Question

A 52 g plastic ball is moving to the left at 24 m/s . how much work must be done on the ball to cause it to move to the right at 24 m/s ?

Answer 1

To cause the plastic ball to move to the right at 24 m/s, 499.04 J of work must be done on it.

Step-by-step explanation:

The work done on an object is equal to the change in its kinetic energy. In this case, the plastic ball is initially moving to the left at 24 m/s. To cause the ball to move to the right at 24 m/s, the work done on it must change its direction and increase its speed by 48 m/s (difference between -24 m/s and 24 m/s). The work done can be calculated using the formula for work: Work = Change in kinetic energy = (1/2) * mass * (final velocity^2 - initial velocity^2).

Given that the mass of the ball is 52 g (0.052 kg) and the change in velocity is 48 m/s, we can plug in these values into the formula:

Work = (1/2) * 0.052 kg * (48^2 - (-24)^2) = 499.04 J

Therefore, 499.04 J of work must be done on the ball to cause it to move to the right at 24 m/s.

Answer 2

For the work-energy theorem, the work done must be equal to the variation of kinetic energy of the ball:

`W=\Delta K = (1)/(2) m (\Delta v)^2`
where
`m=52 g=0.052 kg` is the mass of the ball, and where
`\Delta v` is the variation of velocity of the ball.
The initial velocity of the ball is +24 m/s, while the final velocity is -24 m/s (the negative sign is due to the fact the ball goes now in the opposite direction), so the variation of velocity is

`\Delta v=24 m/s-(-24 m/s)=48 m/s`
Therefore, substituting all the numbers in the formula we find the work done:

`W= (1)/(2)(0.052 kg)(48 m/s)^2=59.9 J`