A horizontal force of 150 N is used to push a 40.5-kg packing crate a distance of 5.05 m on a rough horizontal surface. If the crate moves at constant speed, find each of the following.

(a) the work done by the 150-N force


(b) the coefficient of kinetic friction between the crate and the surface

To find the work done by the 150-N force and the coefficient of kinetic friction, we need to use the following equations:

(a) Work = Force × Distance
(b) Work done against friction = Force of friction × Distance
(c) Force of friction = coefficient of kinetic friction × Normal force

First, let's find the work done by the 150-N force to move the crate a distance of 5.05 m.

(a) The work done by the 150-N force is equal to the force multiplied by the distance:
Work = Force × Distance = 150 N × 5.05 m = 757.5 J

Now, let's find the coefficient of kinetic friction between the crate and the surface.

(b) We need to find the force of friction first. The force of friction can be calculated using the equation:
Force of friction = coefficient of kinetic friction × Normal force

Since the force required to move the crate at constant speed is equal to the force of friction, we can use the given force of 150 N as the normal force.

Force of friction = 150 N

Next, let's find the work done against friction:
Work done against friction = Force of friction × Distance = 150 N × 5.05 m = 757.5 J

Since the crate is moving at constant speed, the work done against friction is equal to the work done by the 150-N force (as stated above).

Work done against friction = Work done by 150-N force = 757.5 J

Now we can solve for the coefficient of kinetic friction using the equation:
Work done against friction = Force of friction × Distance

Therefore:
757.5 J = Force of friction × 5.05 m

Rearranging the equation to solve for the coefficient of kinetic friction:
Force of friction = Work done against friction / Distance

Coefficient of kinetic friction = Force of friction / Normal force

Coefficient of kinetic friction = (757.5 J / 5.05 m) / 150 N = 0.25

Therefore, the coefficient of kinetic friction between the crate and the surface is 0.25.