You are trying to push a crate across the rough floor of a warehouse. Just before the crate begins to move, you have applied a force of 140 N. The shipping label on the crate says it is 54 kg. Calculate the coefficient of static friction between the crate and the floor. (Use g=9.8ms-2)
To calculate the coefficient of static friction between the crate and the floor, we need to use the equation:
Fs ≤ μs * N
where:
Fs is the force of static friction,
μs is the coefficient of static friction, and
N is the normal force.
The normal force (N) is equal to the weight of the crate, which can be calculated using the formula:
N = m * g
where:
m is the mass of the crate (54 kg),
g is the acceleration due to gravity (9.8 m/s^2).
N = 54 kg * 9.8 m/s^2
N = 529.2 N
Now, we can rearrange the equation for static friction to solve for the coefficient (μs):
Fs ≤ μs * N
Since the crate is just about to move, the force of static friction is equal to the force applied (140 N).
140 N = μs * 529.2 N
Now we can solve for μs:
μs = 140 N / 529.2 N
μs ≈ 0.264
To calculate the coefficient of static friction between the crate and the floor, we need to first determine the maximum force of static friction.
The maximum force of static friction can be found using the formula:
F_max = μ_s * N
where F_max is the maximum force of static friction, μ_s is the coefficient of static friction, and N is the normal force.
The normal force, N, is equal to the weight of the crate, which can be calculated as:
N = m * g
where m is the mass of the crate and g is the acceleration due to gravity.
Let's plug in the given values:
m = 54 kg (mass of the crate)
g = 9.8 m/s^2 (acceleration due to gravity)
N = 54 kg * 9.8 m/s^2
≈ 529.2 N
Now, we can substitute the value of N into the equation for the maximum force of static friction:
F_max = μ_s * 529.2 N
Given in the problem statement, just before the crate begins to move, you have applied a force of 140 N. This force is equal to the maximum force of static friction, F_max.
Thus, we have:
140 N = μ_s * 529.2 N
Now, we can solve for the coefficient of static friction, μ_s:
μ_s = 140 N / 529.2 N
≈ 0.264
Therefore, the coefficient of static friction between the crate and the floor is approximately 0.264.