Question

A 4 kg box is at rest on a table. The static friction coefficient , between the box and table is 0.30, and the kinetic friction coefficient fx is 0.10. Then, a 10 N horizontal force is applied to the box. What is the best estimate of the magnitude of the box's acceleration?

Round the answer (if non-zero) to two significant digits.

Answer 1

The box will not move and the acceleration will be 0 since the applied force is less than the maximum static friction force.

Step-by-step explanation:

The magnitude of the box's acceleration can be determined by comparing the applied force to the maximum static friction force that can be exerted. The static friction force can be calculated by multiplying the coefficient of static friction by the normal force, which is equal to the weight of the box (mass times gravity). If the applied force is less than or equal to the maximum static friction force, the box will not move and the acceleration will be 0. If the applied force is greater than the maximum static friction force, the box will start to move and the acceleration will be determined by the difference between the applied force and the maximum static friction force, divided by the mass of the box.

In this case, the maximum static friction force can be calculated as follows:

Fs(max) = μs × N

where μs is the coefficient of static friction and N is the normal force, equal to the weight of the box:

N = mg = 4 kg × 9.8 m/s2 = 39.2 N

So, Fs(max) = 0.3 × 39.2 N = 11.76 N

Since the applied force is 10 N, which is less than the maximum static friction force, the box will not move and the acceleration will be 0.