The gravitational attraction between two masses varies inversely as the square of the distance between them. If the attraction force between them is 75 lbs. when the bodies are eight feet apart, find the attraction when the masses are twelve feet apart.

a) 33 1/3 lbs. b) 50 lbs. c) 168 3/4 lbs.

Answer: Option a) 33 1/3 lbs

Solution:

Be

Attraction force (F) varies inversely as the square of the distance between them:

F=k/d^2

Constant of proportionality: k

Distance between the two masses: d

F=75 lbs when d=8 feet

Replacing in the formula above:

F=k/d^2

75 lbs=k / (8 feet) ^2

Squaring in the denominator:

75 lbs=k / (64 feet^2)

Solving for k: Multiplying both sides of the equation by 64 feet^2:

(64 feet^2) (75 lbs) = (64 feet^2) [k / (64 feet^2) ]

4,800 lbs*feet^2=k

k=4,800 lbs*feet^2

F=k/d^2

F=4,800 lbs*feet^2/d^2

Find the attraction when the masses are twelve feet apart:

F=?

d=12 feet

Replacing in the formula:

F=4,800 lbs*feet^2 / (12 feet) ^2

Squaring in the denominator:

F=4,800 lbs*feet^2 / (144 feet^2)

Dividing:

F = (4,800/48) / (144/48) lbs

F=100/3 lbs

F = (99+1) / 3 lbs

F = (99/3+1/3) lbs

F=33 1/3 lbs