A dock worker loading crates on a ship finds that a 29 kg crate, initially at rest on a horizontal surface, requires a 90 N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 60 N is required to keep it moving with a constant speed. The acceleration of gravity is 9.8 m/s^2

Find the coefficient of static friction be- tween the crate and floor.

Fc = m*g = 29kg * 9.8N/kg = 284.2 N. =

Force of crate.

Fap-Fs = m*a
90-u*Fc = m*0
90 - u*284.2 = 0
u*284.2 = 90
us = 0.317

To find the coefficient of static friction between the crate and the floor, we need to use the given information about the force required to set the crate in motion and the force required to keep it moving with a constant speed.

Let's break down the problem into steps:

Step 1: Find the force of static friction (fs)

The force required to set the crate in motion is equal to the force of static friction (fs):
fs = 90 N

Step 2: Find the weight of the crate (Fg)

The weight of the crate can be calculated using the formula:
Fg = m * g

where m is the mass of the crate (29 kg) and g is the acceleration due to gravity (9.8 m/s^2).

Fg = 29 kg * 9.8 m/s^2
Fg = 284.2 N

Step 3: Find the force of kinetic friction (fk)

The force required to keep the crate moving with a constant speed is equal to the force of kinetic friction (fk):
fk = 60 N

Step 4: Calculate the coefficient of static friction (μs)

The coefficient of static friction can be calculated using the formula:
μs = fs / Fg

μs = 90 N / 284.2 N
μs ≈ 0.316

Therefore, the coefficient of static friction between the crate and the floor is approximately 0.316.