Gravitational Potential Energy Problem

In summary, the problem involves calculating the speed at which the moon would strike the Earth if it were at rest at its current distance from the Earth, assuming the Earth is infinitely massive compared to the moon. The solution involves using the equations for gravitational potential energy and kinetic energy, and taking into account the radius of both the Earth and the moon. The correct answer is 9.8 km/s.
  • #1
brendan3eb
54
0
[SOLVED] Gravitational Potential Energy Problem

Homework Statement


Suppose that the moon were at rest at its present distance from the earth, rather than orbiting it. With what speed would it strike the earth? (Take the Earth to be infinitely massive relative to the moon)


Homework Equations


Mass of Earth = 5.98x10^24 kg
Distance from center of Earth to center of moon = R = 3.82x10^8 m
Mean radius of Earth = Re = 6.37x10^6 m
Gravitational potential energy = -GMm/R
K1+U1=K2+U2

The Attempt at a Solution


K1=0
k2=(1/2)Mmv^2
U1=-GMeMm/R
U2=-GMeMm/Re
(1/2)Mmv^2-GMeMm/R=-GMeMm/Re
when I eliminate the mass of the moon and plug in all the numbers to solve I get 11.10 km/s, but I know the right answer is 9.8 km/s. Anyone see what I am doing wrong?
 
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  • #2
The radius of the moon?
 
  • #3
a-ha! Bingo! Thank you so much. The second potential energy distance would have be the sum of the radius of the Earth AND the moon! Let's see our numbers...yep 9.8 km/s!

Thank you so much!
 
  • #4
No problem, glad to see you got it. :)
 

FAQ: Gravitational Potential Energy Problem

What is gravitational potential energy?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is the energy that is stored in an object when it is lifted or raised above the ground.

How is gravitational potential energy calculated?

The formula for calculating gravitational potential energy is GPE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the ground.

What factors affect the gravitational potential energy of an object?

The gravitational potential energy of an object is affected by its mass, the strength of the gravitational field, and its distance from the source of the gravitational field.

What is the relationship between gravitational potential energy and kinetic energy?

Gravitational potential energy and kinetic energy are two forms of energy that are related by the law of conservation of energy. As an object's gravitational potential energy decreases, its kinetic energy increases, and vice versa.

How is gravitational potential energy used in real life?

Gravitational potential energy is used in many real-life situations, such as hydroelectric power plants, roller coasters, and parachutes. It is also used in everyday activities like throwing a ball or lifting an object. Understanding gravitational potential energy is crucial in designing and engineering structures that involve lifting or moving heavy objects.

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