The drawing shows box 1 resting on a table, with box 2 resting on top of box 1. A massless rope passes over a massless, frictionless pulley. One end of the rope is connected to box 2, and the other end is connected to box 3. The weights of the three boxes are W1 = 56.2 N, W2 = 34.9 N, and W3 = 27.7 N. Determine the magnitude of the normal force that the table exerts on box 1.
To determine the magnitude of the normal force that the table exerts on box 1, we need to consider the forces acting on box 1 in the vertical direction.
First, we'll calculate the tension in the rope. Since box 2 is resting on top of box 1, the tension in the rope is equal to the weight of box 2 (W2). Therefore, Tension = W2 = 34.9 N.
Next, we'll calculate the net force acting on box 1 in the vertical direction. The net force is the difference between the weight of box 1 (W1) and the tension in the rope. Net Force = W1 - Tension = 56.2 N - 34.9 N = 21.3 N.
Since the box 1 is at rest on the table, the vertical net force on it must be zero. Therefore, the normal force exerted by the table on box 1 must be equal in magnitude and opposite in direction to the net force acting on it. Thus, the magnitude of the normal force exerted by the table on box 1 is 21.3 N.
To summarize:
Magnitude of the normal force on box 1 = Magnitude of the net force on box 1 in the vertical direction
Normal Force = Net Force = W1 - Tension = 56.2 N - 34.9 N = 21.3 N.