I have to build a roller coaster with 3 hills. Hill A is 15 inches high,it drops down to 3 inches, rises to 8 inches, drops again to 5 inches and rises a last time to 3 inches before dropping off. My question is when using a tennis ball as the car..

1. What is the initial velocity of the tennis ball at the moment of its released at the top of the track? Use this insight to calculate the initial kinetic and potential energy
2. Calculate the amount of gravitationAL potential energy at the top of each hill and at the bottom of each valley. Be sure to convert your distance measurements to meters. Use an approximate value of 58.0 g. for the mass of the tennis ball, and 9.81 m/s ^2 as the excelleration due to gravity.
3. Suppose that the force due to friction is negligible. What can you say about the total energy of the tennis ball? Continue to assume that the force due to friction is negligible. Use the information you've gathered to calculate the kinetic energy and the total energy at each location. Describe the relationship between the potential and Kinetic energy of the tennis ball as it travels the length of the roller coaster.
5. Compare your answer to the previous question with your observations in conducting this experiment. Discuss weather energy was conserved in your experiment. Was friction negligible?

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I need help with this as well.

To answer these questions, we will need to apply the principles of conservation of energy and equations related to potential and kinetic energy. Let's go through each question step by step:

1. To calculate the initial velocity of the tennis ball at the moment of its release at the top of the track, we can use the concept of conservation of energy. At the top of the track, the tennis ball will have potential energy due to its height above the ground. This potential energy will be converted into kinetic energy as it rolls down the track.

The initial potential energy (PE) can be calculated using the equation:
PE = m * g * h
where m is the mass of the tennis ball, g is the acceleration due to gravity, and h is the height of the hill.

Similarly, the initial kinetic energy (KE) can be calculated using the equation:
KE = (1/2) * m * v^2
where m is the mass of the tennis ball and v is the initial velocity.

Since the ball is released at the top, its initial velocity will be zero. Therefore, the initial kinetic energy will also be zero. The initial potential energy will be the maximum at the top of the first hill.

2. To calculate the amount of gravitational potential energy at the top of each hill and at the bottom of each valley, we need to convert the given distances from inches to meters and use the same equation as in the previous step.

First, convert the height measurements from inches to meters:
15 inches = 0.381 meters
3 inches = 0.0762 meters
8 inches = 0.2032 meters
5 inches = 0.127 meters

Now, calculate the gravitational potential energy at each location using the equation: PE = m * g * h

For the first hill:
PE1 = (0.058 kg) * (9.81 m/s^2) * (0.381 m)

For the first valley:
PE2 = (0.058 kg) * (9.81 m/s^2) * (0.0762 m)

For the second hill:
PE3 = (0.058 kg) * (9.81 m/s^2) * (0.2032 m)

For the second valley:
PE4 = (0.058 kg) * (9.81 m/s^2) * (0.127 m)

For the third hill:
PE5 = (0.058 kg) * (9.81 m/s^2) * (0.127 m)

3. The question states that the force due to friction is negligible. In such a case, the total energy of the tennis ball should remain constant throughout the roller coaster's motion. This means that the sum of potential energy and kinetic energy at any location should be the same at all other locations.

To calculate the kinetic energy at each location, we can use the equation mentioned earlier:
KE = (1/2) * m * v^2

For the initial location (top of the first hill), we know the kinetic energy is zero, as the tennis ball is released from rest.

For each subsequent location, we can calculate the kinetic energy using the equation with the velocity corresponding to that location.

The total energy at each location can be calculated by summing the potential and kinetic energy at that location.

By comparing the potential and kinetic energy at each location, we can observe how the energy is transferred between them as the ball travels the length of the roller coaster.

5. To compare the calculated values with your observations in conducting the experiment, you would need to measure the actual velocity and heights accurately. You can use a stopwatch to measure the time it takes for the ball to travel between different points in the roller coaster and calculate its velocity. By comparing these measured values with the calculated ones, you can evaluate if the energy was conserved in your experiment.

Regarding friction, the question assumes that the force due to friction is negligible. However, in a real-world scenario, friction would likely play a role and some energy would be lost due to friction. If you observed any differences between the calculated and measured values, it could be due to energy loss through friction or other factors not accounted for in the calculations.

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