1. The potential energy of an object constrained to the
x
axis is given by
U
(
x
) =
6
x
2
−
8
x
3
,
where
U
is in joules and
x
is in meters.
(a) Determine the force
F
x
associated with this potentialenergy function.
F
x
=
(b) Assuming no other forces act on the object, at what positions is this object in equilibrium?
(Enter your answers from smallest to largest.)
x
1
=
x
2
=
(c) Which of these equilibrium positions are stable and which are unstable?
point
x
1
is in
point
x
2
is in
2. A simple Atwood's machine uses two masses,
m
1
and
m
2
. Starting from rest, the speed of
the two masses is
6.0
m/s at the end of
3.0
s. At that instant, the kinetic energy of the system
is
50
J and each mass has moved a distance of
9.0
m. Determine the values of
m
1
and
m
2
.
m
1
= kg
m
2
= kg
3. The
5.0
kg object below is released from rest at a height of 5.0 m on a curved frictionless
ramp. At the foot of the ramp is a spring of force constant
k
=
400
N/m. The object slides
down the ramp and into the spring, compressing it a distance
x
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 Spring '10
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 Physics, Energy, Force, Mass, Potential Energy, kg roller coaster, potentialenergy function

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