A boy pushes a cabinet with a 85 kg mass a distance of 3.1 km at a constant velocity over a rough surface. The coeffient of friction Uk between the cabinet and floor is 0.22 .Calculate the magnitude of all the forces acting on the cabinet.
To calculate the magnitude of all the forces acting on the cabinet, we need to consider the forces involved.
1. Weight (force of gravity): This force is exerted downwards and can be calculated using the equation F = m * g, where m is the mass of the cabinet and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Weight = 85 kg * 9.8 m/s^2.
2. Normal force: This force is exerted by the surface perpendicular to the horizontal surface. In this case, since the cabinet is not accelerating vertically, the normal force is equal in magnitude and opposite in direction to the force of gravity.
Normal force = Weight = 85 kg * 9.8 m/s^2.
3. Friction force: This force opposes the motion of the cabinet and can be calculated using the equation F_friction = Uk * N, where Uk is the coefficient of friction and N is the normal force.
Friction force = 0.22 * Normal force.
4. Applied force: Since the cabinet is moving at a constant velocity, the applied force must be equal in magnitude and opposite in direction to the friction force.
Applied force = Friction force = 0.22 * Normal force.
Therefore, the magnitude of all the forces acting on the cabinet can be calculated by substituting the values:
Weight = 85 kg * 9.8 m/s^2,
Normal force = Weight,
Friction force = 0.22 * Normal force, and
Applied force = Friction force = 0.22 * Normal force.