exp. #1-2 : measurement of the motion of objects by using...

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 : 2018-02-21

Exp. #1-2 : Measurement of the Motion of Objects by Using a Computer Interface and

Understanding of Newton’s Law of Motion |

Measurement of the Characteristics of the Frictional Force by Using a Computer Interface

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.

▶ The Experiment Report score per each Experiment Class is evaluated by

max. 50 points (basically 15 points).

▶ Solutions of Problems in Experiment Reports are not announced to the

public according to the General Physics Laboratory - Administration Rule.

▶ If a student permits other students to pirate one’s Experiment Reports or

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.

▶ Unless Experiment Reports are submitted to the place due to the time

specified by Experiment Lecturers, the corresponding Experiment Report score

will be zero.

▶ If the submission rate of Experiment Reports is less than or equal to two

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

▶ In order to decide grades of General Physics Laboratory at the end of current

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

for the confirmation of opposition, students should keep one’s Experiment

Reports completed evaluation by Experiment Lecturers until the Experiment

Report score decision

▶ If a student is absent from the Experiment Class because of proper causes,

the corresponding student should submit documents related to absence causes

to Introductory Physics Office regardless of cause occurrence time until the

grade decision of General Physics Laboratory.

▶ If a student moves the Experiment Class arbitrarily without permission of

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

A. Measurement of the Motion of Objects by Using a Computer Interface and Understanding of Newton’s Law of Motion : Newton's law of motion will be understood

through the measurement of the relation between the force, the mass, and the acceleration. The basic formulas describing the motion of an object in a straight

line with a constant acceleration will also be understood.

B. Measurement of the Characteristics of the Frictional Force by Using a Computer Interface : The characteristics of the frictional force will be understood through

the measurement of the relation among the frictional force, the normal force, and the roughness of the contact surface.

2. Theory

A. Measurement of the Motion of Objects by Using a Computer Interface and

Understanding of Newton’s Law of Motion

(1) Introduction to Newton's equation of motion

When the mass of an object is constant, the acceleration of the object

increases as the force applied to the object increases. That is, the acceleration

of the object is directly proportional to the force applied to the object

as shown in Fig. 1.

∝ (Eq. 1)

Fig. 1. The relation between acceleration and force for a constant mass.

When the force applied to the object is constant, the acceleration of the

object decreases as the mass of the object increases. That is, the acceleration

of the object is inversely proportional to the mass of the object as shown

in Fig. 2.

∝

(Eq. 2)

Fig. 2. The relation between acceleration and mass for a constant force.

According to Newton's second law of motion, the acceleration of the object

is directly proportional to the force applied to the object and inversely

proportional to the mass of the object which can be summarized as follows:

∝

(Eq. 3)

By introducing the proportionality constant

, the following result can be

obtained.

, (Eq. 4)

Now, let us define the force needed for the object with mass kg to

move with the acceleration ms as kg·ms . From this

definition, so that the following result is obtained.

(Eq. 5)

The SI unit of the force kg·ms is written briefly as N (newton). Since the

force and the acceleration are vectors, the above relation can be rewritten as

follows:

(Eq. 6)

This equation is called as Newton's equation of motion. When various forces

are applied to the object, the net force should be used as follows:

(Eq. 7)

Student ID Name



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(2) Application of Newton's equation of motion

Consider the case that an object A with the mass A on a horizontal plane

is connected to a hanging object B with the mass B by a massless rope through

a frictionless pulley as shown in Fig. 3. When the object B moves downward

due to the gravitational force, let us assume that the length of the rope is constant

and the pulley does not rotate.

Fig. 3. Application of Newton's equation of motion.

If the horizontal plane is frictionless, the gravitational force A , the normal

force A and the tension A are applied to the object A, while the gravitational

force B and the tension B are applied to the object B. If the length of

the rope is constant, the tensions involved in Newton’s third law of motion have

the equal magnitude A B and the two object have the equal

acceleration A B .

※ Answer the following questions.

1. In this case, show that the acceleration A B and the tension

A B are given as follows:

A B

B , A B

AB

(3) Object moving in a straight line with a constant acceleration

Assume that an object moves in a straight line with a constant acceleration .

The velocity of the object increases by a constant rate in the case of

and the velocity of the object decreases by a constant rate in the case of .

Let us consider the basic formulas describing the motion in the case of .

1) Acceleration of an object moving in a straight line with a constant acceleration

Since the acceleration of the object is constant, the acceleration vs. time

graph is given as shown in Fig. 4.

constant (Eq. 8)

Fig. 4. Acceleration of an object moving in a straight line with a constant

acceleration ( ).

Since the acceleration is a constant function of time , the acceleration

vs. time graph has the form of the horizontal line located above the -axis.

Since the acceleration of the object is constant, the force applied to the object

is given as follows:

constant (Eq. 9)

That is, a constant force applied to an object makes the object move with a

constant acceleration.

2) Velocity of an object moving in a straight line with a constant acceleration

Since the velocity can be obtained by integrating the acceleration with

respect to time , the velocity vs. time graph is given as shown in Fig. 5.

(Eq. 10)

Fig. 5. Velocity of an object moving in a straight line with a constant acceleration

( ).



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Since the velocity is a linear function of time , the velocity vs. time

graph has the form of the upwardly rising straight line. In the velocity vs.

time graph, the slope corresponds to the acceleration and the intercept

passing across the -axis corresponds to the initial velocity at time .

From (Eq. 10), the area of the acceleration vs. time graph corresponds to

the velocity change which is a positive value.

3) Position of an object moving in a straight line with a constant acceleration

Since the position can be obtained by integrating the velocity with respect

to time , the position vs. time graph is given as shown in Fig. 6.

(Eq. 11)

Fig. 6. Position of an object moving in a straight line with a constant acceleration

( ).

Since the position is a quadratic function of time , the position vs. time

graph has the form of the downwardly convex parabola. In the position

vs. time graph, the slope corresponds to the velocity and the intercept passing

across the -axis corresponds to the initial position at time . The

increasing slope in the position vs. time graph means that the velocity is

increasing. From (Eq. 11), the area of the velocity vs. time graph corresponds

to the position change which has a positive value as follows:

,

(Eq. 12)

In general, the position is not proportional to the square of time ( ). However,

in the special case when the initial position and the initial velocity is zero ( ,

), the relation ∝ can be made.

4) Summary of the basic formulas describing the motion of an object in a straight

line with a constant acceleration

Regarding the initial position and initial velocity as constants and checking

if the velocity , acceleration , time , and position are used as variables

in the basic formulas, they can be summarized as the following table.

Formula

○ ○ ○ ×

? ○ ○ × ○

○ × ○ ○

× ○ ○ ○

In this table, the formula that has the velocity , acceleration , and position

as variables is missing. That formula can be found by inserting

obtained from the formula to the formula

as follows:

,

(Eq. 13)

B. Measurement of the Characteristics of the Frictional Force by Using a Computer

Interface

(1) Introduction to the frictional force

From usual experience, it is well known that the minimum force needed for an

object to move on a surface. Once the object starts to slide on the surface,

the force needed to keep the speed of the object constant is less than the force

needed to start the object to slide. The static frictional force and the kinetic

frictional force were distinguished by Euler in 1784. The static frictional force

opposes the object moving on the surface. If the object keeps stationary, the

magnitude of the external force is equal to that of the static frictional force

until the static frictional force arrives to its maximum value. If the magnitude

of the external force is greater than that of the maximum static frictional force,

the object starts to slide on the surface and the kinetic frictional force will be

applied. When the object starts to slide on the surface, the friction decreases

rapidly. In an actual situation with high speed, the kinetic frictional force is nearly

constant with a slight decrease as the speed increases. In an actual situation

with low speed, the friction is characterized by the combination of the static

frictional force and the kinetic frictional force.

(2) Static frictional force

Assume that the external force is applied to a stationary object lying on the

surface with friction. If the object keeps stationary, the static frictional force

is equal to the external force .

(Eq. 14)



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If the external force continues to increase until the static frictional force arrives

to its maximum value, the object starts to slide on the surface eventually. The

maximum static frictional force represents the degree of contact between the

object and the surface, and the degree of contact can be described by the normal

force. The maximum static frictional force max is proportional to the normal

force (∝ ), which can be written by introducing the proportionality

constant as follows:

max (Eq. 15)

Here, the subscript means the static state of the object and with no unit

is called as the coefficient of static friction.

(3) Kinetic frictional force

Assume that the object starts to move on the surface due to the external force

greater than the maximum static frictional force. If no external force is applied

after the start of the motion, the object becomes slower to stop eventually due

to the kinetic frictional force. Therefore, the external force equal to the kinetic

frictional force is needed for the object to keep its speed constant. The kinetic

frictional force is proportional to the normal force (∝ ), which can

be written by introducing the proportionality constant as follows:

(Eq. 16)

Here, the subscript means the kinetic state of the object and with no unit

is called as the coefficient of kinetic friction.

(4) Properties of the frictional force

From the external force vs. the frictional force graph as shown in Fig. 7,

the properties of the frictional force can be summarized as follows:

Fig. 7. Relation between the external force and frictional force.

(i) The straight line describing the static frictional force has the angle of ,

if the scales of horizontal and vertical axes are equal.

(ii) Since the maximum static frictional force is greater than the kinetic frictional

force (max ), the coefficient of static friction is greater than the coefficient

of kinetic friction ( ).

(iii) The horizontal line describing the kinetic frictional force implies that the kinetic

frictional force is independent of the magnitude of the external force. In a

theoretical situation, the kinetic frictional force is a constant without regard to

the speed of the object.

(5) Frictional force applied to the object lying on the horizontal plane

Consider the case that the object with the mass lies on the horizontal plane

as shown in Fig. 8. In this case, the gravitational force , the normal force

, the external force , and the frictional force are applied to the object.

Fig. 8. Frictional force applied to the object lying on the horizontal plane.

1) Case of the static state

In the case of the static state, the magnitude of the external force is equal

to that of the static frictional force . Therefore, applying Newton’s

equation of motion, the following results about the net force are obtained.

,

,

Form (Eq. 15), the maximum static frictional force max and the acceleration

of the object are given as follows.

max (Eq. 17)

2) Case of the kinetic state

In the case of the kinetic state, the magnitude of the external force is greater

than that of the kinetic frictional force . Therefore, applying Newton’s

equation of motion, the following results about the net force are obtained.

,

Form (Eq. 16), the kinetic frictional force and the acceleration of the object

are given as follows.

(Eq. 18)



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(i) (Eq. 17) and (Eq. 18) imply that the frictional force is independent of the area

of the contact surface. The coefficients of static and kinetic friction representing

the roughness of the contact surface are independent of the area of the contact

surface also.

(ii) As the roughness of the contact surface decreases, the coefficient of static

and kinetic friction decreases. However, if the contact surface is ground to the

level of atoms or molecules, the object adheres to the contact surface. This

phenomena is called as cold welding unlike welding which requires much heat.

※ Answer the following questions.

2. Investigate other procedures measuring the coefficients of static and

kinetic friction.



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3. Experimental Instruments

A. Measurement of the Motion of Objects by Using a Computer Interface and Understanding of Newton’s Law of Motion

Items Quantity Usage Clean up method

Computer 1 set It is used to acquire and analyze data.It should be placed at the center of the

experiment table.

Computer interface 1 set It is used to convert analog signals to digital signals.It should be placed inside the basket of

the experiment table.

Computer interface

-to-power adaptor &

connection cable

1 ea. It is used to connect the computer interface to the wall power.It should be placed inside the basket of


Motion sensor

-to-computer interface

connection cable

1 ea. It is used to connect the motion sensor to the computer interface.It should be placed inside the basket of


USB cable 1 ea. It is used to connect the computer interface to the computer.It should be placed inside the basket of


Force sensor 1 set It is used to measure the force applied to a mechanical cart.It should be attached to a mechanical

cart.

Motion sensor 1 setIt is used to measure the position, velocity, and acceleration of

a mechanical cart.It should be placed on the track.



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Track 1 set A mechanical cart moves on the track.It should be placed at the center of the

experiment table.

Mechanical cart 1 ea. A mechanical cart moves on the track. It should be placed on the track.

Additional masses 2 ea.They are added to a mechanical cart so as to change the mass

of a mechanical cart.

They should be placed inside the basket

of the experiment table.

Mass that stops a cart 1 ea. It is used to stop a mechanical cart from moving. It should be placed on the track.

Mass that moves a cart 1 ea.A mass connected to a mechanical cart with a rope drops, which

will make the mechanical cart move.



Electric balance 1 setIt is used to measure the mass of a mechanical cart, additional

masses, and masses that stops or moves a cart.

It should be placed at the center of the

common experiment table.



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B. Measurement of the Characteristics of the Frictional Force by Using a Computer Interface


Computer 1 set It is used to acquire and analyze data.It should be placed at the center of the

experiment table.

Computer interface 1 set It is used to convert analog signals to digital signals.It should be placed inside the basket of


Computer interface

-to-power adaptor &

connection cable

1 ea. It is used to the computer interface to the wall power.It should be placed inside the basket of


USB cable 1 ea. It is used to connect the computer interface to the computer.It should be placed inside the basket of


Economy force sensor 1 set It is used to measure the force applied to a block.It should be placed inside the basket of




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Block 3 ea.They consist of one acril surface block, one cork surface block, and

one felt surface block.



Additional masses 4 ea. They are put inside a block so as to change the mass of a block.They should be placed inside the basket


Rubber board 1 ea. It provides a place to measure the frictional force of a block.It should be placed inside the basket of


Electric balance 1 set It is used to measure the mass of a block and additional masses.It should be placed at the center of the

common experiment table.



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< How to Use the Computer Interface) >

[1] After confirming that the computer interface is off, use the computer

interface-to-power adaptor & connection cable to connect the computer

interface to the wall power and keep the computer interface off.

[2] Connect the sensors to the proper analog channels or digital channels and

use the USB cable to connect the computer interface to the computer. Note

that the connection among all experimental instruments should be completed

before the computer interface is turned on. Note that the computer interface

must not be damaged by connecting the computer interface to the computer

while the computer interface is on.

[3] After turning on the computer and the computer interface, open the

Capstone program. If the Capstone window appears, select “Tools → Hardware

Setup → Choose Interface → PASPORT or ScienceWorkshop 750”.

[4] Select the sensors at the positions in the screen that are equivalent to

the positions of the computer interface in the actual experiment by clicking.

[5] After selecting “Displays → Graph or Table” by double-clicking, show graphs

or tables on the screen.

[6] Click the “Record” button of the Capstone program to start the measurement

and check if the acquired data is displayed in the screen. After checking if

the zero status is displayed in the data, click the “Stop” button of the Capstone

program to stop the measurement.

[7] After completing the check of the zero status, click the “Record” button

of the Capstone program again to start the measurement. If the data is

acquired, click the “Stop” button of the Capstone program to stop the

measurement. Repeat this procedure to acquire the correct data.

[8] Save the data in the computer by selecting “File → Export Data → ******.txt”

in the menu of the Capstone program and copy the text files to a USB memory

prepared beforehand.

[9] After the experiment is finished, close the Capstone program and turn off

the computer interface and the computer. Clean up the experimental

instruments according to the suggested method.



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4. Experimental Procedures

A. Measurement of the Motion of Objects by Using a Computer Interface and

Understanding of Newton’s Law of Motion

(1) After confirming that the computer interface is off, use the computer



(2) After measuring the mass A of a mechanical cart and additional masses

located on a mechanical cart by using an electric balance, place the mechanical

cart without additional masses on the track. Control the horizontal status of the

track to keep the mechanical cart at rest. Place the motion sensor on the track.

(3) Connect the force sensor to the analog channel A of the computer interface

and use the motion sensor-to-computer interface connection cable to connect

the motion sensor to the digital channels 1 and 2 of the computer interface.

Connect the yellow and black lines of the motion sensor-to-computer interface

connection cable to the digital channels 1 and 2 of the computer interface,

respectively. Use the USB cable to connect the computer interface to the

computer.

(4) After turning on the computer and the computer interface, open the Capstone

program. If the Capstone window appears, select “Tools → Hardware Setup →

Choose Interface → PASPORT or ScienceWorkshop 750”.

(5) Select “Force Sensor” and “Motion Sensor II” at the positions in the screen

that are equivalent to the positions connected to the computer interface in the

actual experiment by clicking.

(6) After selecting “Displays → Graph” by double-clicking, show the position

vs. time , the velocity vs. time , the acceleration vs. time , and the

tension vs. time graphs on the screen.

(7) Click the “Record” button of Capstone program to start the measurement

and check if the acquired data is displayed in the screen. Check if the zero status

is displayed in the tension vs. time graph, when no force is applied to

the force sensor. Otherwise, set it to zero by pressing the TARE button of the

force sensor. Click the “Stop” button of the Capstone program to stop the

measurement.

(8) After measuring the mass B that moves the cart by using an electric balance,

connect the mass to the hook of the force sensor with a rope and prevent the

mechanical cart from moving by locating the mass that stops the cart. Click the

“Record” button of the Capstone program again to start the measurement (at

the time ) and remove the mass that stops the cart to make the mechanical

cart start to move (at the time ). When the mass that moves the cart drops

onto the ground (at the time ), prevent the mechanical cart from moving by

locating the mass that stops the cart and click the “Stop” button of the Capstone

program to stop the measurement (at the time ). Repeat this procedure to

acquire the correct data.

(9) Save the data in the computer by selecting “File → Export Data → ******.txt”



(10) After changing the mass A of the mechanical cart by adding max. 2

additional masses to the mechanical cart, repeat the experimental procedures

(6) ~ (9).

(11) If the measurement is finished, close the Capstone program and turn off

the computer interface and the computer. Clean up the experimental instruments

according to the suggested method.

(12) Draw the position vs. time , the velocity vs. time , the acceleration

vs. time , and the tension vs. time graphs by using a proper program.

The tension is given by a negative value so that the absolute value of

should be used to draw the tension vs. time graph. Show only the data

that has a physical meaning (from the time to the time ) on the graphs.

(13) Find the acceleration and the tension from the graphs, and investigate

the acquired data in terms of Newton's law of motion and the basic formulas

describing the motion of an object in a straight line with a constant acceleration.

(14) Compare the weight B of the mass that moves the cart measured

by the electric balance, A B measured by the motion sensor, and

A

A B measured by the force sensor. Calculate the error, regarding

the value measured by the electric balance as the reference value.



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B. Measurement of the Characteristics of the Frictional Force by Using a Computer

Interface

(1) After confirming that the computer interface is off, use the computer



(2) Connect the economy force sensor to the analog channel A of the computer

interface and use the USB cable to connect the computer interface to the

computer.

(3) After turning on the computer and the computer interface, open the Capstone

program. If the Capstone window appears, select “Tools → Hardware Setup →

Choose Interface → PASPORT or ScienceWorkshop 750”.

(4) Select “Force Sensor, Economy” at the position in the screen that is equivalent

to the position connected to the computer interface in the actual experiment

by clicking.

(5) After selecting “Displays → Graph” by double-clicking, show the frictional

force vs. time graph on the screen.

(6) Click the “Record” button of the Capstone program to start the measurement

and check if the acquired data is displayed on the screen. Check if the zero

status is displayed in the frictional force vs. time graph, when no force

is applied to the economy force sensor. Otherwise, set it to zero by pressing

the TARE button of the economy force sensor. Click the “Stop” button of the

Capstone program to stop measurement.

(7) After putting one additional mass inside an acril surface block, measure the

mass of the acril surface block and one additional mass using an electric

balance. Locate the acril surface block on the rubber board and connect the

hook of the acril surface block to the hook of the economy force sensor with

a rope. After inserting one's fingers into the finger hold of the economy force

sensor, click the “Record” button of Capstone program again to start the

measurement (at the time ) and pull the acril surface block (at the time ).

Increase the force pulling the acril surface block steadily until the acril surface

block starts to move and keep the force constant while the acril surface block

is moving. Stop pulling on the acril surface block (at the time ) and click the

“Stop” button of the Capstone program to stop the measurement (at the time

). Repeat this procedure to acquire the correct data.

(8) Save the data in the computer by selecting “File → Export Data → ******.txt”



(9) After putting max. 4 additional masses inside the acril surface block, repeat

the experimental procedures (5) ~ (8).

(10) Repeat the experimental procedures (5) ~ (8) by using the cork surface block

and the felt surface block. For the cork surface block and the felt surface block,

use the same number of additional masses.

(11) If the measurement is finished, close the Capstone program and turn off

the computer interface and the computer. Clean up the experimental instruments

according to the suggested method.

(12) Draw the frictional force vs. time graph by using a proper program.

The frictional force is given by a negative value so that the absolute value

of should be used to draw the frictional force vs. time graph. Show

only the data that has a physical meaning (from the time to the time )

on the graphs.

(13) Find the maximum static frictional force max and the kinetic frictional

force from the graphs, and calculate the coefficient of static friction and

the coefficient of kinetic friction . Investigate the relations among the frictional

force, the mass of the object, and the roughness of the contact surface.



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5. Experimental Values

A. Measurement of the Motion of Objects by Using a Computer Interface and Understanding of Newton’s Law of Motion

(1) Mechanical cart + 0 additional mass

# of additional masses Mass A of the mechanical cart

+ additional masses (g )

Mass B that moves the cart (g ) Gravitational acceleration (ms )

1) Position measured by the motion sensor 2) Velocity measured by the motion sensor

3) Acceleration measured by the motion sensor

Acceleration (ms )

4) Tension measured by the force sensor

Tension (N )

Experiment FormulaWeight of the mass

that moves the cart (N )

Error

(%)Value measured by the

electric balance [Reference value] B

Value measured by the

motion sensor A B


force sensor A

A B



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(2) Mechanical cart + 1 additional mass






Acceleration (ms )


Tension (N )



Error




motion sensor A B


force sensor A

A B



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(3) Mechanical cart + 2 additional masses






Acceleration (ms )


Tension (N )



Error




motion sensor A B


force sensor A

A B



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B. Measurement of the Characteristics of the Frictional Force by Using a Computer Interface

(1) Acril surface block

1) Acril surface block + 1 additional mass

# of additional masses

Mass of the block + additional masses (g )

Maximum static frictional force max (N )

Kinetic frictional force (N )

2) Acril surface block + 2 additional masses

















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(2) Cork surface block





(3) Felt surface block





※ For the cork surface block and the felt surface block, use the same number of additional masses.

(4) Calculation of the coefficient of friction

Gravitational acceleration (ms )

Block# of additional

masses

Mass of the block

+ additional masses

(g )

Maximum

static frictional force

max (N )

Kinetic frictional force

(N )

Coefficient of

static friction

max

Coefficient of

kinetic friction

Acril

surface block

Average

Cork

surface blockFelt

surface block



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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. (1) Explain the relation among the mass of the mechanical cart, the acceleration, and the tension.

(2) Confirm how the relations B , A B , A

A B can be made.

2. (1) Explain the relation between the frictional force and the mass of the block when the coefficient of friction is constant.

(2) Explain the relation between the frictional force and the coefficient of friction when the mass of the block is constant.

3. Explain why the values measured from the force sensor are displayed as negative values.

4. (1) Try the appropriate fitting in the vs. , vs. , vs. , and vs. graphs.

(2) Try the appropriate fitting in the frictional force vs. graphs.



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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. #1-2 : measurement of the motion of objects by using...

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