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.
To solve this problem, we need to consider the forces acting on each box.
For box 1:
- The weight of box 1 is acting downward with magnitude W1 = 55 N.
- The normal force exerted by the table on box 1 is acting upward and is what we need to find.
For box 2:
- The weight of box 2 is acting downward with magnitude W2 = 35 N.
- The tension T in the rope is acting upward.
For box 3:
- The weight of box 3 is acting downward with magnitude W3 = 28 N.
- The tension T in the rope is acting downward.
Since the rope is massless and frictionless, the tension T is the same for boxes 2 and 3.
Now, we can set up equations of motion for each box:
For box 1:
Sum of forces in the vertical direction = 0
N - W1 = 0
N = W1
N = 55 N
So, the normal force that the table exerts on box 1 is 55 N.