To determine the horizontal force of pushing, we need to consider the forces acting on the object on the incline plane. The main forces involved are the gravitational force (mg), the normal force (N), and the frictional force (f). The force of pushing (F) opposes the frictional force.
Given: Mass (m) = 20 kg Angle of incline (θ) = 30° Coefficient of friction (μ) = 0.2
To calculate the horizontal force of pushing (F), we'll follow these steps:
- Resolve the forces: Break down the forces acting on the object into their components. The gravitational force (mg) can be split into two components:
- The component perpendicular to the incline is mg * cos(θ).
- The component parallel to the incline is mg * sin(θ).
Calculate the normal force (N): The normal force (N) acts perpendicular to the incline and counterbalances the component of the gravitational force perpendicular to the incline. Since there is no vertical acceleration, N = mg * cos(θ).
Calculate the frictional force (f): The frictional force (f) acts parallel to the incline and opposes the motion. It can be calculated using the formula: f = μN where μ is the coefficient of friction.
Calculate the force of pushing (F): The force of pushing (F) opposes the frictional force. Therefore, F = -f.
Now let's perform the calculations:
Gravitational force parallel to the incline: mg * sin(θ) = 20 kg * 9.8 m/s² * sin(30°) ≈ 98 N * 0.5 ≈ 49 N
Normal force: N = mg * cos(θ) = 20 kg * 9.8 m/s² * cos(30°) ≈ 98 N * 0.866 ≈ 85 N
Frictional force: f = μN = 0.2 * 85 N = 17 N
Force of pushing: F = -f = -17 N
Therefore, the horizontal force of pushing required is approximately -17 Newtons (N). The negative sign indicates that the force is opposing the direction of motion due to the frictional force.