1.A 24 kg crate initially at rest on a horizon floor requires a 75 N horizontal force to set it in motion, once the crate is in motion, a horizontal force 53 N keeps the crate moving with a constant velocity. Find the coefficient of kinetic friction, between the floor and crate.
To find the coefficient of kinetic friction between the floor and the crate, we can use the equation:
Fnet = μk * N
where Fnet is the net force acting on the crate, μk is the coefficient of kinetic friction, and N is the normal force.
First, let's calculate 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 and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the crate is 24 kg, we can calculate the weight and the normal force:
N = 24 kg * 9.8 m/s^2
N = 235.2 N
Next, we need to find the net force acting on the crate in both cases (when it initially starts moving and when it is moving with a constant velocity).
Case 1: When the crate initially starts moving
The net force is equal to the applied force that sets the crate in motion:
Fnet = 75 N
Case 2: When the crate is moving with a constant velocity
The net force in this case is equal to the force required to overcome the kinetic friction:
Fnet = 53 N
Now, we can use the formula for the coefficient of kinetic friction to find its value:
Fnet = μk * N
Case 1: μk * N = Fnet
μk = Fnet / N
μk = 75 N / 235.2 N
μk ≈ 0.319
Case 2: μk * N = Fnet
μk = Fnet / N
μk = 53 N / 235.2 N
μk ≈ 0.225
Therefore, the coefficient of kinetic friction between the floor and the crate is approximately 0.319 when the crate initially starts moving and approximately 0.225 when the crate is moving with a constant velocity.
To find the coefficient of kinetic friction between the floor and the crate, we can use the following equation:
Coefficient of kinetic friction (μk) = (Force of friction) / (Normal force)
First, let's find the force of friction. When the crate is in motion with a constant velocity, the force of friction is equal to the applied force keeping it moving:
Force of friction = Applied force = 53 N
Next, let's find the normal force. The normal force is the force exerted by the floor on the crate, which is equal to the weight of the crate since it is on a horizontal floor:
Weight of the crate = mass x acceleration due to gravity
= 24 kg x 9.8 m/s^2
= 235.2 N
Therefore, the normal force exerted by the floor on the crate is 235.2 N.
Now, we can calculate the coefficient of kinetic friction:
Coefficient of kinetic friction (μk) = (Force of friction) / (Normal force)
= 53 N / 235.2 N
≈ 0.225