A box with a mass of 4.0kg is sitting on a plane angled at 60degrees above the horizontal. The coefficient of friction between the box and the plane is 0.3. What is the horizontally applied force necessary to stop the box from sliding down the ramp?
mg = (4kg)(9.81m/s^2) = 39.24N. @ 60deg
m = mass in kg.
g = acceleration due to gravity.
Fp = mgsin60 = 39.24sin60 = 34N = Force parallell to plane.
Fv = mgcos60 = 39.24cos60 = 19.62N =
force Perpendicular to plane.
F = Fp + u*Fv = 34 + 0.3*19.62
F = 34 + 5.89 = 39.89N Parallel to
plane.
Fh = Fcos60 = 39.89cos60 = 19.95N =
The required hor. force.
CORRECTION!
F = Fp - uFv = 34 - 0.3*19.62,
F = 34 - 5.89 = 28.11N parallel to plane.
Fh = Fcos60 = 28.11cos60 = 14.06N =
The required hor. force.
To determine the horizontally applied force necessary to stop the box from sliding down the ramp, we need to analyze the forces acting on the box.
1. Start by drawing a diagram of the situation. This will help us visualize the forces involved. Draw a box on an inclined plane angled at 60 degrees above the horizontal.
2. Identify the forces acting on the box:
- Weight (W): It is the force due to gravity acting on the box with a magnitude of W = m * g, where m is the mass of the box and g is the acceleration due to gravity.
- Normal force (N): It is the force exerted by the plane perpendicular to it. In this case, it would be equal to the vertical component of the box's weight, N = m * g * cos(θ), where θ is the angle of inclination.
- Frictional force (Ff): It opposes the motion of the box down the plane and is calculated using the equation Ff = μ * N, where μ is the coefficient of friction.
3. Determine the normal force (N):
N = m * g * cos(θ)
N = 4.0 kg * 9.8 m/s² * cos(60°)
N ≈ 19.6 N * 0.5
N ≈ 9.8 N
4. Calculate the frictional force (Ff):
Ff = μ * N
Ff = 0.3 * 9.8 N
Ff ≈ 2.94 N
5. The horizontally applied force necessary to stop the box from sliding down the ramp is equal to the frictional force (Ff):
Force applied = Ff
Force applied ≈ 2.94 N
Therefore, the horizontally applied force necessary to stop the box from sliding down the ramp is approximately 2.94 N.