Physics I help

Question

Joey weighs 600 N on Earth (that is, the force of gravity pulling him down is 600 N). Some strange and inexplicable things begin happening. Let the radius of the earth be Re, and its mass Me (e is in subscript).

 

a. The earth were to keep its radius of Re, but have twice the mass (2me). Answer: 1200N.

 

b. Joey were to suddenly have half his original mass (but the earth was back to normal). Answer: 300 N.

 

c. The earth doubled in mass (as in part A) and Joey's mass is cut in half (as in part B). Answer: 600 N.

 

How do I get these answers? Thanks!

Answer 1

The gravitational force on Joey is:

 

F = GMm/R²

 

Where:

• F = the force in newtons (N)
• G = the gravitational constant
• M = the earth's mass
• m = Joey's mass
• R = the Earth's radius

 

Normally the force is 600 N:

 

600 = GMm/R²

 

If we double the Earth's mass = 2M, but keep everything else the same:

 

F = G(2M)m/R²

F = 2(GMm/R²) = 2(600 N) = 1200 N

 

If we cut Joey's mass in half = m/2 but keep everything else the same:

 

F = GM(m/2)/R² = (1/2)(GMm/R²) = (1/2)(600 N) = 300 N

 

If we doubled earth's mass = 2M and halved Joey's = m/2:

 

F = G(2M)(m/2)/R² = GMm/R² = 600 N