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 at a constant speed. Find the coefficients of static and kinetic friction between the crate and floor.

Question

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 at a constant speed. Find the coefficients of static and kinetic friction between the crate and floor.

Answer 1

{F_s} = {\mu _s}N

N=mg.
{F_k} = {\mu _k}N
{F_s}=72 N
{F_k}=51 N

Answer 2

Your turn to try.

Answer 3

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

1. Calculate the force of gravity:
- The force of gravity can be calculated using the formula F = m * g, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2).
- In this case, the crate's mass is given as 34.0 kg, so the force of gravity acting on it is F_gravity = 34.0 kg * 9.8 m/s^2.

2. Determine the static friction:
- The static friction is the force needed to overcome the initial resistance and set the crate in motion. This force is equal to the minimum horizontal force required to move the crate.
- In this case, the initial force required to set the crate in motion is given as 72.0 N.
- Therefore, the static friction force acting on the crate is F_static = 72.0 N.

3. Calculate the kinetic friction:
- Once the crate is in motion, it experiences a different type of friction called kinetic friction. This force opposes the motion of the crate and acts to keep it moving at a constant speed.
- In this case, the force required to keep the crate moving at a constant speed is given as 51.0 N.
- Therefore, the kinetic friction force acting on the crate is F_kinetic = 51.0 N.

Now we can determine the coefficients of static and kinetic friction using the following formulas:

1. Coefficient of static friction (μ_s):
- The coefficient of static friction is given by the formula μ_s = F_static / F_gravity.

2. Coefficient of kinetic friction (μ_k):
- The coefficient of kinetic friction is given by the formula μ_k = F_kinetic / F_gravity.

Plugging in the given values, we can calculate both coefficients:

μ_s = F_static / F_gravity = 72.0 N / (34.0 kg * 9.8 m/s^2)

μ_k = F_kinetic / F_gravity = 51.0 N / (34.0 kg * 9.8 m/s^2)

Now we can calculate the coefficients of static and kinetic friction.