A dockworker loading crates on a ship finds that a 19-kg crate, initially at rest on a horizontal surface, requires a 70-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. Find the coefficients of static and kinetic friction between crate and floor.

Take a look at the definitions of the friction coefficients. That should tell you how to do this problem, which is:

Divide the required forces by the weight. Use 70 N for the static coefficient, and 60 N for the kinetic one.

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

Let's break down the problem into two parts: the crate at rest and the crate in motion.

1. Crate at rest:
When the crate is at rest, the applied horizontal force will be equal to the maximum static friction force, which can be calculated using the formula:
Fs = μs * N
where Fs is the static friction force, μs is the coefficient of static friction, and N is the normal force acting on the crate.

In this case, we only have the weight of the crate acting downward, which is given by:
N = mg
where m is the mass of the crate (19 kg) and g is the acceleration due to gravity (9.8 m/s²).

So, the equation for maximum static friction becomes:
70 N = μs * (19 kg * 9.8 m/s²)

2. Crate in motion:
Once the crate is in motion, the applied horizontal force will now be equal to the force of kinetic friction, which can be calculated using the formula:
Fk = μk * N
where Fk is the kinetic friction force, μk is the coefficient of kinetic friction, and N is the normal force acting on the crate (same as before).

In this case, the normal force and the weight of the crate remain the same as when it was at rest, so we have:
N = mg
Fk = 60 N = μk * (19 kg * 9.8 m/s²)

Now, we can solve the two equations simultaneously to find the coefficients of static and kinetic friction.

Solving equation (1) for μs:
μs = 70 N / (19 kg * 9.8 m/s²)

Solving equation (2) for μk:
μk = 60 N / (19 kg * 9.8 m/s²)

Calculating these values should give you the coefficients of static and kinetic friction between the crate and the floor.