Gravitational Potential Energy Function - Engineering Physics - Lecture Slides, Slides of Engineering Physics

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Gravitational Potential Energy Function

U = −

Gm 1 m 2

r

f 1 ,^2

f 2 ,^1

move together

v

v

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Gravitational Potential Energy Function

U = −

Gm 1 m 2

r

f 1 ,^2

f 2 ,^1

move together

v

v

U (^) g

0 r

Gravitational Potential Energy Function

U = −

Gm 1 m 2

r

f 1 ,^2

f 2 ,^1

rotate around

each other

v

v

Gravitational Potential Energy Function

U = −

Gm 1 m 2

r

f 1 ,^2

f 2 ,^1

rotate around

each other

v

Energy K+U is constant

U

K

r 0

Attraction: two stars

Clicker Quiz

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Consider a sattelite of mass m in orbit around a planet

of mass M at a radius r from the center of the planet.

What is the total energy of the sattelite?

1. Etot = −

GmM

r

2. Etot =

GmM

2 r

3. Etot =

GmM

2 r^2

4. Etot =

GmM

2 r^2

5. Etot = −

GmM

2 r

Potential Energy Function Repulsive Forces

U =

q 1 q 2

r

Energy

K+U^ is constant

U

K

0

0

Repulsion: two protons

r → ∞

Negative Total Energy

Negative Total Energy

Out of

K-energy

Clicker Quiz

Clicker Quiz

Bound States

Not enough

total energy

K + U < 0

K + U ≥ 0

Bound

Unbound

Application - Escape Velocity

Not enough

total energy

K + U < 0

K + U ≥ 0

Neglecting air resistance,

how fast must a projectile be fired to

escape from Earth's orbit?

Does it depend on:

t
*OJUJBM
LJOFUJD
FOFSHZ

t
.BTT
PG
QSPKFDUJMF

t
.BTT
PG
&BSUI

Bound

Unbound

Application - Escape Velocity

vesc

1. vf =

vrock − vesc

2. vf = vrock^2 + v^2 esc

3. vf =

vrock + vesc

4. vf = 2

vrock − vesc

5. vf = vrock^2 − v^2 esc

Suppose the escape velocity from an asteroid is

If you throw a rock away from the asteroid at speed larger

than the escape velocity.

What is the final velocity of the rock?