Chapter 12, Problem 41A

Explain why the faster Earth spins, the less a person weighs, whereas the faster a space station spins, the more a person weighs.

To determine

To Explain: The reason for less weight of a person as Earth spins faster and more weight of a person as space station spins faster.

Explanation of Solution

Introduction:

The Earth rotates about its own axis in 24 hours. Gravitational force will act on the person , standing on the surface of the Earth, in the downward direction. Person will feel its weight because of this gravitational force. When body move around the circle, centripetal force acts on it. The centripetal force is proportional to the square of its velocity.

Person standing on the surface of the Earth acquire the rotational as well as translational velocity, due to rotational and translational motion of the Earth. But the weight (mg) of the body still remains constant. As Earth rotates with more speed, centripetal force on the person increases accordingly. But in order to balance the weight force, component of the upward balancing force decreases accordingly. So, due to decrease in the balancing normal force, person standing on the Earth weighs less.

Person feels weightlessness when standing in the space station. No gravitational force exerted on the person in space station. When space station starts rotating, man standing in the space station starts rotating. Person acquires the velocity which results into the centripetal force. Scale is used to measure the person’s weight. The force acting on the person which balance the centripetal force is the force by the scale. As space station starts rotating fast the centripetal force increasing. Due to this, force exerted on the scale increases and it shows large weight of the person.

Conclusion:

Therefore, when person standing on the rotating earth shows the less weigh due to the presence of the gravitational field. So, when space station starts rotating with high speed, centripetal force is increasing and balancing force is exerted on the scale.