Agirl exerts a horizontal force of 109 n on a crate with a mass of 31.2 kg. hint (a) if the crate doesn't move, what's the magnitude of the static friction force (in n)? 109 correct: your answer is correct. the static friction force is fs ≤ μsn. for an object with no acceleration at rest on a surface, fs equals the particular value required to keep the object at rest on the surface. n (b) what is the minimum possible value of the coefficient of static friction between the crate and the floor? (assume the crate remains stationary.)

(a) Magnitude of static friction force is 109 N

(b) Minimum possible value of static friction is 0.356

Solution:

As per the question;

Horizontal force exerted  by the girl, F = 109 N

Mass of the crate, m = 31.2 kg

Now,

(a) To calculate the magnitude of static friction force:

Since, the crate is at rest, the forces on the crate are balanced and thus the horizontal force is equal to the frictional force, f:

F = f = 109 N

(b) The maximum possible force of friction between the floor and the crate is given by:

where

N = Normal reaction = mg

Thus

For the crate to remain at rest, The force exerted on the crate must be less than or equal to the maximum force of friction.