A dock worker loading crates on a ship finds

that a 25 kg crate, initially at rest on a hori-
zontal surface, requires a 90 N horizontal force
to set it in motion. However, after the crate
is in motion, a horizontal force of 51 N is
required to keep it moving with a constant
speed.
The acceleration of gravity is 9.8 m/s2 .
Find the coefficient of static friction be-
tween crate and floor.

90 N = M * g * mu_s

Solve for the static friction coefficient, mu_s

M = 25 kg
g = 9.8 m/s^2

The 51 N force can be used to compute the kinetic friction coefficient, but they didn't ask for that.

To find the coefficient of static friction between the crate and the floor, we will need to analyze the forces acting on the crate.

1. Determine the weight of the crate: The weight of an object is given by the formula W = mg, where m represents the mass of the crate and g is the acceleration due to gravity. In this case, the mass is given as 25 kg, and the acceleration due to gravity is 9.8 m/s^2. So the weight of the crate is W = 25 kg × 9.8 m/s^2 = 245 N.

2. Determine the force required to set the crate in motion: The force required to overcome the static friction and set the crate in motion is given as 90 N.

3. Determine the force required to keep the crate moving: Once the crate is in motion, it experiences kinetic friction, which requires a lesser force to maintain motion. Here, the force required to keep the crate moving is given as 51 N.

Now, let's calculate the coefficient of static friction:

The force required to set the crate in motion is equal to the maximum static friction force between the crate and the floor, which can be represented as F_s = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force.

Since the crate is on a horizontal surface, the normal force is equal to the weight of the crate, which we calculated as 245 N.

Therefore, 90 N = μ_s * 245 N.

We can solve for the coefficient of static friction (μ_s):

μ_s = 90 N / 245 N = 0.367

So, the coefficient of static friction between the crate and the floor is 0.367.