Question

8. What is the force of gravity on a dog in a space suit that's running around on the moon? The dog's body has a mass of 20 kilograms. Round to the nearest hundredth place. A. 196 N B. 1,176 N C. 2 N D. 32.67 N

Answer 1

Answer:

D. around 32 N.

Given that:

• The mass of the moon is approximately $7.348\times 10^{22}\;\text{kg}$, and
• The (mean) radius of the moon is approximately $1.7371\times 10^{6}\;\text{m}$.

Explanation:

The dog is much smaller and lighter than the moon; it behaves like a point mass. Consider the equation for the size of gravity between a spherical mass and a point mass outside that spherical mass:

$\displaystyle F = \frac{G\cdot M \cdot m}{r^{2}}$,

where

• $F$ is the size of gravity,
• The gravitational constant $G \approx 6.67\times 10^{-11}\;\text{kg}^{-1}\cdot \text{m}^{-1}\cdot \text{s}^{-2}$,
• $M$ is the mass of the sphere,
• $m$ is the size of the point mass, and
• $r$ is the separation between the point mass and the center of mass of the sphere.

The dog is at the surface of the moon. As a result, the $r$ shall be the same as the radius of the moon. Make sure all values are in SI units (kilograms and meters.) Apply the formula:

$\displaystyle \begin{aligned}F &= \frac{G\cdot M \cdot m}{r^{2}} \\ &= \frac{(6.67\times 10^{-11})\times(7.348\times 10^{22})\times 20}{(1.7371\times 10^{6})^{2}}\\&= 32.48\;\text{N}\end{aligned}$.

This value may vary slightly depending on the position of the dog on the moon.

Answer 2

Weight = (mass) x (acceleration of gravity)

Gravity on or near the moon's surface = 1.63 m/s^2

Dog's weight = (20 kg) x (1.63 m/s^2)

Weight = 32.6 Newtons (D)