Gravitational Potential Energy

Click For Summary

Homework Help Overview

The discussion revolves around gravitational potential energy and escape velocity in the context of a rocket's motion near Earth's surface. The original poster presents a problem involving a rocket accelerated to a specific speed and its ability to escape Earth's gravitational influence.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the concept of escape velocity and its relation to gravitational potential energy. There are attempts to clarify the definition of escape velocity and its implications for the rocket's motion. Questions arise regarding the setup of the problem and the transition from potential energy to kinetic energy.

Discussion Status

The discussion is active, with participants providing insights into the definitions and implications of gravitational potential energy and escape velocity. Some guidance has been offered regarding the expressions for potential energy, but there is no explicit consensus on the setup for part b of the problem.

Contextual Notes

Participants are navigating the definitions and implications of gravitational potential energy in relation to the escape velocity, with some assumptions about the initial conditions and the nature of the energy transformations being questioned.

slayer16
Messages
10
Reaction score
0

Homework Statement


A rocket is accelerated to speed v=2√gR (where R is the radius of Earth 6370 km) near Earth's surface surface and it then coasts upward. a) show that it wil escape from Earth. b) Show that very far from Earth its speed will be v=2√gR.


Homework Equations


Gravitational potential energy
Escape Speed
Conservation of Mechanical Energy

The Attempt at a Solution


I got part A, but I do not know how to set up part b correctly.
 
Physics news on Phys.org
Remember the escape velocity is the velocity required to take the rocket from zero to infinity.

What is the expression for Gravitational potential energy?
 
rock.freak667 said:
Remember the escape velocity is the velocity required to take the rocket from zero to infinity.

What is the expression for Gravitational potential energy?

PE=-GmM/R.
Also what do you mean when you say that the escape velocity is the velocity required to take the rocket from zero to infinity?
 
slayer16 said:
PE=-GmM/R.
Also what do you mean when you say that the escape velocity is the velocity required to take the rocket from zero to infinity?

Gravitational PE is the energy required to take a point mass from infinity to a point. In this case you want a velocity to go from one point to infinity.

So in one case U is negative, so in the other case U is ?

And then this U should be changed into kinetic energy.
 

Similar threads

Replies
15
Views
2K
Replies
2
Views
1K
  • · Replies 11 ·
Replies
11
Views
1K
  • · Replies 15 ·
Replies
15
Views
2K
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
5
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K