box full of books rests on a wooden floor. The normal force the floor exerts on the box is 235 N.

a) You push horizontally on the box with a force of 121 N, but it refuses to budge. What can you say about the coefficient of static friction between the box and the floor?

(b) If you must push horizontally on the box with a force of at least 135 N to start it sliding, what is the coefficient of static friction?

(c) Once the box is sliding, you only have to push with a force of 118 N to keep it sliding. What is the coefficient of kinetic friction?

453

To answer these questions, we need to understand the concepts of static friction and kinetic friction.

Static friction is the force that resists the motion of an object when it is at rest, while kinetic friction is the force that opposes the motion of an object when it is already in motion. The coefficient of friction, denoted as μ, is a dimensionless constant that represents the frictional properties between two surfaces.

a) If you push horizontally on the box with a force of 121 N, but it refuses to budge, it means that the applied force is equal to or less than the maximum static friction force. Therefore, we can say that the maximum static friction force is at least 121 N. In this case, the coefficient of static friction between the box and the floor cannot be determined exactly, but we do know it is greater than or equal to the ratio of the maximum static friction force (121 N) to the normal force (235 N).

μ (coefficient of static friction) ≥ Maximum static friction force / Normal force
μ ≥ 121 N / 235 N

b) If you must push horizontally on the box with a force of at least 135 N to start it sliding, that means the applied force exceeds the maximum static friction force and overcomes its resistance. Therefore, we can say that the applied force (135 N) is equal to the maximum static friction force.

μ (coefficient of static friction) = Maximum static friction force / Normal force
μ = 135 N / 235 N

c) Once the box is sliding, the force required to keep it sliding is the force of kinetic friction. In this case, the force of kinetic friction is 118 N. Therefore, we can find the coefficient of kinetic friction by dividing the force of kinetic friction by the normal force.

μ (coefficient of kinetic friction) = Force of kinetic friction / Normal force
μ = 118 N / 235 N

By calculating these ratios, you can determine the coefficients of static and kinetic friction between the box and the floor.

This is not a homework dump site. Show your work if you need assistance.