Need help, I need to answer the following for a lab where we tossed a basketball

Question

Need help, I need to answer the following for a lab where we tossed a basketball in the air.

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

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

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

4. 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?

Explanation / Answer

1.

KE = 1/2*mv^2

But v = u - gt where u is initial velocity.

Thus, KE = 1/2*m*(u-gt)^2

From the above equation we see that KE is a function of (u-gt)^2. Therefore, KE will decrease parabolically with time t.

2.

At height h from the ground, PE = mgh

Suppose inital height = H.

So, H - h = 1/2*gt^2

h = H - 1/2*gt^2

Thus, PE = mg*(H - 1/2*gt^2)

We deduce that PE is decreasing parabolically with time t. Its shape would therefore be parabolic.

3.

For the free-fall, KE = 1/2*mv^2

and v = gt

Thus, KE = 1/2*m*g^2 t^2

Total energy = KE + PE

= 1/2*mg^2 *t^2 + mg*(H - 1/2*gt^2)

= mgH

= constant.

Hence, total energy will remain constant with time.

4.

Total remains constant.

It should remain constant because of Law of Conservation of Energy.

If it is not, then missing energy might have gone into overcoming wind resistance etc.

PLEASE RATE FULL STARS. THANKS.

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