A dockworker loading crates on a ship finds that a 34.0-kg crate, initially at rest on a horizontal surface, requires a 72.0-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 51.0 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.

For coefficient of static = 72 / (34 x 9.81) = 0.22

For coefficient of kinetic = 51 / (34 x 9.81) = 0.15

Turned out my answers were wrong. Can someone explain what I did wrong?

Perhaps need three significant figures

for example
72.0 not 72 / (34.0*9.81) = 0.21587.. = 0.216

To find the coefficients of static and kinetic friction, you need to use the correct formulas.

The formula for the force of static friction (Fs) is given by:

Fs = μs * N

Where:
Fs is the force of static friction
μs is the coefficient of static friction
N is the normal force (equal to the weight of the crate, which is mg)

Similarly, the formula for the force of kinetic friction (Fk) is given by:

Fk = μk * N

Where:
Fk is the force of kinetic friction
μk is the coefficient of kinetic friction
N is the normal force

In this case, the normal force is the weight of the crate, which is given by:

N = mg

Thus, the correct calculations are as follows:

For static friction, the force required to set the crate in motion is 72.0 N. Therefore:

72.0 N = μs * (34.0 kg * 9.81 m/s^2)
μs = 72.0 N / (34.0 kg * 9.81 m/s^2)
μs ≈ 0.22 (rounded to two decimal places)

For kinetic friction, the force required to keep the crate moving at a constant speed is 51.0 N. Therefore:

51.0 N = μk * (34.0 kg * 9.81 m/s^2)
μk = 51.0 N / (34.0 kg * 9.81 m/s^2)
μk ≈ 0.16 (rounded to two decimal places)

So, the correct coefficients of static and kinetic friction are approximately 0.22 and 0.16, respectively.

To find the coefficients of static and kinetic friction, you need to re-evaluate your calculations. Let's go through the steps again:

Given:
Mass of the crate (m) = 34.0 kg
Force required to set the crate in motion (F_s) = 72.0 N
Force required to keep the crate moving at a constant speed (F_k) = 51.0 N
Acceleration due to gravity (g) = 9.81 m/s^2

To find the coefficient of static friction (μ_s), we can use the formula:

μ_s = F_s / (m * g)

Plugging in the values:

μ_s = 72.0 N / (34.0 kg * 9.81 m/s^2) ≈ 0.222

So the coefficient of static friction is approximately 0.222.

To find the coefficient of kinetic friction (μ_k), we can use the formula:

μ_k = F_k / (m * g)

Using the given values:

μ_k = 51.0 N / (34.0 kg * 9.81 m/s^2) ≈ 0.156

So the coefficient of kinetic friction is approximately 0.156.

Please note that the coefficients of friction represent dimensionless quantities and should be reported without units.