Final answer:
To change the plastic ball's direction from left to right at the same speed, 11.52 Joules of work must be done, which is twice the kinetic energy when it is moving to the left.
Step-by-step explanation:
To determine how much work must be done on the ball to change its direction while maintaining the same speed, we use the work-energy theorem. This theorem states that the work done on an object is equal to the change in its kinetic energy.
First, we calculate the initial kinetic energy (KEinitial) using the formula:
KEinitial = ½ × mass × (speed)2
For a plastic ball of 80 g (0.08 kg) moving at 12 m/s, the initial kinetic energy is:
KEinitial = ½ × 0.08 kg × (12 m/s)2 = 5.76 Joules
The final kinetic energy (KEfinal) when the ball is moving to the right at the same speed is the same, as kinetic energy depends only on mass and the square of the speed.
Hence, the total work done on the ball to stop it and then accelerate it to the same speed but in the opposite direction is equal to the change in kinetic energy, which in this case, is:
Work = KEfinal - KEinitial = 5.76 J (moving right) - (-5.76 J moving left)
This means the work required is twice the kinetic energy when it was moving to the left, which gives us:
Work = 2 × 5.76 Joules = 11.52 Joules.
Therefore, 11.52 Joules of work must be done on the ball to change its direction while keeping the speed constant at 12 m/s.