Final answer:
39.16 Joules of work must be done on a 68 g plastic ball to reverse its direction of motion and have it move to the right at 17 m/s, calculated using the work-energy principle.
Step-by-step explanation:
The student's question pertains to the concept of work within the Physics field. Specifically, the problem involves reversing the velocity of a moving object, implying a change in kinetic energy. To calculate the amount of work needed to cause a 68 g plastic ball to move in the opposite direction at the same speed, we can use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy (Work = ΔKE). The initial kinetic energy (KEi) when the ball is moving to the left at 17 m/s is KEi = 0.5 * m * vi^2, and the final kinetic energy (KEf) when it moves to the right at the same speed is KEf = 0.5 * m * vf^2.
Since the magnitudes of velocity are the same but in opposite directions, the change in kinetic energy will be the sum of KEi and KEf. Thus, the work done will be twice the initial kinetic energy: Work = 2 * KEi = 2 * (0.5 * m * vi^2). Plugging in the values, we get Work = 2 * (0.5 * 0.068 kg * (17 m/s)^2) = 39.16 Joules. Therefore, 39.16 Joules of work must be done on the ball to reverse its direction at the same speed.