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 Wy = 55 N, W2
= 35 N, and W3 = 28 N. Determine
the magnitude of the normal force that the table exerts on box 1.
•8N
• 62 N
• 118 N
OON
2-118 N
To find the magnitude of the normal force that the table exerts on box 1, we need to consider the forces acting on each box.
For box 1:
- The weight of box 1 is acting downward with a force of W1 = 55 N.
- The normal force exerted by the table on box 1 is acting upward, perpendicular to the table's surface.
For box 2:
- The weight of box 2 is acting downward with a force of W2 = 35 N.
- The tension in the rope is acting upward with the same force as the weight of box 2, T2 = 35 N.
For box 3:
- The weight of box 3 is acting downward with a force of W3 = 28 N.
- The tension in the rope is acting upward with the same force as the weight of box 3, T3 = 28 N.
Because box 2 is at rest and box 1 is connected to box 2, the tension in the rope T2 must be equal to the sum of the weight of box 1 and the normal force exerted by the table on box 1.
T2 = W1 + Fn
Substitute the values:
35 N = 55 N + Fn
Fn = 35 N - 55 N
Fn = -20 N
The negative sign indicates that the normal force is acting in the opposite direction to that assumed. Therefore, the correct magnitude of the normal force that the table exerts on box 1 is 20 N.