Question

In: Physics

Answer the following multi-step problem on Gravity a) Select ALL true statements regarding the gravitational potential...

Answer the following multi-step problem on Gravity

a) Select ALL true statements regarding the gravitational potential energy expression U = - G m₁ m₂/r.

[1.The gravitational potential energy is a scalar.,

2.One choose U = 0 at r = infinity since only the ΔU matters in physics and ΔU does not depend on where one chooses U = 0. 3.The gravitational potential energy increases as objects approach each other since the potential energy is zero at infinite separation.,

4.This expression for U can be used for two spheres if "r" is distance between centers of the spheres.,

5.In a problem involving a rocket launched from Earth into geosynchronous orbit, one can apply conservation of energy by using U = mgh for the initial energy and U = -G m M_E/r for the potential energy in orbit.]

b)How does one calculate the escape speed from a planet? Only one answer is correct.

[1.Use constant acceleration kinematics to determine the initial speed needed to just reach infinity.,

2. Use conservation of energy to determine the initial speed needed to reach r = infinity with no kinetic energy left over.,

3.Use conservation of energy to determine the initial speed needed to reach the top of the atmosphere.,

4.Use conservation of energy and circular motion dynamics to determine the initial speed needed to go into a circular orbit with a radius equal to twice the radius of the planet.]

c)A satellite of mass 817 kg is in a circular orbit of radius 1.4 Earth radii. It is struct by a micro-meteorite causing the orbit to decay and the satellite to eventually hit the Earth. What is the change in gravitational potential energy during this decay? Answer in mega-joules (10⁶ joules)

d) The value of G was first determined by Henry Cavendish in 1798 while the Greek mathematician/scientist Hipparchus (190 BC - 120 BC) found that the radius of the moon's orbit was between 60 and 80 Earth radii. (It is actually about 59 Earth radii). The period of the Moon's orbit is about 29 days. From the period and radius you can find the speed of the Moon in its orbit.

What can be determined if the radius and period of the Moon's orbit and the value of G are known?

[1.The mass of the Earth., 2.The diameter of the Moon., 3. The mass of the Moon. 4.The mass of both the Earth and the Moon.]

Expert Solution

genius_generous answered 2 years ago

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