E-305
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EXPERIMENTS Conservation of mechanical energy during a free fall
the timer tape, one can find for each mark both how far
the weight has fallen from the initial position as well as
the speed of the weight at the moment in question.
The first portion of the timer tape could look as follows
after a typical experiment.
Figure 1
It is apparent that the distance between the marks incre-
ases as the speed of the falling weight increases. For
each of the selected points on the tape two distances L
∇
and s should be measured as illustrated in figure 2
∇
s
Figure 2
L
In order to determine the speed of the weight at a parti-
cular point one can use the fundamental definition of
∇ ∇ ∇
speed: v = s/ t, where s is the distance through
∇
which the weight has traveled in the time interval
t.
For a given mark on the tape using the distance from the
previous mark to the following mark corresponds to a
time interval of 0.02 seconds
2
. The speed is thus given
∇
by v = s/0.02 s.
For each of the selected marks on the timer tape the
potential energy E
pot
and the kinetic energy E
kin
can be
determined.
Purpose
In this exercise the conservation of mechanical energy
during a free fall is studied.
the mechanical energy can be written as
Theory
The total mechanical energy of an object is determined
by the sum of its potential energy and its kinetic energy
The potential energy can be set equal to zero at the initial
position of the weight. Thus the potential energy will be
negative during the fall, while the kinetic energy will
increase due to the increase in speed. The sum of the
In this experiment we will consider the kinetic energy to
potential and the kinetic energy should thus remain close
be equal to zero when the accelerated mass is at rest
to zero.
(v = 0). The zero point of the potential energy will be the
position of the accelerated mass just before it is re-
leased. As the potential energy decreases (becomes
negative) during the fall of the mass, the kinetic energy
1 This is only true for an AC (mains) frequency of 50 Hz.
will increase (becomes positive) by – ideally – the same
If the frequency is 60 Hz the correct number is 1/120.
amount, so that the total mechanical energy should
equal zero. In practice some energy losses due to fricti-
2 For 60 Hz mains frequency the time interval is 0.01667 seconds.·
on, air resistance, etc. will be observed.
By letting a weight pull a timer tape through a timer, the
timer can place a mark on the tape every 1/100 of a
second
1
and by selecting a number of marks (e.g. 20) on
®
Science Equipment for Education Physics
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