A dockworker loading crates on a ship finds that a 22-kg crate, initially at rest on a horizontal surface, requires a 76-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 59 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.

Wc = m*g = 22kg * 9.8N/kg = 215.6 = Wt.

of crate.

Fc = 215.6N.[0o] = Force of crate.
Fp = 215.6*sin(0) = 0 = Force parallel to floor.
Fv = 215.6*cos(0) = 215.6 N. = Force
perpendicular to floor.

Fs = u*Fv = Force of static friction.

Fap-Fp-u*Fv = m*a
76-0-u*215.6 = m*0 = 0.
u*215.6 = 76
u = 0.353 = Coefficient of static friction.

59-0-u*215.6 = m*a =m*0 = 0
u*215.6 = 59
u = 0.274 = Coefficient of kinetic friction.

To find the coefficients of static and kinetic friction, we can use the following equations:

1. The equation for static friction is given by:
Fs = μs * N

2. The equation for kinetic friction is given by:
Fk = μk * N

Where:
- Fs is the force of static friction
- Fk is the force of kinetic friction
- N is the normal force (equal to the weight of the crate in this case)
- μs is the coefficient of static friction
- μk is the coefficient of kinetic friction

Given:
- The weight of the crate is equal to its mass multiplied by the acceleration due to gravity (g = 9.8 m/s^2): W = m * g, with m = 22 kg
- The force required to set the crate in motion is 76 N: Fs = 76 N
- The force required to keep the crate moving at a constant speed is 59 N: Fk = 59 N

We can proceed with the calculations step-by-step as follows:

Step 1: Calculate the weight of the crate.
W = m * g
W = 22 kg * 9.8 m/s^2
W = 215.6 N

Step 2: Calculate the coefficient of static friction.
Using Fs = μs * N, we can rearrange the equation to solve for μs:
μs = Fs / N
μs = 76 N / 215.6 N
μs ≈ 0.352

Step 3: Calculate the coefficient of kinetic friction.
Using Fk = μk * N, we can rearrange the equation to solve for μk:
μk = Fk / N
μk = 59 N / 215.6 N
μk ≈ 0.273

Therefore, the coefficient of static friction is approximately 0.352, and the coefficient of kinetic friction is approximately 0.273.

To find the coefficients of static and kinetic friction between the crate and the floor, we can use the equations that relate the frictional force to the normal force.

1. Static friction (fs) is the force required to set the crate in motion. It can be calculated using the formula fs = μs * N, where μs is the coefficient of static friction and N is the normal force.

2. Kinetic friction (fk) is the force required to keep the crate moving at a constant speed. It can be calculated using the formula fk = μk * N, where μk is the coefficient of kinetic friction and N is the normal force.

Given:
Mass of the crate (m) = 22 kg
Force required to set the crate in motion (fs) = 76 N
Force required to keep the crate moving (fk) = 59 N

Now, let's calculate the normal force (N) acting on the crate:

Since the crate is at rest on a horizontal surface, the vertical forces must be balanced. The normal force (N) is equal to the weight of the crate. The weight can be calculated using the formula weight = mass * gravity, where gravity (g) is approximately 9.8 m/s^2. Therefore, the weight would be:

Weight (W) = m * g
W = 22 kg * 9.8 m/s^2
W = 215.6 N

Since the crate is at rest, the force of static friction (fs) is equal to the applied force to set it in motion (fs = 76 N). We can now find the coefficient of static friction (μs):

fs = μs * N
76 N = μs * 215.6 N

Solving for μs, we get:
μs = 76 N / 215.6 N
μs ≈ 0.353

Now, since the crate is already in motion, the force of kinetic friction (fk) is equal to the applied force to keep it moving (fk = 59 N). We can now find the coefficient of kinetic friction (μk):

fk = μk * N
59 N = μk * 215.6 N

Solving for μk, we get:
μk = 59 N / 215.6 N
μk ≈ 0.274

Therefore, the coefficients of static friction and kinetic friction between the crate and the floor are approximately 0.353 and 0.274, respectively.