A box is pushed across the floor against a constant frictional force. The box is pushed across the room to the east in 30 seconds and returned to its starting point (pushed to the west) in 60 seconds. Which of the following is true about the work done and the power expended in both directions?

My answer: a

a. Work going east > work going west; power going east = power going west

b. Work going east < work going west; power going east = power going west

c. Work going east = work going west; power going east = power going west

d. Work going east = work going west; power going east < power going west

e. Work going east = work going west; power going east > power going west

The work going east and west is the same, since the friction force and distance moved are the same. The power is higher in the direction requiring less time.

That logic should help you pick one of the choices.

The correct answer is b. Work going east < work going west; power going east = power going west.

This is because the work done by a force is equal to the force multiplied by the distance moved in the direction of the force. In this case, the work done when pushing the box to the east is greater than the work done when pushing it back to the west because the distance is the same, but the time it took to push the box east is shorter.

However, the power expended is calculated as the work done divided by the time taken. Since the work done is greater when pushing the box east, and the time taken is shorter, the power expended in that direction is greater. This means that the power going east is greater than the power going west.

To determine the relationship between the work done and the power expended in both directions, we need to consider the concept of work and power.

Work is defined as the transfer of energy that occurs when a force is applied to an object and it moves in the direction of the force. The formula for work is given by W = F * d * cosθ, where F is the force applied, d is the displacement, and θ is the angle between the force and the displacement.

Power, on the other hand, is the rate at which work is done or the amount of work done per unit of time. The formula for power is P = W / t, where W is the work done and t is the time taken.

In the given scenario, the box is pushed to the east and then pushed back to its starting point in the opposite direction. Since the box is displaced in both directions, work is being done in both cases.

Let's consider the work done and power expended in both directions:

1. Work going east:
The box is pushed to the east against a constant frictional force. The work done in this case is given by the formula W = F * d * cosθ. Since the force and displacement are in the same direction (east), the angle θ is 0 degrees and cosθ = 1. This means W = F * d.

2. Work going west:
The box is pushed to the west against the same constant frictional force. The work done in this case is also given by the formula W = F * d * cosθ. Since the force and displacement are in opposite directions (west), the angle θ is 180 degrees and cosθ = -1. This means W = -F * d. Note that the negative sign indicates that work is being done in the opposite direction.

Since the magnitudes of the force and displacement are the same in both directions (east and west), the work done is equal in magnitude but differs in sign.

Now let's consider the power expended in both directions:

Power is the rate at which work is done, so we can calculate the power using the formula P = W / t. Since the work done in both directions is equal in magnitude but differs in sign, the power expended will have the same magnitude but opposite sign as well.

In conclusion, the correct answer is:

d. Work going east = work going west; power going east < power going west