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
