the force of gravity varies inversely as the square of the distance between the centers of the two masses. If an object weighs 500 pounds at a distance of 12,000 miles from the center of the earth, at what distance will the weight be 50 pounds
mass = k/d^2
when mass = 500, d = 12000
500 = k/12000^2
k = 500(12000)^2
so
50 = 500(12000)^2 /d^2
50 d^2 = 500(12000)^2
d^2 = 10(12000)^2
d = 12000√10 miles
To solve this problem, we can use the inverse square law formula:
Force = k / (distance^2)
Where:
- Force is the force of gravity
- k is the constant of variation
- distance is the distance between the centers of the two masses
Let's assign the given values:
Force1 = 500 pounds
distance1 = 12,000 miles
Force2 = 50 pounds
distance2 = ?
We can write the problem as an equation using the inverse square law formula:
500 = k / (12,000^2)
To find the constant of variation, k, we can rearrange the equation:
k = 500 × (12,000^2)
Now, we can use k and the new Force value to solve for distance2:
50 = k / (distance2^2)
Substituting the value of k, we have:
50 = (500 × (12,000^2)) / (distance2^2)
To solve for distance2, we need to isolate it on one side of the equation:
(distance2^2) = (500 × (12,000^2)) / 50
Now, we can take the square root of both sides to solve for distance2:
distance2 = √((500 × (12,000^2)) / 50)
Calculating this expression will give us the distance at which the weight will be 50 pounds.