Rita throws a ball straight up into the air and catches it at the same position from which she threw it. The ball has 18 J of mechanical energy when it leaves her hand.

If no energy is lost due to friction, which statements about the energy of the ball are true? Check all that apply.

The potential energy at the top of the ball’s motion is 18 J.
The kinetic energy is less when the ball is thrown than when it is caught.
The kinetic energy increases as the potential energy decreases.
The kinetic energy decreases as the potential energy increases.
The total mechanical energy of the ball stays constant.
The mechanical energy decreases as the ball moves up and increases as the ball comes down.

The statements (a), (c) and (d) are the correct statements that justifies the explanation for the condition related to mechanical energy .

Given data:

The mechanical energy of ball is, ME = 18 J.

The mechanical energy of any object is equal to the sum of kinetic energy and potential energy. The expression is,

ME = KE + PE

KE is the kinetic energy

PE is the potential energy.

(a)

At top, the ball will be at rest, so KE = 0. So, the potential energy is,

ME = 0 + PE

18 J = PE

The statement is correct.

(b)

When the ball is thrown, the speed of ball was maximum and as it goes up, the speed decreases and when it is caught it again follow the same trend. So, the kinetic energy cannot be compared at any point accurately.

The statement is incorrect.

(c)

Clearly when the motion of ball comes to rest, it will acquire zero kinetic energy and highest potential energy and vice versa.

So, the statement is correct.

(d)

The mechanical energy of ball always remains constant either it is equal to kinetic energy or the potential energy at any point.

So, the statement is correct.

(e)

Since, mechanical energy remains constant so there will be no variation in the mechanical energy. So, the statement is incorrect .

Thus, we can conclude that the statements (a), (c) and (d) are the correct statements that justifies the explanation for the condition related to mechanical energy .

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