Question

Suppose the earth were a sphere of uniform mass. If there were a deep elevator shaft going 15,000 m into the earth, what would be the loss in weight at the bottom of this deep shaft for a student who weighs 800 N at the surface of the earth?

Answer 1

The weight of a person at the bottom of a deep shaft into the Earth can be calculated based on the change in distance from the center of mass.

Step-by-step explanation:

The weight of a person at the surface of the Earth is determined by the acceleration due to gravity, which is approximately 9.8 m/s². As you descend into a deep shaft into the Earth, the distance between you and the center of mass decreases. Consequently, the gravitational force acting on you decreases, leading to a reduction in weight. In this case, the weight of the student would decrease by a factor of:

(15,000 m / 6,400,000 m)² = 0.036

Therefore, the student would weigh approximately 0.036 * 800 N = 28.8 N at the bottom of the deep shaft.