A 120kg box is sliding down a hill at a constant speed. The angle of the incline is 32 degrees. Determine the normal force of the hill on the box. Determine the amount of friction on the box.
To determine the normal force and friction on the box, we need to analyze the forces acting on the box.
First, let's identify the forces involved:
1. Weight (W): The force due to gravity, acting vertically downwards with a magnitude of the box's mass multiplied by the acceleration due to gravity (9.8 m/s^2).
2. Normal force (N): The force exerted by the surface perpendicular to the box, supporting its weight.
3. Friction force (F): The force opposing the motion of the box, acting parallel to the surface and in the opposite direction to its motion.
Since the box is sliding down the hill at a constant speed, we can conclude that the net force is zero. This means the force of friction is equal in magnitude and opposite in direction to the component of the weight parallel to the incline.
To calculate the normal force (N), we can use trigonometry. The weight (W) can be represented as the product of the mass (m) and the acceleration due to gravity (g).
W = m * g
W = 120 kg * 9.8 m/s^2
W = 1176 N
Next, we need to find the component of the weight parallel to the incline. In this case, it is equal to W * sin(θ), where θ is the angle of incline (32 degrees) in radians.
Component of weight parallel to incline = W * sin(θ)
Now, we can calculate the normal force (N) using the equation:
N = W * cos(θ)
N = 1176 N * cos(32 degrees)
N ≈ 994.22 N
Therefore, the normal force exerted by the hill on the box is approximately 994.22 N.
To determine the amount of friction force (F), we can use the following equation:
F = W * sin(θ)
F = 1176 N * sin(32 degrees)
F ≈ 610.75 N
Thus, the amount of friction acting on the box is approximately 610.75 N.