Word Problem help

Question

The gravitational force, F, between an object and the earth is inversely proportional to the square of the distance, d, from the object to the center of the earth. If an astronaut weighs 185 pounds on the surface of the earth, what will he weigh 150 miles above the earth? Assume the radius of earth is 4000 miles.

 

I am not very good at word problems. Can someone help me with this and explain every step in detail? I would be so grateful. Thanks.

Answer 1

I assume you are not doing physics and this is a problem about proportion.

 

inversely proportional means F = k/d² where k is the proportionality constant

 

For weight on earth, F = 185 pounds and d = 4000 miles

 

For weight above the earth, F is unknown and d = 4000 + 150 miles

 

So k =185(4000)² = F(4150)² = k

 

Therefore F = 185 (4000)² / (4150)²

 

F ≈ 172 pounds

Answer 2

The force due to gravity is:

 

F = -GMm/r²

 

Where G is the gravitational constant, M is the Earth's mass, m is the astronaut's mass, and r is the astronaut's distance form the center of the Earth.  At  the surface of the Earth, the astronaut weighs 185 lbs, which is the force F, and is 4000 miles form the center of the earth: 

 

185 lbs = GMm/(4000)²

 

185*(4000)² = GMm

 

At 150 miles above the surface, the astronaut is 4150 miles from the center of the Earth.  His weight is given by:

 

W= GMm/(4150)²

 

Since GMm = 185*(4000)²

 

W = 185*(4000)²/(4150)²

 

W = 185*(0.93)

 

W = 171.87 lbs