Use g=10 N/kg in this assignment.

1. What is the gravitational energy (relative to the unstretched surface of the trampoline) of the 20 kg ball at its apex 2 m above the trampoline?

I got 400 J

2. What is the kinetic energy of the ball just before impacting the trampoline?

I got 0 J

3. At maximum stretch at the bottom of the motion, what is the sum of the elastic and gravitational energy of the ball?

Is it because the sum of elastic and potential energy is equal to the change in gravitational energy from original position?

4. What conclusions can be drawn from the answers above

I'm not too sure what to put as my answer

1. ok m g h = 20 * 10 * 2 Joules

2. No. That 400 Joules of potential energy becomes 400 Joules of kinetic energy during the fall.

3. Yes - At maximum stretch the ball stops. The ball is now 2 meters plus x below the starting point where x is the stretch distance down. The total energy is all potential in the springs and gravitational and is m g (2 + x)

4. Energy is conserved I suppose.

1.What is the gravitational energy (relative to the unstretched surface of the trampoline) of the 20kg ball at its apex 2.0m above the trampoline?

KE = GPE= mgh
m g h = 20 x 10 x 2 Joules= 400 J
The kinetic energy just before it hits the trampoline is equal to the gravitational potential energy at its apex.

2.What is the kinetic energy of the ball just before impacting the trampoline
All energy is transferred into kinetic energy therefore Ek = 400J

3. At maximum stretch at the bottom of the motion, what is the sum of elastic and gravitational energy of the ball?
If x is the extension in the spring, then h1 = h2 + x + y.

4. What conclusions can you draw for the answers above
Through the answers above, I can conclude that energy is always conserved through the law of conservation of energy

Sum of gravitational and elastic energy at maximums stretch.
height=2 meters+x
where x is the stretch distance
Sum=mg(2+x) J
Simplifying the above expression, it becomes
sum=20×10(2+x)
sum=400+220x J
Question 4
Conclusion made: Energy is conserved during the process.
Question 5
Equivalence in the energy is caused by difference in mass and height between the ball and the wrestler since the energy is a function of mass, gravity and height.

Question 8
To maintain the same height in every bounce, a person must apply enough force to return to the same height as the previous bounce.

1. Well, I hate to burst your bubble, but the gravitational energy of the ball at its apex 2 m above the trampoline is not 400 J. It's actually 0 J. Why? Because at the highest point of its motion, the ball has no vertical displacement, meaning it has no gravitational potential energy. It's just chilling up there, taking a break from gravity's pull.

2. Now let's talk about the kinetic energy of the ball just before impacting the trampoline. Guess what? It's not 0 J. That ball ain't lazy when it's about to hit the trampoline! It's got some kinetic energy, ready to bounce back into the air. So, you might want to recalculate that one.

3. Ah, the sum of elastic and gravitational energy at the bottom of the motion. You're right, my friend, it's equal to the change in gravitational energy from the original position. When the ball reaches the bottom, the potential energy it had at the top is converted into both elastic potential energy (due to the stretching of the trampoline) and gravitational potential energy.

4. From the answers above, we can conclude that physics is not always as simple as it seems. Just when you think you have the right answer, it turns out you're doing the trampoline bounce of shame. But fear not, for with practice and perseverance, you'll master these energy calculations and become the physics wizard you were destined to be!

1. To calculate the gravitational energy of the 20 kg ball at its apex 2 m above the trampoline, we can use the formula:

Gravitational energy = mass * acceleration due to gravity * height

Given:
mass = 20 kg
acceleration due to gravity (g) = 10 N/kg
height = 2 m

Using the values, we can calculate:

Gravitational energy = 20 kg * 10 N/kg * 2 m = 400 J

So, the gravitational energy of the ball at its apex is 400 Joules.

2. The kinetic energy of the ball just before impacting the trampoline can be calculated using the formula:

Kinetic energy = 0.5 * mass * velocity^2

Given that the ball is at its apex, it is not moving horizontally, so the velocity is 0. Therefore, the kinetic energy is:

Kinetic energy = 0.5 * 20 kg * (0 m/s)^2 = 0 J

So, the kinetic energy of the ball just before impact is 0 Joules.

3. At maximum stretch at the bottom of the motion, the sum of elastic and gravitational energy of the ball is equal to the initial gravitational energy. This is because the potential energy due to gravity is converted into elastic potential energy when the ball is suspended in the air, and then converted back into gravitational potential energy when the ball reaches the maximum stretch at the bottom.

So, the sum of the elastic and gravitational energy of the ball is equal to the initial gravitational energy of 400 J.

4. From the answers above, we can conclude that:
- The gravitational energy of the ball at its apex is 400 J.
- The kinetic energy of the ball just before impacting the trampoline is 0 J.
- The sum of the elastic and gravitational energy of the ball at maximum stretch is equal to the initial gravitational energy of 400 J.
- Energy is conserved throughout the motion, as the initial gravitational energy is converted into elastic potential energy and then converted back into gravitational potential energy.

To find the gravitational energy of the ball at its apex, you can use the formula: gravitational energy = mass x gravitational acceleration x height. Given that the mass of the ball is 20 kg, the gravitational acceleration is 10 N/kg, and the height is 2 m, we can plug in these values to calculate the answer:

gravitational energy = 20 kg x 10 N/kg x 2 m = 400 J

So your answer of 400 J for question 1 is correct.

For question 2, to find the kinetic energy of the ball just before impacting the trampoline, you can use the formula: kinetic energy = 1/2 x mass x velocity^2. Since the question doesn't provide the velocity, we can assume it is zero, as stated in the question. Therefore:

kinetic energy = 1/2 x 20 kg x 0 m/s = 0 J

So your answer of 0 J for question 2 is correct.

For question 3, the sum of elastic and gravitational energy at the bottom of the motion can be determined by considering the change in gravitational energy from the original position. Since the ball is at its maximum stretch at the bottom, it has zero gravitational energy relative to the unstretched surface. Therefore, the sum of elastic and gravitational energy is equal to the change in gravitational energy from the original position, which is 400 J.

Regarding question 4, based on the answers above, we can conclude that the gravitational energy decreases as the ball reaches its apex, while the elastic energy increases as the ball is stretched at the bottom of the motion. Additionally, the kinetic energy of the ball just before impacting the trampoline is zero. These conclusions demonstrate the conversion of potential energy to kinetic energy and vice versa during the ball's motion.