- #1
Eunjung
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Homework Statement
Hello, I am currently a gr 12 high school student, and I am stuck in a problem. Please help :)
The problem: Consider the motion of a rocket near the surface of the Earth. In this case, mass, in the form of gas is expelled from the rocket to propel the rocket upwards. A simple model of this would be the ejection of cannonballs from the back end of a frictionless cart initially at rest. What happens to the rocket when all the fuel is exhausted?
i) Explain the physics of the problem
ii) Graphical output to display variables that are relevant to the problem.
Homework Equations
Force of gravity (global) = G * Mass of Earth * Mass of rocket / (Earth's radius + distance rocket travels above the surface)^2
G= 6.67*10^-11 Nm^2/kg^2
Mass of Earth = 5.98 * 10^24 kg
Mass of rocket = unknown
Earth's radius = 6.4 x 10^6 m
The local gravitational force formula F = mg
The Attempt at a Solution
I got up to the point where the rocket goes up for a bit, due to inertia, which may carry it outside of the Earth's atmosphere. But, what if the rocket can't escape the atmosphere?
The rocket will be at 0 velocity at the peak of its motion, but I cannot think of how to calculate the acceleration in the rocket's way down.
The gravitational force grows weaker as you get further away from the surface of the Earth, so it can't possibly be F = ma (the force of gravity on the rocket will constantly change, so I don't think I can use that one since it generalizes everything).
I tried using the global gravitational force formula, but I don't know the maximum height of the rocket, so I can't calculate the force of gravity at different heights. Will it not make a difference because of the large radius of the Earth? I don't know.
If I assume that the mass of the rocket and the height in which the rocket flies above the surface is insignificant, then the force of gravity will be 9.7379N for the entire downward motion of the rocket. Gravity changes as you go out of Earth's atmosphere, so that can't be right.
I'm totally lost, can someone please help?
-Eunjung :)