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Chapter 7
Conservation of Energy
Conceptual Problems
*1
•
Determine the Concept
Because the peg is frictionless, mechanical energy is conserved
as this system evolves from one state to another. The system moves and so we know that
∆
K
> 0. Because
∆
K
+
∆
U
=
constant
,
∆
U
< 0.
correct.
is
)
(
a
2
•
Determine the Concept
Choose the zero of gravitational potential energy to be at ground
level. The two stones have the same initial energy because they are thrown from the same
height with the same initial speeds. Therefore, they will have the same total energy at all
times during their fall. When they strike the ground, their gravitational potential energies
will be zero and their kinetic energies will be equal.
Thus, their speeds at impact will be
equal. The stone that is thrown at an angle of 30
°
above the horizontal has a longer flight
time due to its initial upward velocity and so they do not strike the ground at the same
time.
correct.
is
)
(
c
3
•
(
a
) False. Forces that are external to a system can do work on the system to change its
energy.
(
b
) False. In order for some object to do work, it must exert a force
over some distance
.
The chemical energy stored in the muscles of your legs allows your muscles to do the
work that launches you into the air.
4
•
Determine the Concept
Your kinetic energy increases at the expense of chemical
energy.
*5
•
Determine the Concept
As she starts pedaling, chemical energy inside her body is
converted into kinetic energy as the bike picks up speed.
As she rides it up the hill,
chemical energy is converted into gravitational potential and thermal energy.
While
freewheeling down the hill, potential energy is converted to kinetic energy, and while
braking to a stop, kinetic energy is converted into thermal energy (a more random form of
kinetic energy) by the frictional forces acting on the bike.
*6
•
Determine the Concept
If we define the system to include the falling body and the earth,
then no work is done by an external agent and
∆
K
+
∆
U
g
+
∆
E
therm
= 0. Solving for the
change in the gravitational potential energy we find
∆
U
g
=
−
(
∆
K
+ friction energy).

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