Chapter 8: Questions
Name: _______________________
Mr. Kepple
Conservation of Energy – HW#3
Date: ___________ Period: _____
1. The figure shows one direct path and four indirect paths
from point to point . Along the direct path and three of
the indirect paths, only a conservative force acts on a
certain object. Along the fourth indirect path, both and
a nonconservative force
act on the object. The change
in the object’s mechanical energy (in joules) in going
from to is indicated along each straight-line segment of
the indirect paths. What is
(a) from to along the direct path? Briefly
justify your answer.
(b) due to
along the one path where it acts?
Briefly justify your answer.
12 J. The three indirect paths each have
a change in mechanical energy of 12 J.
We know that since the force acting
over the direct path is conservative it
must have the same change in energy.
−2 J. The nonconservative force causes
mechanical energy to be lost. Since the
third path has a change in mechanical
energy of 12 J this indicated that 2 J was
lost due to the nonconservative force.
2. In the figure to the right, a horizontally
moving block can take three frictionless routes,
differing only in elevation, to reach the dashed
finish line. Rank the routes (and justify your
ranking) according to the
(a) speed of the block at the finish line.
(b) travel time to the finish line, greatest first.
Rank: 3, 2, 1. Since the path is
frictionless the mechanical energy is
conserved. The path with the lowest
potential energy (height) will have the
greatest kinetic energy (speed).
Rank: 1, 2, 3. The path with the greatest
potential energy at the finish line will
take the longest to traverse, since it will
have the lowest average speed.
3. The figure shows three situations involving a
plane that is not frictionless and a block sliding
along the plane. The block begins with the same
speed in all three situations and slides until the
kinetic frictional force has stopped it. Rank the
situations according to the increase in thermal energy due to the sliding, greatest first.
Rank: 2, 1, 3. In situation (2) all of the block’s initial kinetic energy and its gravitational
potential energy is transformed into thermal energy. In situation (1) only the initial
kinetic energy is transformed into thermal energy. Finally in situation (3) only part of the
initial kinetic energy is transformed into thermal energy, the rest is transformed into
gravitational potential energy.
4. The figure gives the potential
energy function of a particle. Briefly
justify each of your answers.
(a) Rank the regions
,
,
, and
according to the magnitude of the
force on the particle, greatest first.
Rank: 𝐴𝐵, 𝐶𝐷, 𝐵𝐶 and 𝐷𝐸 tie.
The force is found from the slope
of the graph.
What value must the mechanical energy
of the particle not exceed if the particle is to be
(b) trapped in the potential well at the left?
(c) trapped in the potential well at the right?
5 J. If the particle has more than 5 J of
mechanical energy it will escape the
potential well at position 𝐷.
5 J. If the particle has more than 5 J of
mechanical energy it will escape the
potential well at position 𝐸.
(d) able to move between the two potential
wells from (b) and (c) but not able to move to
the right of ?
(e) for the situation of (d), in which of the
regions
,
, and
will the particle have
the least speed?
6 J. The two potential wells are bound
by 8 J of potential energy on the left
and 6 J on the right. Therefore the
mechanical energy cannot exceed 6 J.
Region 𝐷𝐸. When the potential energy
is at its highest value the kinetic
energy, and therefore the speed, will
be at its lowest value.
5. In the figure, a block slides along a track
that descends through distance . The track
is frictionless except for the lower section.
There the block slides to a stop in a certain
distance because of friction.
(a) If we decrease , will the block now slide to
a stop in a distance that is greater than, less
than, or equal to ?
___ Greater than
X Less than
___
___ Equal to
(b) If, instead, we increase the mass of the
block, will the stopping distance now be greater
than, less than, or equal to ?
___ Greater than
___ Less than
___
X Equal to
Justify your answer.
Justify your answer.
With less height the block will have less
initial mechanical energy. As a result,
friction will not require as much
distance to transform all of the
mechanical energy into thermal energy.
Increasing the mass increases the
amount of mechanical energy which
needs to be transformed. However,
increasing the mass also increases the
power output of friction. As a result,
the block stops in the same distance.