Momentum Principle Related to Velocity

In summary: So the satellite has a constant speed (in terms of revolutions per minute) as long as the gravitational force on the Earth is the same.
  • #1
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Homework Statement



You will need to use the Momentum Principle to do the first part of this problem, and the Energy Principle to do the second part.

A satellite of mass 2500 kg orbits the Earth in a circular orbit of radius of 8.3 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 1024 kg.
What is the speed of the satellite?
I have the 2nd part of the problem, so all I need is the momentum principle


Homework Equations



Pfinal = Pinitial + Fnet*DeltaT
GMm/r^2

The Attempt at a Solution


I'm not sure how to start this one. The directions say that I'm supposed to use the momentum principle, but I'm not given the speed of the satellite. I was thinking maybe the derivative form of the momentum principle and find the perpendicular component of dP/dT, but I'm not sure how long it takes for the satellite to go around th earth. I'm completely stuck.
 
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  • #2
I have no idea what you mean by the "momentum principle". If you mean conservation of momentum, I don't see how that is relevant.

Instead, apply Newton's 2nd law to the satellite, recognizing that its motion is circular.
 
  • #3
By momentum principle I mean DeltaP = Fnet*DeltaT
 
  • #4
OK, I see. Your initial thought was correct: Use F = dP/dt. (Note that this is another way of stating Newton's 2nd law.)

Use what you know (or should know) about circular motion to evaluate d(mv)/dt = m dv/dt.
 
  • #5
Here's the problem I have with using dP/dt: In order to find the velocity, or the change in momentum, I need to know the time it takes for one rotation around the earth...that's why I didn't use that formula in the first place. v = dr/dt, but again, I don't have dt.
 
  • #6
Call the speed "v" and express dP/dt in terms of it (along with other known variables).
 
  • #7
v= dr/dt I can find dr because I know the radius of orbit, but I have no way of finding dt.
 
  • #8
You can express the period (if you need it) in terms of v, since you know the radius of the orbit.
 
  • #9
I don't understand how you can express the period in terms of v if you don't know the time.
 
  • #10
Ok, I figured out the problem.

v = sqrt(G*Mearth/r)
 
  • #11
Excellent.
 

1. What is the Momentum Principle?

The Momentum Principle is a fundamental concept in physics that states that the momentum of an object is equal to its mass multiplied by its velocity. In simpler terms, it describes the relationship between an object's mass and its velocity.

2. How is the Momentum Principle related to velocity?

The Momentum Principle is directly related to velocity because it states that the momentum of an object is directly proportional to its velocity. This means that as an object's velocity increases, its momentum also increases in proportion.

3. What is the formula for calculating momentum?

The formula for calculating momentum is p = m x v, where p is the momentum, m is the mass of the object, and v is the velocity. This formula is derived from the Momentum Principle.

4. How does the Momentum Principle apply to real-life situations?

The Momentum Principle applies to real-life situations in various ways. For example, it explains why it is more difficult to stop a moving object with a larger mass compared to an object with a smaller mass. It also helps in understanding the effects of collisions and impacts between objects.

5. Is the Momentum Principle always conserved?

According to the law of conservation of momentum, the total momentum of a closed system remains constant. This means that in a closed system, the Momentum Principle is always conserved. However, in real-life situations, external forces such as friction can affect the momentum of objects, causing it to change.

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