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PHYS171
Exam 3
Fall 2011
Name: _____________________
Student ID #: ________
1
Short Answer Questions
1)
A planet is the same density as the earth, but twice the radius.
What is the
acceleration of gravity on the surface of this planet (given that on earth
g
= 9.8 m/s
2
)? (5
points)
For earth,
E
E
E
E
E
r
G
r
r
G
r
Gm
g
π
ρ
3
4
2
3
3
4
2
=
=
=
.
where the mass of the earth has been
expressed as the density
multiplied by the volume.
After cancelation of
r
E
, the
acceleration of gravity is proportional to
r
E
. In the new planet
r
= 2
r
E
, so the acceleration
of gravity increases by a factor of 2.
g
= 2(9.8 m/s
2
) = 19.6 m/s
2
2) You jump into the air and throw a baseball before hitting the ground again.
During the
process of throwing the baseball is momentum conserved?
Is kinetic energy conserved?
(5 points)
Momentum is conserved.
You and the baseball exert force on each other, and momentum
gained by one is lost by the other.
Energy is not conserved since you are using your
muscles to generate force, converting chemical energy to mechanical energy.
3)
A particle moves in one dimension under the influence of the potential energy
function
U(x)=kx
2
, where k is a positive constant. Locate the equilibrium position and
say whether it is stable or unstable. (5 points)
Force is
kx
kx
x
x
U
F
x
2
2
−
=
∂
∂
−
=
∂
∂
−
=
.
Equilibrium occurs when
F
= 0, which occurs at
x
=0.
Equilibrium is stable if
0
2
2
>
∂
∂
x
U
.
In this case
k
x
U
=
∂
∂
2
2
, so equilibrium is stable.
4) Assume you have mass 70 kg.
At the Dupont Circle metro station the escalator is
broken (not moving).
(a)
You climb 200 steps of 10 cm each.
how much work does
your body do?
(b)
You climb a downward moving escalator, climbing 200 steps while
remaining fixed in place, how much work does your body do?
(c)
You climb an upward
moving escalator and climb 100 steps before you reach the top of the 200 step escalator.
How much work does your body do?
(15 points)
(a) As you climb the stairs you exert a constant force equal to your weight (assuming you
move at constant velocity, no acceleration)
Work is therefore
F
Δ
s
, where
Δ
s
is the
displacement, and we replace
F
with
mg
.
Each time you climb a step you extend your
leg the height of one step, so the work done is
mgh
,where
h
is the height of a step.
You
do this
N
times when climbing
N
steps, so the total work is
Nmgh
= 200 (70kg) (0.1m)
(9.8m/s
2
)
= 13720 J.
(b)
The work your body does is the same.
You are still extending
your leg a distance
h
for every step and exerting force equal to your weight.
The work
done by your body contributes to moving the escalator, rather than increasing your
potential energy.
(c)
You only do half as much work since you only climb half as many
steps.
You still experience the full change in gravitational potential energy, but half of
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 Fall '11
 LA PORTA
 mechanics, Acceleration, Gravity

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