PAGE 1/20 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 ID Major Name Team No. Experiment Lecturer Student's Mentioned Items Experiment Class Date Submission Time Submission Place Introductory 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
PAGE 2/20 1. Objective Student ID Name 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. 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. 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. 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)
PAGE 3/20 (2) Application of Newton's equation of motion 1) Acceleration of an object moving in a straight line with a constant acceleration 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 Since the acceleration of the object is constant, the acceleration vs. time graph is given as shown in Fig. 4. 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. constant (Eq. 8) Fig. 4. Acceleration of an object moving in a straight line with a constant acceleration ( ). 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. 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. Answer the following questions. 1. In this case, show that the acceleration A B and the tension A B are given as follows: B A B A, A B B (3) Object moving in a straight line with a constant acceleration Assume that an object moves in a straight line with a constant acceleration. (Eq. 10) 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. Fig. 5. Velocity of an object moving in a straight line with a constant acceleration ( ).
PAGE 4/20 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. Formula? 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. 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) (Eq. 11) B. Measurement of the Characteristics of the Frictional Force by Using a Computer Interface 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. (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. 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. (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)
PAGE 5/20 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. (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. (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. Fig. 8. Frictional force applied to the object lying on the horizontal plane. (4) Properties of the frictional force 1) Case of the static state 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: 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 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. 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 (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 ( ). are given as follows. (Eq. 18)
PAGE 6/20 (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.
PAGE 7/20 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. Computer interface 1 set It is used to convert analog signals to digital signals. It should be placed at the center of the experiment table. It should be placed inside the basket of the experiment table. Computer interface -to-power adaptor & connection cable Motion sensor -to-computer interface connection cable 1 ea. It is used to connect the computer interface to the wall power. 1 ea. It is used to connect the motion sensor to the computer interface. It should be placed inside the basket of the experiment table. It should be placed inside the basket of the experiment table. USB cable 1 ea. It is used to connect the computer interface to the computer. It should be placed inside the basket of the experiment table. 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 set It is used to measure the position, velocity, and acceleration of a mechanical cart. It should be placed on the track.
PAGE 8/20 Items Quantity Usage Clean up method 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. They should be placed inside the basket of the experiment table. Electric balance 1 set It 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.
PAGE 9/20 B. Measurement of the Characteristics of the Frictional Force by Using a Computer Interface Items Quantity Usage Clean up method Computer 1 set It is used to acquire and analyze data. Computer interface 1 set It is used to convert analog signals to digital signals. It should be placed at the center of the experiment table. It should be placed inside the basket of the experiment table. 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 the experiment table. USB cable 1 ea. It is used to connect the computer interface to the computer. It should be placed inside the basket of the experiment table. Economy force sensor 1 set It is used to measure the force applied to a block. It should be placed inside the basket of the experiment table.
PAGE 10/20 Items Quantity Usage Clean up method Block 3 ea. They consist of one acril surface block, one cork surface block, and one felt surface block. They should be placed inside the basket of the experiment table. Additional masses 4 ea. They are put inside a block so as to change the mass of a block. Rubber board 1 ea. It provides a place to measure the frictional force of a block. Electric balance 1 set It is used to measure the mass of a block and additional masses. They should be placed inside the basket of the experiment table. It should be placed inside the basket of the experiment table. It should be placed at the center of the common experiment table.
PAGE 11/20 < How to Use the Computer Interface) > [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. [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.
PAGE 12/20 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 interface-to-power adaptor & connection cable to connect the computer interface to the wall power and keep the computer interface off. (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. 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 in the menu of the Capstone program and copy the text files to a USB memory prepared beforehand. (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 (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 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 B A measured by the force sensor. Calculate the error, regarding the value measured by the electric balance as the reference value.
PAGE 13/20 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 interface-to-power adaptor & connection cable to connect the computer interface to the wall power and keep the computer interface off. (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 putting max. 4 additional masses inside the acril surface block, repeat the experimental procedures (5) ~ (8). (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. (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. (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. (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. (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. (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. (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.
PAGE 14/20 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 4) Tension measured by the force sensor Acceleration (ms ) Tension (N ) Experiment Value measured by the electric balance [Reference value] Value measured by the motion sensor Value measured by the force sensor Formula B A B A B A Weight of the mass that moves the cart (N ) Error (%)
PAGE 15/20 (2) Mechanical cart + 1 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 4) Tension measured by the force sensor Acceleration (ms ) Tension (N ) Experiment Value measured by the electric balance [Reference value] Value measured by the motion sensor Value measured by the force sensor Formula B A B A B A Weight of the mass that moves the cart (N ) Error (%)
PAGE 16/20 (3) Mechanical cart + 2 additional masses # 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 4) Tension measured by the force sensor Acceleration (ms ) Tension (N ) Experiment Value measured by the electric balance [Reference value] Value measured by the motion sensor Value measured by the force sensor Formula B A B A B A Weight of the mass that moves the cart (N ) Error (%)
PAGE 17/20 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) 2) Acril surface block + 2 additional masses # of additional masses Mass of the block + additional masses (g) Maximum static frictional force max (N ) Kinetic frictional force (N ) Maximum static frictional force max (N ) Kinetic frictional force (N ) 3) Acril surface block + 3 additional masses # of additional masses Mass of the block + additional masses (g) 4) Acril surface block + 4 additional masses # of additional masses Mass of the block + additional masses (g) Maximum static frictional force max (N ) Kinetic frictional force (N ) Maximum static frictional force max (N ) Kinetic frictional force (N )
PAGE 18/20 (2) Cork surface block (3) Felt surface block # of additional masses Mass of the block + additional masses (g) # of additional masses Mass of the block + additional masses (g) Maximum static frictional force max (N ) Kinetic frictional force (N ) Maximum static frictional force max (N ) Kinetic frictional force (N ) 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 block Felt surface block
PAGE 19/20 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. A B (2) Confirm how the relations B, A B, A 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.
PAGE 20/20 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