Experiment 8
Conservation of Energy
The Inclined Plane
A glider coasts down an inclined air track. The potential energy and the kinetic energy of
the glider are found at four different positions, and the total mechanical energy at those positions
are compared.
Theory
The energy relationship for an object moving from some initial position 1 to a final position
2 is
K 1 +U 1 +W n = K 2 +U 2 ,
(1)
2
where K represents the kinetic energy of the body, (1/2)m v , U the gravitational potential energy,
mgy , and W n the work done by forces other than conservative forces that act on the body as it
moves from position 1 to position 2.
When only conservative forces are present, or when the net work done by the forces that are
not conservative is zero, then mechanical energy is conserved and (1) can be written as
K 1 +U 1 = K 2 +U 2 .
(2)
In other words, the total mechanical energy, E = K + U , is conserved.
When a glider coasts down an inclined air track, the frictional forces acting on it are
negligible and we can say that mechanical energy is conserved for this motion. This means that the
sum of the kinetic energy and potential energy for the glider at all positions on the air track must
have the same values.
In this experiment, the kinetic energy and the potential energy of the glider at four positions
on the air track are found, and the total mechanical energy at the four positions are compared. The
inclination of the air track is produced by placing metal "spacers" under the single foot of the air
track. The spacers are of known thickness and produce different angles of inclination,  . From
Figure 1, it can be seen that sin  = h / d , where h is the height of the spacers and d is the
distance between the supports for the air track. In this case d is a distance of one meter. This
makes sin  equal to the value of h in meters.
1
Figure 1. The air track inclined at the angle  by spacers.
The glider is released from rest at the top of the track and accelerates down the incline.
Simultaneously, a spark timer produces sparks at regular intervals of time, t , and the location of
the sparks is recorded on a strip of thermal spark paper. These data are then used to find the kinetic
energy and the potential energy at four positions on the air track.
Figure 2 shows an example of the data recorded on the thermal spark paper. The spacing
indicates that the glider accelerated to the right. The four positions are also marked indicating
where the kinetic energy and the potential energy are to be calculated. Position 1 represents the
position from which the glider was released. Because the glider was released from rest, the kinetic
energy is zero. The gravitational potential energy at 1 relative to 4 is mg y14 , where y14 is the
difference in heights between positions 1 and 4. This height equals d 14 sin  . The quantity d 14 is
the distance from position 1 to position 4 on the spark tape.
Figure 2.
The spark tape with the four positions shown at which kinetic and
potential energies are to be found.
Because the glider is moving at position 2, the glider possesses kinetic energy. The velocity
then needs to be found. In order to accomplish this, the distance from a data point preceding
position 2 to a point following position 2 is measured (  x 2 ). By dividing this distance by twice the
2
time interval of the sparker, the average velocity is found. However, for constant acceleration, the
average velocity between points equals the instantaneous velocity halfway in time between the two
points In this case, the instantaneous velocity at position 2 is v 2 = (  x 2 ) / ( 2t ) . The
gravitational potential energy at 2 is found in same manner as at position 1. The kinetic and
potential energies at positions 3 and 4 are calculated in the same manner as at position 2.
Apparatus
o
o
o
o
air track with air supply and sparker
glider
2 m meter stick
metal spacers
o spark tape
o masking tape
o double pan balance
Procedure
1) Use the double pan balance to measure the mass of the glider. Record its value in
kilograms.
2) Use masking tape to attach a one meter length of spark tape to the center portion of the
yellow-colored mounting strip on the air track.
3) Place the appropriate thickness of metal spacer under the single foot of the air track, and
adjust the spark timer timing interval to the value indicated for your group. (Refer to
Figure 3.) Record the spacer height and the timing interval.
Group
Number
Spacer
Height
(cm)
Timing
Interval
(sec)
Group
Number
Spacer
Height
(cm)
Timing
Interval
(sec)
1
1.00
1/10
7
2.50
1/15
2
1.25
1/10
8
2.75
1/15
3
1.50
1/12
9
3.00
1/15
4
1.75
1/12
10
3.25
1/15
5
2.00
1/12
11
3.50
1/20
6
2.25
1/12
12
3.75
1/20
Figure 3. Values of spacer heights, h , and timing intervals, t , for each group.
4) Carefully place the glider on the air track. Place your finger in front of the glider to
prevent the glider from moving. Turn on the air supply.
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5) Start the timer, then release the glider. Keep the spark timer engaged until the glider
passes the end of the spark tape.
6) Carefully remove the spark tape. Lay the tape on a flat surface and circle the first dot, a
second dot approximately 1/3 the distance down the tape, and third dot another 1/3
distance, and a fourth dot near the end of the tape. These dots represent the positions at
which the kinetic and potential energies are to be calculated.
7) Be sure that the mass of the glider, the spacer height, and the timing interval are
recorded. In a table similar to the one shown in Figure 4, record the distance to dot 4
from dots 1, 2, and 3. These distances are d 14 , d 24 , and d 34 . Also record the distances
 x 2 ,  x 3 , and  x 4 .
data
point
distance, d
(m)
height, y
(m)
1
distance, x
(m)
velocity, v
(m/s)
0
0
2
3
4
0
0
Figure 4. A suggested form for the data table.
Analysis
Complete the table in Figure 4 by calculating the heights, y , of points 1, 2, and 3 relative to
4. Also calculate the velocities at 2, 3, and 4.
Calculate the gravitational potential energies at the four positions from the height
information, and the kinetic energies from the velocity information at the same four positions.
Report these values together with the total mechanical energy at the four positions in a results table
so that the values can be easily compared.
Conclusions
Describe the major sources of error in the experiment and how they affect the values of the
total mechanical energy. Explain whether or not the values of total mechanical energy reflect the
presence of the sources of error.
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