Question

You are moving into a new apartment, and you are trying to slide your 100 kg sofa into place. Your lazy 40 kg mass dog won’t move their butt off the sofa while you try to slide it. The coefficient of static friction between the four feet of the sofa is 0.4. How much horizontal force do you have to apply to get the sofa started moving?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the sofa = M = 100 kg

Mass of the dog = m = 40 kg

Normal force on the sofa from the floor = N

The normal force on the sofa supports the weight of the sofa and the dog.

N = (m + M)g

Coefficient of friction between the feet of the sofa = = 0.4

Friction force on the sofa = f

f = 549 N

Horizontal force you need to apply to move the sofa = F

To get the sofa moving you will have to overcome the force of friction on the sofa therefore,

F = f

F = 549 N

Horizontal force you need to apply to move the sofa = 549 N