Question

A 2 kg box is placed on a ramp that is inclined at an angle of 30 degrees with respect to the horizontal. The box is at rest and there is no friction between the box and the ramp. Determine the magnitude and direction of the normal force, the gravitational force, and the net force acting on the box. Draw a free-body diagram to support your answer.

Answer

To solve this problem, we need to draw a free-body diagram and analyze the forces acting on the box.

1. Gravitational Force (mg): The gravitational force acting on the box can be calculated using the equation Fg = mg, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the gravitational force is given by: Fg = (2 kg)(9.8 m/s^2) = 19.6 N. The gravitational force points vertically downwards.

2. Normal Force (N): The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. In this case, since there is no vertical acceleration (the box is at rest), the normal force must be equal in magnitude and opposite in direction to the gravitational force. Therefore, the normal force is also 19.6 N and points vertically upwards.

3. Net Force (Fnet): The net force is the vector sum of all the individual forces acting on an object. Since the box is at rest, the net force must be zero according to Newton's first law (net force = 0 if there is no acceleration). Therefore, the net force can be calculated as the vector sum of the gravitational force and the normal force: Fnet = Fg + N = 19.6 N + 19.6 N = 39.2 N. The net force points down the inclined plane.

In summary, the magnitude of the normal force, gravitational force, and net force acting on the box are all 19.6 N. The normal force and gravitational force cancel each other out, resulting in a net force of 39.2 N pointing down the inclined plane.