exp. #1-3 : measurement of the motion of objects on an air...

General Physics Laboratory – Experiment Report

1st Semester, Year 2018

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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

Experiment Class Date Submission Time Submission PlaceIntroductory Physics Office

Report Box #

※ Students should write down Student’s Mentioned Items at the cover page of Experiment Reports, and then complete Experiment Reports by adding contents

to the attached papers (if needed) in terms of the following sections. Contents of the reports should be written by hand, not by a word processor. Instead, it

is allowed that figures and tables are copied and attached to papers. Completed Experiment Reports should be submitted to the place due to the time specified

by Experiment Lecturers.

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max. 50 points (basically 15 points).

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public according to the General Physics Laboratory - Administration Rule.

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a student pirates Experiment Reports of other students regardless of permission

of original creators, the corresponding Experiment Report score and Active

Participation score will be zero in case of exposure of such situation.

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specified by Experiment Lecturers, the corresponding Experiment Report score

will be zero.

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thirds, the grade of General Physics Laboratory will be F level.

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semester, the detailed scores of General Physics Laboratory will be announced

at Introductory Physics Office homepage. Based on the announcement,

students can raise opposition of score error. Since the public evidence is needed

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Reports completed evaluation by Experiment Lecturers until the Experiment

Report score decision

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the corresponding student should submit documents related to absence causes

to Introductory Physics Office regardless of cause occurrence time until the

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Introductory Physics Office, it is noted that the total Experiment Scores will

be zero.

Lecturer's

Mentioned

Items

Submission Time/Place Check Experiment Report Score Evaluation Completion Sign

50



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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



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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.



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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


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


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.



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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.


box.



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Auto launch unit 1 setThe glider attached to the electromagnet is launched by pressing

the launch switch of the auto launch unit.


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.



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< 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.



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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.



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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.


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.



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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.



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5. Experimental Values


Length of the screen attached to glider #1 (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



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# 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



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# 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



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# 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



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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).



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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

exp. #1-3 : measurement of the motion of objects on an air...

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