Problem 1) you are on a planet with no atmosphere its gravity is 20 m/s sq and i

Question

Problem 1) you are on a planet with no atmosphere its gravity is 20 m/s sq and it radius R=10,000 KM. use g=GM/r^2 (solve for GM as necessary). the gravitaional force, directed forward the planet's center is (GM*m/r^2): M is the planet's mass, m is the object's mass, r is the distance from the center of the planet.

a) what is the potential energy function? (Derrive it)

b) what minimum speed do you have to throw something up at, so that it will never comes back down? (you may wish to do problem 2 first)

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Problem 2) in the previous sitiuation, you throw an object upward at the following speeds. Either tell the distance(r value) where the object stops and falls back, or the object's speed in the limit as (r---> goes to infinity)

a) 15 km/s = initial speed

b) 25 km/s

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Explanation / Answer

A) potential energy function u = -G*M*m/r

B) v = sqrt(2*g*R) = sqrt(2*20*10000*1000) = 20000 m/s

2) apply law of conservation of energy

-G*M*m/r = 0.5*m*v^2

r = G*M/(0.5*v^2)

and GM = g*r^2

then r = g*r^2/(0.5*v^2)

A) r = 0.5*v^2/g = 0.5*15000^2/9.81 = 11467.88 km from the center of the planet

again for v = 25 km/s

B) r = 0.5*25000^2/9.8 = 31855.25 km from the center of the planet

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