A 10kg suitcase is placed on a horizontal conveyor belt the top of which moves to the right. The coefficient of static friction between the belt and box is µs = 0.5 and that of kinetic friction is µk = 0.3.
a) Sketch a free body diagram for the suitcase, showing all forces acting and the net force if the conveyor belt moves with increasing speed and the suitcase does not slip.
b) Imagine now that the conveyor belt is moving with constant speed. The box is dropped from a height and lands to slide on the belt without bouncing. state in which direction the force of kinetic friction acts and why.
a) To sketch a free body diagram for the suitcase when the conveyor belt moves with increasing speed and the suitcase does not slip, we need to consider the forces acting on the suitcase:
1. Weight (W): This is the force due to gravity and acts vertically downward. Its magnitude can be calculated using the formula W = m * g, where m is the mass of the suitcase (10 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). The weight can be shown as a downward arrow.
2. Normal Force (N): This is the force exerted by the conveyor belt on the suitcase perpendicular to the belt's surface. Since the suitcase is not accelerating vertically, the normal force is equal in magnitude and opposite in direction to the weight. It can be shown as an upward arrow.
3. Static Friction (Fs): This force opposes the tendency of the suitcase to slip on the conveyor belt. The maximum static friction force can be calculated using the formula Fs = µs * N, where µs is the coefficient of static friction (0.5 in this case) and N is the normal force. The static friction force acts in the direction opposite to the movement of the conveyor belt, so it can be shown as an arrow to the left.
4. Net Force (Fnet): Since the suitcase does not slip, the net force on the suitcase should be zero. Therefore, the magnitude of the static friction force should be equal to the horizontal component of the weight. The net force can be shown as an arrow pointing to the right, balancing the static friction force.
b) When the conveyor belt is moving with constant speed and the suitcase slides without bouncing, the force of kinetic friction acts in the opposite direction to the movement of the conveyor belt. This is because the kinetic friction force opposes the relative motion between the suitcase and the conveyor belt.
In this case, the suitcase is already sliding, so the kinetic friction force will come into play. The magnitude of the kinetic friction force can be calculated using the formula Fk = µk * N, where µk is the coefficient of kinetic friction (0.3 in this case) and N is the normal force.
Therefore, the force of kinetic friction acts in the direction opposite to the movement of the conveyor belt, which is to the left.