once a 21 kg crate is in motion on a hoizontal floor, a horizontal force of 58 N keeps the crate moving with a constant velocity.

the acceleration of gravity is 9.81 m/s^2. what is mu k , the coefficient of kinetic friction, between the crate and the floor?

To find the coefficient of kinetic friction (μk) between the crate and the floor, you can use the formula:

μk = (Fk) / (N)

Where Fk is the force of kinetic friction and N is the normal force.

First, let's find the normal force (N):
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the crate.

N = m * g

Where m is the mass of the crate and g is the acceleration due to gravity.

Given:
Mass of the crate (m) = 21 kg
Acceleration due to gravity (g) = 9.81 m/s²

N = 21 kg * 9.81 m/s²
N = 205.01 N

Now, we can find the force of kinetic friction (Fk):
The force of kinetic friction can be calculated using the formula:

Fk = μk * N

We know the force of kinetic friction (Fk) to be equal to the applied force (58 N) that keeps the crate moving at a constant velocity.

Fk = 58 N

Now we can substitute the values to find μk:

58 N = μk * 205.01 N

μk = 58 N / 205.01 N

μk = 0.2829 (rounded to four decimal places)

Therefore, the coefficient of kinetic friction (μk) between the crate and the floor is approximately 0.2829.

The friction force equals the applied force (58N) in this no-acceleration case. They are in opposite directions, and cancel out.

58 = M*g*muk

Solve for muk