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The gravitational force on an object of mass m a distance r
mM E
from the centre of the Earth is given by F  G 2 .
r
The potential energy of the object is taken to be zero when
the object is an infinite distance from the Earth.
When it is a distance r from the centre of the Earth its
potential energy is
(a) negative
(b) positive
(c) not enough information to tell
The gravitational force on an object of mass m a distance r
mM E
from the centre of the Earth is given by F  G 2 .
r
The potential energy of the object is taken to be zero when
the object is an infinite distance from the Earth.
When it is a distance r from the centre of the Earth its
potential energy is
(a) U(r) = GmME/r
(b) U(r) =- GmME/r
(c) U(r) = mgr
(d) U(r) = -GmME/r2
U(r)
0
At the right is the
gravitational potential
energy diagram for a
meteor at a distance r
from the centre of the
Earth.
r
If the meteor started with almost zero velocity when it was far from
the Earth, which of the following diagram best represents its kinetic
energy K(r) as it approaches the Earth?
(a)
K(r)
(b)
0
U(r)
0
K(r)
U(r)
r
r
The potential energy of an object of mass m a distance r from the
centre of the earth is given by U(r) = -GmME/r . Which of the
following curves best represents U(r)?
U(r)
0
U(r)
0
(a)
(c)
r
U(r)
0
(b)
r
r
The gravitational potential energy
of a satellite is chosen to be zero
U  0 at
r
when it is an “infinite” distance
from the earth. Which of the
following expressions best
mE
describes its potential energy
when it is a distance r above the
center of the earth?
Be sure you know why the wrong ones cannot be right, as well as
which one is correct.
GmE ms
a) U (r ) 
r2
GmE ms
c) U (r ) 
r
e) u (r )  mgr
GmE ms
b) u (r )  
r2
GmE ms
d) u (r )  
r

A rocket ship (mass m) is shot vertically from the surface of the Earth
(mass M) with a velocity v that it maintains for the short time until
the fuel is gone. Which of the following gives the best way to
calculate its maximum height h above the surface of the Earth? (RE
is the radius of the Earth.)
1 2
(a) mv  mgh
2
1 2
Mm
mv   G
(b)
2
RE
1 2
Mm
(c) mv  G
2
RE
1 2
Mm
Mm
(d) mv   G
G
2
RE  h
RE
1 2
Mm
Mm
(e) mv  G
G
2
RE  h
RE