Question

The force of gravitational attraction between two masses is 64 N. What will be the force if one mass is doubled and the distance between them is quadrupled?

Answer 1

Answer on Question #41298, Physics, Mechanics

The force of gravitational attraction between two masses is 64 N. What will be the force if one mass is doubled and the distance between them is quadrupled?

Solution:

Newton's Law of Universal Gravitation states that there is a gravitational force between any two masses that is equal in magnitude for each mass, and is aligned to draw the two masses toward each other. The formula is:

$$F = G \frac {m _ {1} m _ {2}}{r ^ {2}}$$

where $m_1$ and $m_2$ are the two masses, $G$ is the gravitational constant, and $r$ is the distance between the two masses.

In our case:

$$F _ {1} = G \frac {m _ {1} m _ {2}}{r ^ {2}} = 64 \mathrm{~N}$$ $$F _ {2} = G \frac {2 m _ {1} m _ {2}}{(4 r) ^ {2}}$$

The ratio of forces is

$$\frac {F _ {1}}{F _ {2}} = G \frac {m _ {1} m _ {2}}{r ^ {2}} \cdot \frac {16 r ^ {2}}{2 G m _ {1} m _ {2}} = \frac {16}{2} = 8$$

Thus,

$$F _ {2} = \frac {F _ {1}}{8} = \frac {64}{8} = 8 \mathrm{~N}$$

Answer. $F_{2} = 8$ N.

http://www.AssignmentExpert.com/