitational potential energy.

DATA TABLE: Mass of the ball

Position After release On the way up Before the Top Top of path After the Top Going down Before catch

(kg)

0.500

Velocity (m/s)

PE (J)

KE (J)

TE (J)

0.463

3.376

2.2687

2.8493

5.1180

3.7

0.641

3.212

3.1409

2.5792

5.7201

3.8

1.024

1.779

5.0176

0.7912

5.8088

4.0

1.188

-0.092

5.8212

0.0021

5.8233

4.2

1.065

-1.672

5.2185

0.6988

5.9173

4.3

0.865

-2.476

4.2385

1.5326

5.7711

4.3

0.728

-2.9

3.5672

2.1025

5.6697

Time (s)

Height (m)

3.6

Mass of the ball

(kg)

0.500

Time (s)

Height (m)

Velocity (m/s)

PE (J)

KE (J)

TE (J)

1.2

-0.6

-1.525

-2.94

0.58140625

-2.35859375

1.25

-0.535

-1.082

-2.6215

0.292681

-2.328819

Before the Top

1.3

-0.492

-0.611

-2.4108

0.09333025

-2.31746975

Top of path

1.35

-0.474

-0.131

-2.3226

0.00429025

-2.31830975

Position After release On the way up

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After the Top going down Before catch

1.45

-0.508

0.838

-2.4892

0.175561

-2.313639

1.55

-0.651

1.778

-3.1899

0.790321

-2.399579

1.65

-0.867

2.604

-4.2483

1.695204

-2.553096

ANALYSIS: 1. Use Logger Pro and graph the energies as a function of time. Please show all energies on the same graph.

2. Inspect your kinetic energy vs. time graph for the toss of the ball. Explain its shape.

y = -1.4429x + 7.2281

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Kinetic Energy Applications: The kinetic energy of the ball can be found with the equationAKE = 0.5mv^2. We can conclude that the ball's kinetic energy is directly proportional/correlated to the ball's velocity. That is, the greater the velocity the greater the KE. The Kinetic Energy portion of the graph looks sort of an inverted parabola. This is because it starts out at zero J as I'm holding it still above the motion detector. Then, as I throw it in the air, it gains KE, therefore the graph goes in the positive y direction. As the ball loses its acceleration and then begins to decelerate and head towards the top of its path, it has more potential energy than kinetic energy, hence why the graph begins to move toward zero, in the negative y direction. As the ball approaches the top of its path it momentarily has no velocity, meaning there is no KE, only PE, hence why the KE graph momentarily is at zero J. As the ball begins to gain velocity as it plummets back towards Earth, the KE rises again. Finally, the KE goes back to zero when I catch the ball, stopping all movement. 3. Inspect your gravitational potential energy vs. time graph for the free-fall flight of the ball. Explain its shape.

y = 1.9397x - 3.5078

Potential Energy Applications: Since the only form of potential energy acting on the ball is gravitational potential energy, we can find the ball's potential energy with the equationAGrav. PE = mgh. By looking at the equation and the data, we can conclude that the GPE of the ball is directly proportional/correlated to the ball's vertical position. That is, the higher the ball is, the greater the GPE. The PE starts above zero J and creates a parabolic pattern as it returns to its original position above zero. First, the reason it does not start at zero is because I'm holding the ball above the motion detector (above the Earth). The formula for PE is mgh, and since there is some height between the motion detector and the ball, there is some PE to start with. The graph creates a parabola because as the ball rises into the air, it gains more height. The higher the ball, the more the PE it has. At the top of its path is the most PE it will have because it's the highest it will travel. 7

4. Inspect your Total energy vs. time graph for the free-fall flight of the ball. Explain its shape.

y = 0.4968x + 3.7203

The TE portion of the graph (black) is almost completely constant throughout the motion. The total energy should remain mostly constant. It should because there aren’t any noticeable nonconservative forces acting on the ball that would reduce the amount of total energy in the system. If there were energy that were reduced, it would have gone in the form of air resistance, sound, and heat. These factors, however, are so minimal in this case that they can be ignored all together. What do you conclude from this graph about the total energy of the ball as it moved up and down in free fall? Does the total energy remain constant? Should the total energy remain constant? Why? If it does not, what sources of extra energy are there or where could the missing energy have gone? According to the graph, the total energy of the ball remained constant as it moved up and down in free fall. According to the data in our data table, however, the total energy does not remain constant, suggesting a small amount of air resistance that was insignificant enough to be hidden in the graph. The total energy should not remain exactly the same, as work is being done on the ball by air resistance (a nonconservative force). For PHY2048 only: 5. Take the derivative with respect to time of the equations describing the energies. Explain their meanings. 6. Calculate the kinetic energy of the basketball for one complete toss, graph it and explain every portion of the graph.

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EXTENSION (PHY2048): ● Complete the experiment again, by placing the detector above the basketball and tossing the ball towards the detector.

Mass of the ball

Position

(kg)

0.500

Time (s)

Height (m)

Velocity (m/s)

PE (J)

KE (J)

TE (J)

After release On the way up Before the Top

1.2

-0.6

-1.525

-2.94

0.58140625

-2.35859375

1.25

-0.535

-1.082

-2.6215

0.292681

-2.328819

1.3

-0.492

-0.611

-2.4108

0.09333025

-2.31746975

Top of path

1.35

-0.474

-0.131

-2.3226

0.00429025

-2.31830975

1.45

-0.508

0.838

-2.4892

0.175561

-2.313639

1.55

-0.651

1.778

-3.1899

0.790321

-2.399579

After the Top going down

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Before catch

1.65

-0.867

2.604

-4.2483

1.695204

-2.553096

1. Use Logger Pro and graph the energies as a function of time. Please show all energies on the same graph. Analisis Missing in all these graphs

2. Inspect your kinetic energy vs. time graph for the toss of the ball. Explain its shape.

y = 2.5123x - 2.9802

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3. Inspect your gravitational potential energy vs. time graph for the free-fall flight of the ball. Explain its shape.

y = -2.905x + 1.1574

4. Inspect your Total energy vs. time graph for the free-fall flight of the ball. Explain its shape.

y = -0.3928x - 1.8229

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CONCLUSION: 1. What would change in this experiment if you used a very light ball, like a beach ball? 2. What would happen to your experimental results if you entered the wrong mass for the ball in this experiment? 3.

Definition of Conservation of Energy and its mathematical representation.

Takeaways: So what have we learned from this lab? The different forms of energy in a system are all related due to the law of conservation of energy. That is, in a system where no non-conservative work (such as friction) is done, the total amount of energy in the system will remain constant. This also means that there is an inverse proportionality between KE and PE in a system. As one increases the other decreases. You can think about this as a change in energy. One type of energy turns into another. Unfortunately, since we live in the real world, our data does not show conservation of energy due to air resistance which transfered some of the ball's energy into the surroundings.

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