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Class PH1110A2007
Assignment 10
Due at 5:00pm on Friday, September 21, 2007
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Learning Goal:
To apply the law of conservation of energy to an object launched upward in the gravitational field
of the earth.
In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed
system is conserved. This is one particular case of the
law of conservation of energy
.
In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The
energy transformations that take place involve the object's kinetic energy
and its gravitational potential
energy
. The law of conservation of energy for such cases implies that the sum of the object's kinetic energy and
potential energy does not change with time. This idea can be expressed by the equation
,
where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the
choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question
posed in the problem.
First, let us consider an object launched vertically upward with an initial speed
. Neglect air resistance.
Part A
As the projectile goes upward, what energy changes take place?
ANSWER:
Both kinetic and potential energy decrease.
Both kinetic and potential energy increase.
Kinetic energy decreases; potential energy increases.
Kinetic energy increases; potential energy decreases.
Part B
At the top point of the flight, what can be said about the projectile's kinetic and potential energy?
Both kinetic and potential energy are at their maximum values.
Both kinetic and potential energy are at their minimum values.
Kinetic energy is at a maximum; potential energy is at a minimum.
Kinetic energy is at a minimum; potential energy is at a maximum.
Strictly speaking, it is not the ball that possesses potential energy; rather, it is the system "Earth-ball." Although
we will often talk about "the gravitational potential energy of an elevated object," it is useful to keep in mind that
the energy, in fact, is associated with the interactions between the earth and the elevated object.
Part C

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The potential energy of the object at the moment of launch __________.
ANSWER:
is negative
is positive
is zero
depends on the choice of the "zero level" of potential energy
Usually, the zero level is chosen so as to make the relevant calculations simpler. In this case, it makes good sense
to assume that
at the ground level--but this is not, by any means, the only choice!
Part D
Using conservation of energy, find the maximum height
to which the object will rise.
Express your answer in terms of
and the magnitude of the acceleration of gravity
.
=
You may remember this result from kinematics. It is comforting to know that our new approach yields the same
answer.

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