Gravitational Field, Potential Energy and Escape Speed

Name: Gravitational Field, Potential Energy and Escape Speed
Author: StemPy Lab

Why can a rocket leave the Earth, but a ball thrown up with the same speed as a bullet always comes back? In this course we define the gravitational field and the gravitational potential energy, we learn why the energy is negative, we find the field and the potential inside and outside a spherical shell and a solid sphere, and we find the escape speed of a planet.

3 lessons, about 1 h 10 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 20 min
Gravitational field and potential energy
A mass sets up a gravitational field around it: the force per kilogram, $\vec{g} = \dfrac{GM}{r^2}$ toward the mass, in N/kg. The potential energy of two masses is $U = -\dfrac{GMm}{r}$ , taking zero when they are far apart; it rises toward zero as they separate. Near the surface, the change is close to $mgh$ , but for big heights the exact formula must be used.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 25 min
Gravitational potential and spherical shells
Gravitational potential is the potential energy per kilogram, $V = -\dfrac{GM}{r}$ , in J/kg; potentials of several masses add as plain numbers. The field is the downhill slope of the potential. A thin uniform shell gives zero field everywhere inside, and a potential that is the same everywhere inside, equal to its value at the shell. Outside, a shell acts like a point mass at its centre.
1 simulation2 practice questions1 Python program4 problems
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Lesson 3about 25 min
Escape speed
The escape speed is the least launch speed that carries a body away for good, ignoring air: $\tfrac12 mv_e^2 = \dfrac{GMm}{R}$ , so $v_e = \sqrt{\dfrac{2GM}{R}} = \sqrt{2gR}$ , about $11.2\ \text{km/s}$ for the Earth. It does not depend on the body's mass or direction. Slower bodies rise to $h = \dfrac{Rv^2}{2gR - v^2}$ and fall back.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Potential Energy and Escape Speed: Practice Paper

20 questions · 50 min

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Gravitational Field, Potential Energy and Escape Speed

Course outline (3 lessons)

Gravitational field and potential energy

Gravitational potential and spherical shells

Escape speed

Test Your Learning

Your teacher

Discussion (0)