Physics 1111
Fall 2008
PS #7 Solutions
Page 1 of 5
Physics 1111
Problem Set #7 Solutions
Problem 1:
Choose whether each of the following statements is true or false. (a) You drop a
ball to the ground from rest, and, from the same height, throw a second ball down to the ground.
Their change in gravitational potential energies are different. (b) If the potential energy of the
system is zero, the force on the object is zero. (c) If the force on an object is zero, the potential
energy of the system is zero. (d) The potential energy of a system can be negative. (e) When
air resistance is taken into account, a ball thrown directly upward spends more time on the way
down than on the way up.
(a)
False.
The potential energies of the balls do not depend on their velocities, only their
positions. Since they begin and end in the same place, their changes in potential energy
are identical.
(b)
False.
If I drop a ball, but take the my potential energy “reference height” to be the
initial height of the ball, then its initial potential energy is zero even though there’s a
force on it.
(c)
False.
If there are no forces acting on an object (i.e., not just no net force, but none
at all), one can say that its potential energy is constant. However, that constant value
can be arbitrary, because only
differences
in potential energy matter. The constant
needn’t be zero.
(d)
True.
The “reference height” can be at any location, in which case everything below
that height will have a negative gravitational potential energy.
(e)
True.
This is the most challenging of the true/false statements. One way to answer
it is to realize that the ball’s final speed when it reaches you again will be less than
its initial speed, because air resistance has done nonconservative work on the ball and
has reduced its kinetic energy. This means that the ball had a higher average speed on
the way up than on the way down. Since the ball traveled the same distance up and
down, it must have taken longer on the way down.
Another way to think about this problem, without using energy, is to look at the forces
acting on the ball. On the way up, gravity and air resistance are both acting downward
on the ball. As the ball falls, however, gravity pulls down while air resistance opposes
it. Since tha ball has a greater net force acting on it on the way up, it will slow down
more quickly.
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Physics 1111
Fall 2008
PS #7 Solutions
Page 2 of 5
Problem 2:
Two objects of unequal mass are connected by a massless rope that passes over a
massless, frictionless pulley. After the objects are released from rest, what can be said about the
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 Spring '08
 plascak
 Physics, Energy, Force, Friction, Potential Energy, Law of Conservation of Energy

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