Conservation of energy problem

In summary, the two rockets launched from Earth's surface at 17 km/s and 22 km/s respectively. To calculate how fast they are moving when they cross the moon's orbit, we can use the equation 0.5mvf^2 - GMm/R = 0.5mv0^2 - GMm/R, where R is the distance from the Earth to the moon. The radius on one side of the equation can be taken as 0, while on the other side, it is the sum of the Earth's radius and the distance to the moon. By solving for vf, we can determine the speed of each rocket when they cross the moon's orbit.
  • #1
darklich21
43
0

Homework Statement


Two rockets are launched from Earth's surface, one at 17 km/s and the other at 22 km/s. How fast is each moving when it crosses the moon's orbit?


Homework Equations


Kf + Uf= K0 + U0
0.5mvf^2 -GMm/R = 0.5mv0^2 - GMm/R


The Attempt at a Solution


So I attempted to use the equation above, using the Earth's mass and the Earth's radius, It didn't work, my speeds came out to be exactly 17 and 22 just like from the start. I'm going to say that the radius of the moon and the mass of the moon comes into play here. Can someone help, with perhaps a better equation?
 
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  • #2
Radius in this case the distance from M, and is different on each side of the equation. So it's R_1 and R_2. You could use the center of the Earth or the surface of the Earth as the origin, as long as you are consistent. the surface is probably easier. So the radius at the start is 0. And the radius at the moon is the distance from the Earth to the moon. Ignore the actual moon. it's not important here.

You should be able to handle it from here.
 
  • #3
how can the radius be 0, the radius in my equation is in the denominator. it would make 1 part of the expression undefined
 
  • #4
nvm i figured it out, but I am going to correct your response. The radius is NOT 0, but instead the raidus of the earth, while on the other side of the equation, it's the radius of the Earth + the distance to the moon.
 

Related to Conservation of energy problem

1. What is the conservation of energy problem?

The conservation of energy problem refers to the principle of energy conservation, which states that energy cannot be created or destroyed, but can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

2. Why is conservation of energy important?

The conservation of energy is important because it is a fundamental law of physics that governs the behavior of energy in all physical systems. It allows us to accurately predict and understand the behavior of objects and systems, and it is the basis for many technological advancements.

3. How does the conservation of energy apply to real-life situations?

The conservation of energy applies to all real-life situations, from simple everyday activities to complex systems. For example, when we turn on a light bulb, the electrical energy is converted into light and heat energy, but the total amount of energy remains the same. In more complex systems, such as a car engine, the chemical energy from fuel is converted into mechanical energy to power the car, again following the principle of energy conservation.

4. Are there any exceptions to the conservation of energy?

There are no known exceptions to the conservation of energy. However, in some situations, it may appear that energy is not conserved, but this is usually due to a lack of understanding or measurement error. For example, in nuclear reactions, a small amount of mass is converted into energy according to Einstein's famous equation, E=mc². This may seem like energy is being created, but in reality, it is simply being transformed from one form to another.

5. How is the conservation of energy related to other laws of physics?

The conservation of energy is closely related to other fundamental laws of physics, such as the laws of thermodynamics and the law of conservation of momentum. These laws work together to explain the behavior of energy and matter in the universe. For example, the first law of thermodynamics, which states that energy cannot be created or destroyed, is essentially another way of stating the principle of energy conservation. Similarly, the conservation of momentum is based on the conservation of energy, as energy is required for any change in momentum to occur.

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