exp. #1-3 : measurement of the motion of objects on an air...
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General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 1/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
Exp. #1-3 : Measurement of the Motion of Objects on an Air Track and
Understanding of the Conservation Law of Linear Momentum
Student's
Mentioned
Items
Student ID Major Name Team No. Experiment Lecturer
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General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 2/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
1. Objective
The conservation law of linear momentum will be demonstrated through the measurement for the one-dimensional collision of objects moving along a straight
line.
2. Theory
(1) Classification of collisions in terms of the coefficient of restitution
Assume that two objects moving along a straight line collide with each other.
If and are the velocities of the two objects before the collision, while
and are the velocities of two objects after the collision, the coefficient
of restitution is defined as the ratio of the relative velocity after the collision
to the relative velocity before the collision. The coefficient of restitution can
be written as follows:
(Eq. 1)
Here, the sign implies that the direction of the relative velocity after the
collision is opposite to that of the relative velocity before the collision. The range
of the coefficient of restitution is ≤ ≤ . For the elastic collision, ,
while for the perfectly inelastic collision, .
(2) Elastic collision
Consider an elastic collision between two objects with masses and as
shown in Fig. 1. For the elastic collision, the relative velocities before and after
the collision are the same, and both the kinetic energy and the linear momentum
of the system are conserved as follows:
(Eq. 2)
(Eq. 3)
(Eq. 4)
Fig. 1. Elastic collision of two objects moving along a straight line.
※ Answer the following questions.
1. In general elastic collision, show that the velocities of two objects
after the collision are given as follows:
(Eq. 5)
(Eq. 6)
If the object with mass is at rest before the collision ( ), (Eq. 5) and
(Eq. 6) can be rewritten as follows:
(Eq. 7)
(Eq. 8)
1) Case of
In the case of two objects with the same mass ( ), and
can be obtained. That is, the moving object becomes stationary after
the collision, while the stationary object moves with the final velocity equal to
the initial velocity of the moving object after the collision. In other words, the
velocity of the moving object and the velocity of the stationary object are
interchanged each other after the collision.
2) Case of ≫
In the case of the moving object with a huge mass compared to the stationary
object ( ≫ ), ≈ and ≈ can be obtained. That is, the
moving object keeps moving with a nearly constant velocity after the collision,
while the stationary object moves with the final velocity nearly twice of the initial
velocity of a moving object after the collision. This situation is often referred
to as the slingshot effect.
Student ID Name
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 3/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
3) Case of ≪
In the case of the stationary object with a huge mass compared to the moving
object ( ≪ ), ≈ and ≈ can be obtained. That is, the
stationary object keeps stationary nearly after the collision, while the moving
object is repulsed with the final velocity nearly opposite to the initial velocity.
(3) Perfectly inelastic collision
Consider a perfectly inelastic collision between two objects with masses and
as shown in Fig. 2. For the perfectly inelastic collision, two objects are
combined together after the collision, and the linear momentum of the system
is conserved, while the kinetic energy of the system decreases as follows:
(Eq. 9)
(Eq. 10)
(Eq. 11)
Fig. 2. Perfectly inelastic collision of two objects moving along a straight line.
In general, the velocity of the combined object after the collision can be obtained
from (Eq. 10) as follows:
(Eq. 12)
If the object with mass is at rest before the collision ( ), (Eq. 12) can
be rewritten as follows:
(Eq. 13)
The following calculation shows how the kinetic energy of the system decreases.
That is, the loss ratio of the kinetic energy of the system is determined from the
mass ratio of the moving object to the stationary object. Note that the loss ratio
of the kinetic energy of the system is independent of the initial velocity of the
moving object.
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 4/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
3. Experimental Instruments
Items Quantity Usage Clean up method
Air Track 1 setThe air flow out of the small holes in the air track decreases the
friction applied to the gliders.
It should be placed at the center of the
experimental table.
Photogate 2 ea. They are used to measure the velocities of the gliders. They should be attached to the stands.
Clamp & Stand 2 ea. They are used to attach the photogates to the stands.They should be placed at the center of
the experimental table.
Photogate
-to-photogate timer
connection cable
2 ea. They are used to connect the photogates to the photogate timer.They should be placed inside the basket
of the experimental table.
Air blower
-to-power
connection cable
1 ea. It is used to connect the air blower to the wall power.It should be placed inside the basket of
the experimental table.
Air blowing tube 1 ea. It is used to connect the air blower to the air track.It should be placed inside the basket of
the experimental table.
Air blower 1 set It is used to supply the air flow to the air track.It should be placed at the center of the
experimental table.
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 5/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
Items Quantity Usage Clean up method
Glider 2 ea. The gliders move on the air track.They should be placed inside the plastic
box.
Screen 2 ea.The screens are attached to the gliders to make them detectable
by the photogates.
They should be placed inside the plastic
box.
Additional masses 1 setThey are added to the gliders so as to change the mass of the
gliders.
It should be placed inside the plastic
box.
Metal bumper 1 ea. It is used to attach the glider to the electromagnet.It should be placed inside the plastic
box.
Band bumper 2 ea. They are attached to the gliders for the elastic collision.They should be placed inside the plastic
box.
Pin bumper &
Rubber bumper1 ea. It is attached to the gliders for the perfectly inelastic collision.
It should be placed inside the plastic
box.
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 6/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
Items Quantity Usage Clean up method
Auto launch unit 1 setThe glider attached to the electromagnet is launched by pressing
the launch switch of the auto launch unit.
It should be placed inside the plastic
box.
Electromagnet 1 set The glider is attached to the electromagnet.It should be placed inside the plastic
box.
Photogate timer 1 set It is used to measure the velocities of the gliders.It should be placed inside the plastic
box.
Auto launch unit
-to-power
connection cable
1 ea. It is used to connect the auto launch unit to the wall power.It should be placed inside the plastic
box.
Electromagnet
-to-auto launch unit
connection cable
2 ea.They are used to connect the electromagnet to the auto launch
unit.
They should be placed inside the plastic
box.
Electric balance 1 set It is used to measure the mass of the gliders.It should be placed at the center of the
common experiment table.
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 7/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
< How to Use the Photogate Timer >[Model 1]
[Model 2]
[1] After confirming that the photogate timer is off, connect the photogate
timer to the wall power and keep the photogate timer off. According to the
experimental procedures, use the photogate-to-photogate timer connection
cables to connect the photogates to the measurement channel #1 (CH1) and/or
#2 (CH2) of the photogate timer. If the size between the measurement channel
of the photogate timer and the photogate-to-photogate timer connection
cable is different, the adaptor can be used. Note that the connection between
the photogates and the photogate timer should be completed before the
photogate timer is turned on.
[2] After turning on the photogate timer, set it to the proper measurement
mode by pressing one of the measurement mode switch and then pressing
the reset switch in the case of [Model 1] or by pressing FUNCTION button
several times in the case of [Model 2]. Note that the switches and buttons
of the photogate timer may be damaged if they are pressed too hard.
[3] While blocking the signal detection line of the photogates, check if the
photogate timer and the photogates are working in accordance with the
measurement mode. In some models of the photogate timer, the working state
of the photogate timer can be checked by the LED light attached to the
photogates or the sound generated from the photogate timer.
[4] Note that the photogate timer and the photogates should be handled
carefully in order to prevent damaged during the measurement. Since bright
light may cause a malfunction to the infrared light photogates, shading sunlight
is required.
[5] After the measurement is finished, turn off the photogate timer and clean
up the experimental instruments according to the suggested method. The
adaptors should be removed from the measurement channels of the photogate
timer. Note that the photogate timer may be damaged if the adaptors are
not removed.
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 8/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
4. Experimental Procedures
(0) Setting before the experiment
1) After confirming that the air blower is off, use the air blower-to-power
connection cable to connect the air blower to the wall power and keep the air
blower off. Use the air blowing tube to connect the air blower to the air track.
2) After placing the electromagnet firmly at the edge of the air track, place a
band bumper at the opposite edge of the air track in order to prevent the gliders
from bumping into the air track. Use two electromagnet-to-auto launch unit
connection cables to connect the electromagnet to the auto launch unit. Note
that the bend or scar formed by careless treatment of the air track may harm
the linearity of the motion of objects on the air track. After confirming that the
auto launch unit is off, use the auto launch unit-to-power connection cable to
connect the auto launch unit to the wall power and turn on the auto launch
unit.
3) After confirming that the photogate timer is off, connect the photogate timer
to the wall power and keep the photogate timer off. Place two stands attaching
the photogates near the air track and use two photogate-to-photogate timer
connection cables to connect two photogates to the photogate timer. When
connecting two photogates to the photogate timer, connect one photogate
located near the electromagnet (photogate #1) and the other photogate located
far from the electromagnet (photogate #2) to the measurement channels #1
and #2 of the photogate timer respectively.
4) After placing one glider near the electromagnet (glider #1) and the other
glider far from the electromagnet (glider #2) on the air track, place photogate
#1 between the electromagnet and glider #1 and photogate #2 far from glider
#2. Note that a scar on the track may be occurred by careless treatment of
the gliders when they are on the air track. If photogate #1 is placed excessively
near glider #1, an increasing velocity of glider #1 will be measured. On the
contrary, if photogate #1 is placed too far from glider #1, a decreasing velocity
of glider #1 will be measured. Therefore, photogate #1 should be located in
the region where glider #1 moves with a nearly constant velocity. If photogate
#2 is placed excessively near glider #2, the measurement for glider #2 will start
before the measurement for glider #1 ends or an increasing velocity of glider
#2 will be measured. On the contrary, if photogate #2 is placed too far from
glider #2, a decreasing velocity of glider #2 will be measured. Therefore,
photogate #2 should be located in the region where glider #2 moves with a
nearly constant velocity.
5) After turing on the photogate timer, set it to the measurement mode S1 by
pressing the FUNCTION button of the photogate timer, and then clear the data
stored in the photogate timer by pressing the CLEAR button of the photogate
timer. While blocking the signal detection line of the photogates, check if the
photogate timer and the photogates are working in accordance with the
measurement mode S1.
6) After confirming that the air blower is set to the minimum, turn on the air
blower and increase the output of the air flow slowly. While supplying the air
flow to the air track, check the horizontal state of the air track so that the gliders
are initially at rest. More output of the air flow decreases the friction applied
to the gliders effectively, but too much output of the air flow makes the gliders
move on the air track even if the air track is at the horizontal state. In order
to find the suitable output of the air flow, place a band bumper at the edge
of the air track and make a slight slope for the air track. Then change the output
of the air flow to make the glider bounce back to its original position as close
as possible. However, if the mass of the glider changes, the suitable output of
the air flow changes so that the above method is not useful at all times.
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 9/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
(1) Elastic collision
1) Measure the lengths and of the screens attached to gliders #1 and
#2 by using the scale attached to the air track. After measuring the mass
of glider #1 attaching a screen and a metal bumper by using an electric balance,
check if glider #1 passes through photogate #1 and attach glider #1 to the
electromagnet. After measuring the mass of glider #2 attaching a screen
and a band bumper by using an electric balance, check if glider #2 passes through
photogate #2 and place glider #2 between photogate #1 and photogate #2.
2) After clearing the data stored in the photogate timer by pressing the CLEAR
button of the photogate timer, launch glider #1 attached to the electromagnet
by pressing the launch switch of the auto launch unit. If glider #1 passes through
photogate #1, the time for glider #1 to pass through photogate #1 is
displayed in the photogate timer. Press the MEMORY button of the photogate
timer to display the first data in the photogate timer which corresponds to .
Calculate the velocity
of glider #1 before the collision from
and the length of the screen attached to glider #1. In the case when the
auto launch unit fails to operate, attach glider #1 to the electromagnet by hand
and then gently release glider #1.
3) If glider #2 repulsed by glider #1 passes through photogate #2, the time
for glider #2 to pass through photogate #2 is displayed in the photogate
timer. Press the MEMORY button of the photogate timer to display the second
data in the photogate timer corresponds to . Calculate the velocity
of glider #2 after the collision from and the length of
the screen attached to glider #2. Stop the motion of glider #2 by one's hand
before glider #2 bumps into the end of the air track.
4) Calculate the theoretical velocity
of glider #2 after the
collision from the mass and the initial velocity of glider #1 and the
mass of glider #2, and compare it with the experimental value.
5) After adding additional masses to glider #1 and glider #2, repeat the
experimental procedures. In order to keep the gliders at the same horizontal
height on the track, place additional masses with the same masses on both bars
of the gliders.
※ Answer the following questions.
2. Calculate the theoretical velocity
of glider #1
after the collision and compare it with the result checked if glider #1
moves forward or backward after collision in the actual experiment.
(2) Perfectly inelastic collision
1) After measuring the mass of glider #1 attaching a screen, a metal bumper,
and a pin bumper by using an electric balance, check if glider #1 passes through
photogate #1 and then attach glider #1 to the electromagnet. After measuring
the mass of glider #2 attaching a screen and a rubber bumper by using
an electric balance, check if glider #2 passes through photogate #2 and place
glider #2 between photogate #1 and photogate #2.
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 10/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
2) After clearing the data stored in the photogate timer by pressing the CLEAR
button of the photogate timer, launch glider #1 attached to the electromagnet
by pressing the launch switch of the auto launch unit. If glider #1 passes through
photogate #1, the time for glider #1 to pass through photogate #1 is
displayed in the photogate timer. Press the MEMORY button of the photogate
timer to display the first data in the photogate timer which corresponds to .
Calculate the velocity
of glider #1 before the collision from
and the length of the screen attached to glider #1. In the case when the
auto launch unit fails to operate, attach glider #1 to the electromagnet by hand
and then gently release glider #1.
3) If glider #2 combined with glider #1 passes through photogate #2, the time
for the glider #2 to pass through photogate #2 is displayed in the photogate
timer. Press the MEMORY button of the photogate timer to display the second
data in the photogate timer which corresponds to . Calculate the velocity
of the combined glider after the collision from and the length
of the screen attached to glider #2. Stop the motion of the combined glider
by one’s hand before glider #2 bumps into the end of the air track.
4) Calculate the theoretical velocity
of the combined glider
after the collision from the mass and the initial velocity of glider #1
and the mass of glider #2, and compare it with the experimental value.
5) After adding additional masses to glider #1 and glider #2, repeat the
experimental procedures. In order to keep the gliders at the same horizontal
height on the track, place additional masses with the same masses on both bars
of the gliders.
6) If the measurement is finished, turn off the photogate timer and control the
air blower to the minimum so as to turn off the air blower. Clean up the
experimental instruments according to the suggested method.
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 11/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
5. Experimental Values
(1) Elastic collision
Length of the screen attached to glider #1 (cm )
Length of the screen attached to glider #2 (cm )
# of
Measurements
Mass of
glider #1
(g )
Mass of
glider #2
(g )
Time for
glider #1
to pass
through
photogate #1
(s)
Time for
glider #2
to pass
through
photogate #2
(s)
Velocity of
glider #1
before the
collision
(ms)
Velocity of glider #2 after the collision
Theoretical
value
(ms)
Experimental
value
(ms)
Error
(%)
#1
Average
#2
Average
#3
Average
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 12/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
Length of the screen attached to glider #1 (cm )
Length of the screen attached to glider #2 (cm )
# of
Measurements
Mass of
glider #1
(g )
Mass of
glider #2
(g )
Time for
glider #1
to pass
through
photogate #1
(s)
Time for
glider #2
to pass
through
photogate #2
(s)
Velocity of
glider #1
before the
collision
(ms)
Velocity of glider #2 after the collision
Theoretical
value
(ms)
Experimental
value
(ms)
Error
(%)
#4
Average
#5
Average
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 13/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
(2) Perfectly inelastic collision
Length of the screen attached to glider #1 (cm )
Length of the screen attached to glider #2 (cm )
# of
Measurements
Mass of
glider #1
(g )
Mass of
glider #2
(g )
Time for
glider #1
to pass
through
photogate #1
(s)
Time for
glider #2
to pass
through
photogate #2
(s)
Velocity of
glider #1
before the
collision
(ms)
Velocity of the combined glider after the collision
Theoretical
value
(ms)
Experimental
value
(ms)
Error
(%)
#1
Average
#2
Average
#3
Average
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 14/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
Length of the screen attached to glider #1 (cm )
Length of the screen attached to glider #2 (cm )
# of
Measurements
Mass of
glider #1
(g )
Mass of
glider #2
(g )
Time for
glider #1
to pass
through
photogate #1
(s)
Time for
glider #2
to pass
through
photogate #2
(s)
Velocity of
glider #1
before the
collision
(ms)
Velocity of the combined glider after the collision
Theoretical
value
(ms)
Experimental
value
(ms)
Error
(%)
#4
Average
#5
Average
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 15/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
6. Results and Discussions (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should
be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.)
※ Write down contents in terms of the following key points.
1. In the case of the experimental values consistently larger or smaller than the theoretical values of the velocity after the collision, estimate the height
change or the slope of the air track by using the conservation law of mechanical energy.
2. In the case of the small experimental values of the velocity after the elastic collision (coefficient of restitution ) and the large experimental values
of the velocity after the perfectly inelastic collision (coefficient of restitution ≠ ), calculate or alternative quantity by using the conservation law
of linear momentum.
3. In the case of too small experimental values of the velocity due to the frictional force caused by the gliders with large mass or the low output of
air flows, estimate the coefficient of friction by using the conservation law of energy (theory experiment , where is the traveling distance of the
glider moving on the air track).
General Physics Laboratory – Experiment Report
1st Semester, Year 2018
PAGE 16/16
Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-03-09
7. Solution of Problems (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should
be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.)
8. Reference