Final answer:
The rate at which the frictional force on a 50 kg crate moving at 8 m/s takes energy away from the crate, causing it to come to rest in 10 seconds, is -160 W.
Step-by-step explanation:
If a crate of mass 50 kg moving at a speed of 8 m/s comes to rest in 10 seconds, we want to find the rate at which the frictional force on the crate takes energy away from the crate, also known as the power of the friction force. To do this, we can use the work-energy principle, where the work done by the friction force is equal to the change in kinetic energy of the crate.
The initial kinetic energy (KEi) of the crate is given by:
KEi = (1/2) × mass × velocity2 = (1/2) × 50 kg × (8 m/s)2 = 1600 Joules
Since the crate comes to rest, the final kinetic energy (KEf) is 0 Joules. The work done by friction (Wf) is thus 1600 Joules, and it is negative since friction is opposite to the direction of motion. The power (P) is the work done per unit time:
P = Wf / Δt = -1600 J / 10 s = -160 Joules per second (J/s), which is equivalent to -160 Watts (W).
The negative sign indicates that the energy is being taken away from the crate, hence the correct answer is (d) -160 W.