Escape Velocity

Learn.

Escape velocity is the minimum velocity an object a non propelled object must travel to escape the gravitational field of another object.

v_e= \sqrt {\frac {2GM}{r}}
v_eescape velocity
Guniversal gravitational constant
Mmass of the body to be escaped from
rdistance from the center of the mass

In order to find escape velocity, you have to assume the objects will travel an infinite distance apart since gravity is a long range force, however, gravity is also a very week force so it can be assumed to be negligible.

To find the escape velocity, you equate the change in KE to the change in GPE as follows

Change in KE = Change in GPE

1/2 mv2 =GMm/r

1/2 v2 =GM/r

rearrange and you have

v_e= \sqrt {\frac {2GM}{r}}

Memorize.

Master.

Question 1. [3 marks]

Explain whether object a, which weighs 4500 N or object b of mass 600 kg will have a greater escape velocity from earth. Use equations to back up your answer.

Question 2. [2 mark]

A satellite 4 km off the surface of the earth orbits earth at constant altitude, explain why the satellite isn’t applying any external force or energy to remain at this altitude.

Question 3. [2 marks]

An object must escape the gravitational pull of earth if it is on the surface of the earth, what is the minimum velocity it must travel?

Question 4. [4 marks]

What initial force is required for an object of mass 300 kg to escape earth from its current altitude of 2 km above the surface of earth, if the force is applied for 5 seconds?

Answers.

Question 1.

Same escape velocity

Question 3.

11200 m/s

Question 4.

672000 N (3 sig fig)

Find formula for escape velocity, find escape velocity, use v = u + at, F = ma

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