Question

A box with a mass of 5 kg

is on a horizontal table. The coefficient of static

friction between the box and the table is 0.72, and the coefficient of kinetic

friction is 0.59. A child pulls on the box with a force of 55 N

in the positive

horizontal direction

.

a.

Does the box move?

If so, what is the acceleration of the box?

b.

What is the maximum force with which the child can pull without moving

the box?

Answer 1

Here,

m = 5 Kg

us = 0.72

uk = 0.59

F = 55 N

a) maximum static friction = us * m * g

maximum static friction = 0.72 * 5 * 9.8

maximum static friction = 35.31 N

as the applied force is more than the maximum static fricion

hence , the box will move

acceleration = (55 - 28.91)/5 = 5.22 m/s^2

the acceleration os box is 5.22 m/s^2

b)

the maximum force is equal to limiting friction

maximum force = us * m * g

maximum force = 0.72 * 5 * 9.8

maximum force = 35.3 N

the maximum force that can be applied is 35.3 N