Conceptual Physics

What is the strategy?

1. Use the shell theorem. Compute the ratio of the volume of the Earth to the volume of the sphere defined by the groundhog’s current
   position. Use this comparison to calculate the mass of the inside sphere.


2. Use the mass of the inside sphere, the mass of the groundhog and the distance between the groundhog and the center of the Earth to
   calculate the gravitational force.

Physics principles and equations

Newton’s law of gravitation

Mathematics principles

The equation for the volume of a sphere is

Step-by-step solution

First, we calculate the mass enclosed by the sphere.

Now that we know the mass of the inner sphere, the shell theorem states that we can use it to calculate the gravitational force on the

groundhog using Newton’s law of gravitation.

This calculation also confirms a point made previously: Inside the Earth, the groundhog’s weight increases linearly with distance from the

planet’s center. At half the distance from the center, his weight is half his weight at the surface.

Step Reason

1. ratio of masses proportional to ratio of volumes

2. rearrange

3. volume of a sphere

4. cancel common factors

5. enter values

6. Ms = 7.46×10^23 kg evaluate

Step Reason

7. law of gravitation

8. enter values

9. F = 24.4 N solve for the force

(^226) Copyright 2000-2007 Kinetic Books Co. Chapter 12