A 24.5-kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force has a magnitude of 77.0 N and is directed at an angle of 30.0° above the horizontal. Determine the coefficient of kinetic friction.
ok, first find the vertical and horizontal components.
for the vertical part, it reduces weight.
frictionforce= (weight-upwardforce)*mu
upward force= 77Sin30
weight=24.5g
Now for friction force, that with no acceleration, horizontal component=24.5*cos30=fricton force
put those in the equation above, solve for mu.
ok according to you the answer must be 1.5 but that is wrong :(
x: Fcosα-μN =0,
y: mg-N-Fsinα=0 =>N= mg-Fsinα,
μ= Fcosα/N = Fcosα/(mg-Fsinα)=
=77•cos30/(24.5•9.8-77•sin30)=
=0.33
To determine the coefficient of kinetic friction, we can use the formula:
μ = Fk / N
where:
μ is the coefficient of kinetic friction
Fk is the force of kinetic friction
N is the normal force
To find the normal force, we need to calculate the vertical component of the pulling force. We can use trigonometry to find this component:
F_vert = F * sin(θ)
where:
F_vert is the vertical component of the force
F is the magnitude of the pulling force
θ is the angle of the pulling force
Next, we calculate the force of kinetic friction using the equation:
Fk = μ * N
Since the sled is being pulled at a constant velocity, the frictional force must be equal in magnitude and opposite in direction to the pulling force:
Fk = F_pull
Finally, we rearrange the equation to solve for the coefficient of kinetic friction:
μ = F_pull / N
Now, let's calculate the coefficient of kinetic friction step by step:
1. Calculate the vertical component of the pulling force:
F_vert = 77.0 N * sin(30.0°) = 77.0 N * 0.5 = 38.5 N
2. Calculate the force of kinetic friction:
Fk = 38.5 N
3. Calculate the coefficient of kinetic friction using the equation:
μ = 38.5 N / N
To find N, we need to consider the forces acting on the sled. Since the sled is on a horizontal surface and not accelerating, the vertical forces must be balanced:
N - m * g = 0
Solve for N:
N = m * g
Given that the mass of the sled, m, is 24.5 kg and the acceleration due to gravity, g, is approximately 9.8 m/s^2, we can calculate N:
N = 24.5 kg * 9.8 m/s^2 = 240.1 N
4. Plug the value of N into the equation to find the coefficient of kinetic friction:
μ = 38.5 N / 240.1 N
Calculating this, we find:
μ ≈ 0.160
Therefore, the coefficient of kinetic friction is approximately 0.160.