Once a 15 kg crate is in motion on a horizontal
floor, a horizontal force of 56 N keeps the crate
moving with a constant velocity.
The acceleration of gravity is 9.81 m/s
2.
What is µk, the coefficient of kinetic friction, between the crate and the floor?
Wc = mg = 15kg * 9.81N/kg = 147.2N. =
Weight of crate.
Fc = 147.2N @ 0deg.
Fp = 147.4sin(0) = 0 = Force parallel to floor.
Fv = 147.4cos(0) = 147.4N. = Force
perpendicular to floor.
Fn = Fap - Fp - Ff = 0,
Fn = 56 - 0 - 147.4u = 0,
147.4u = 56,
u = 0.380.
To find the coefficient of kinetic friction (µk) between the crate and the floor, we can use the formula:
µk = Fk / N
where Fk is the force of kinetic friction and N is the normal force.
In this case, since the crate is moving with a constant velocity, the force of kinetic friction is equal to the applied force, which is 56 N.
Now, let's calculate the normal force:
The weight of the crate, which is the force due to gravity, can be found using the formula:
W = mg
where m is the mass of the crate (15 kg) and g is the acceleration due to gravity (9.81 m/s^2).
W = (15 kg) * (9.81 m/s^2)
W = 147.15 N
The normal force (N) is equal to the weight of the crate because the floor is perpendicular to the force of gravity:
N = W
N = 147.15 N
Now, we can substitute the values of Fk and N into the formula to find the coefficient of kinetic friction:
µk = Fk / N
µk = 56 N / 147.15 N
Calculating this division, we get:
µk ≈ 0.38
Therefore, the coefficient of kinetic friction (µk) between the crate and the floor is approximately 0.38.