Chapter 20, Problem 34A

Atmospheric pressure is nicely demonstrated with the pair of hemispheres shown below. When placed together, the hemispheres make up a hollow sphere. After a vacuum pump evacuates much of the air inside, a considerable force is needed to separate the hemispheres. Suppose two people find they must pull with 150 N each to separate them. If instead, one end of the sphere is attached to a wall and only one person pulls the other end, how much force would the one person have to supply to separate the hemispheres?

To determine

The force required to separate a hollow sphere joined by two hollow hemispheres.

Answer to Problem 34A

  $150\text{ N}$ need to be applied by the person when another end is attached to the wall.

Explanation of Solution

Introduction:

According to Newton’s third law of motion, every force applied to an object produces equal and opposite reaction.

When the hollow sphere is pulled from both opposite ends then both persons are applying $150\text{ N}$ to pull it in their respective directions.

Similarly, when one end is fixed to the wall then other end must pull with equal amount of force to pull apart hemispheres. Thus, an equal amount of force that is $150\text{ N}$ must be applied to separate both hollow hemispheres.

Conclusion:

Thus, $150\text{ N}$ force is required to pull apart two hemispheres when an end is fixed to the wall.