Exp. #1-6 : Measurement of the Motion of Objects on an Inclined Plane and Understanding of the Conservation Law of Mechanical Energy

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1 PAGE 1/14 Exp. #1-6 : Measurement Motion of Objects on an Inclined Plane and Understanding Conservation Law of Mechanical Energy 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 following sections. Contents 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 2/14 1. Objective Student ID Name The acceleration and the velocity of objects moving on an inclined plane will be measured in this experiment.

2 PAGE 2/14 1. Objective Student ID Name The acceleration and the velocity of objects moving on an inclined plane will be measured in this experiment. In addition, the conservation law of mechanical will be considered for objects in translational motion and rotational motion simultaneously. 2. Theory (1) Motion with a constant acceleration 2) Consideration conservation law of mechanical Assume that an object at rest initially starts to move with a constant acceleration on an inclined plane. If the initial velocity object is and the object moves downward on the inclined plane by the distance during time, the acceleration and the velocity object at time are given as the following.,, (Eq. 1) (Eq. 2) If the object moves downward on the inclined plane by the distance, the height object decreases by sin and the potential object changes by sin. Instead, the velocity and the angular speed object increase by and respectively, and the kinetic due to the translational motion and rotational motion changes by and respectively. Therefore, the change mechanical is given as follows: (2) Motion of an object sliding without rolling on an inclined plane sin (Eq. 6) Consider the motion of an object sliding without rolling on an inclined plane as shown in Fig. 1. Since the mechanical is constant in the case of no friction ( ) and the object slides without rolling ( ), the following result is obtained from (Eq. 6). sin (Eq. 7) Differentiating (Eq. 7) with respect to time, the acceleration object can be determined as follows: sin, sin (Eq. 8) Here, the velocity object is used. Note that this result is the same as (Eq. 5). Fig. 1. Motion of an object sliding without rolling on an inclined plane. If the object moves downward on the inclined plane by the distance, the height object decreases by sin and the velocity object increases 1) Consideration of Newton s law of motion In this case, the gravitation force and the normal force are applied to by the following result., sin sin, (Eq. 9) the object, but the frictional force is neglected. Therefore, applying Newton s law of motion, the following results about the net force are obtained. sin, sin (Eq. 3) cos, cos cos (Eq. 4) From the (Eq. 3), the acceleration object can be determined as follows. Answer the following questions. 1. Explain the relation between the acceleration and the mass object when the angle inclined plane is constant. sin (Eq. 5)

3 PAGE 3/14 (3) Motion of an object rolling without sliding on an inclined plane Consider the motion of an object rolling without sliding on an inclined plane as shown in Fig. 2. sin (Eq. 16) Differentiating (Eq. 16) with respect to time, the acceleration object can be determined as follows: sin, sin (Eq. 17) Here, the velocity object is used. Note that this result is the same as (Eq. 15). If the object is a solid sphere with a radius, the rotational inertia of this object is known as and the acceleration object is given as follows: sin (Eq. 18) Fig. 2. Motion of an object rolling without sliding on an inclined plane. If the object has a shape with a radius, the following relation between the velocity and the angular speed object can be made., (Eq. 10) In addition, the following relation between the acceleration and the angular acceleration object can be made., (Eq. 11) Note that the point where the object rolling without sliding is in contact with the inclined plane is at rest all the time. 1) Consideration of Newton s law of motion Since the point where the object is in contact with the inclined plane is at rest, the frictional force is treated as static. In this case, not only the gravitational force and the normal force but also the static frictional force is applied to the object. Therefore, applying Newton s law of motion, the following results about the net force and the net torque are obtained. sin, sin (Eq. 12) cos, cos cos (Eq. 13),, (Eq. 14) Inserting (Eq. 14) into (Eq. 12), the acceleration object can be determined as follows: sin, sin (Eq. 15) If the object moves downward on the inclined plane by the distance, the height object decreases by sin and the velocity object increases by the following result., sinsin, (Eq. 19) Answer the following questions. 2. In this experiment, it is assumed that the object rolls without sliding ( ). If the object rolls and slides simultaneously ( ), the kinetic frictional force instead static frictional force is applied to the object. Under such a situation, investigate how the motion of the object can be described. 2) Consideration conservation law of mechanical Since the point where the object is in contact with the inclined plane is at rest, there is no work done by the static frictional force. Since the mechanical is constant in the case of no work done by friction ( ) and the object rolls without sliding, the following result is obtained from (Eq. 6).

PAGE 4/14 3. Experimental Instruments Items Quantity Usage Clean up method Inclined plane 1 set A mechanical cart and a steel bead move on the inclined plane.

They should be attached to the inclined plane. Clamp & Stand 2 ea. They are used to attach photogates to the inclined plane. They should be attached to the inclined plane.

4 PAGE 4/14 3. Experimental Instruments Items Quantity Usage Clean up method Inclined plane 1 set A mechanical cart and a steel bead move on the inclined plane. It should be placed at the center experiment table. Photogate 2 ea. They are used to measure the time for a mechanical cart and a steel bead that move downward on the inclined plane. They should be attached to the inclined plane. Clamp & Stand 2 ea. They are used to attach photogates to the inclined plane. They should be attached to the inclined plane. Photogate timer 1 set It is used to measure the time for a mechanical cart and a steel bead to move downward on an inclined plane. It should be placed inside the basket of the experiment table. Mechanical cart 1 ea. The acceleration and the velocity of a mechanical cart moving on the inclined plane is measured. It should be placed inside the basket of the experiment table. Steel bead 1 ea. The acceleration and the velocity of a steel bead moving on the inclined plane are measured. It should be placed inside the basket of the experiment table. Photogate -to-photogate timer connection cable 1 ea. It is used to connect the photogate to the photogate timer. It should be placed inside the basket of the experiment table. Vernier calipers 1 ea. It is used to measure the radius of a steel bead. It should be placed inside the basket of the common experiment table. Electric balance 1 set It is used to measure the mass of a mechanical cart and a steel bead. It should be placed at the center common experiment table.

PAGE 5/14 [Model 1] < How to Use the Photogate Timer > [4] Note that the photogate timer and the photogates should be handled carefully in order to prevent damaged during the measurement.

[5] After the measurement is finished, turn off the photogate timer and clean up the experimental instruments according to the suggested method.

5 PAGE 5/14 [Model 1] < How to Use 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 photogate timer. Note that the photogate timer may be damaged if the adaptors are [Model 2] not removed. [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) photogate timer. If the size between the measurement channel 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 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 photogate timer may be damaged if they are pressed too hard. [3] While blocking the signal detection line photogates, check if the photogate timer and the photogates are working in accordance with the measurement mode. In some models photogate timer, the working state photogate timer can be checked by the LED light attached to the photogates or the sound generated from the photogate timer.

the integer value main scale. 2 Find the position where the lines main scale and the vernier scale meet, and read the decimal value vernier scale. 3 The measured scale is given by the sum two values.

6 PAGE 6/14 < How to Use the Vernier Callipers > [1] For digital vernier calipers, the measured scale is directly displayed. For the analog vernier calipers, the measured scale should be read as follows: 1 Find the position pointed by the leftmost line vernier scale (it does not mean the left end vernier scale), and read the integer value main scale. 2 Find the position where the lines main scale and the vernier scale meet, and read the decimal value vernier scale. 3 The measured scale is given by the sum two values. (Example) In the case of 39 scales main scale divided by 20 identical parts, it is possible to measure up to 0.05 mm. Main scale 9 + vernier scale 0.15 = 9.15 mm [2] By using the outside jaws, the inside jaws and the depth bar vernier calipers, the outer radius, the inner radius, and the depth object can be measured respectively. The following picture shows the correct usage vernier calipers.

Use two photogate-to-photogate timer connection cables to connect two photogates to the photogate timer.

2) After turning on the photogate timer, set it to the measurement mode S2 by pressing the FUNCTION button photogate timer, and then clear the data stored in the photogate timer by pressing the CLEAR

3) In order to set the initial velocity mechanical cart to zero, place the mechanical cart to the upper photogate as close as possible.

7 PAGE 7/14 4. Experimental Procedures (0) Setting before the experiment 1) After confirming that the photogate timer is off, connect the photogate timer to the wall power and keep the photogate timer off. 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 the upper and lower photogates attached to the inclined plane to the measurement channels #1 and #2 photogate timer respectively. 2) After turning on the photogate timer, set it to the measurement mode S2 by pressing the FUNCTION button photogate timer, and then clear the data stored in the photogate timer by pressing the CLEAR button photogate timer. While blocking the signal detection lines photogates, check if the photogate timer and the photogates are working in accordance with the measurement mode S2. 3) In order to set the initial velocity mechanical cart to zero, place the mechanical cart to the upper photogate as close as possible. After clearing the data stored in the photogate timer by pressing the CLEAR button photogate timer, let go mechanical cart on the inclined plane. (1) Measurement motion of a mechanical cart 1) Control the height photogates where the pole mechanical cart passes through the signal detection lines photogates. Note that the photogates should not collide with the mechanical cart. 2) Measure the mass mechanical cart by using an electric balance. Measure the distance between the two photogates placed on the inclined plane by using a scale attached to the inclined plane. This distance corresponds to the traveling distance mechanical cart moving downward on the inclined plane. It is expected that the two distances are somewhat different if the photogates are not placed perpendicular to the inclined plane. Measure the angle inclined plane by using a protractor attached to the inclined plane. In the protractor showed in the following picture, note that the angle inclined plane is obtained by subtracting the value read by the protractor from. 4) When the mechanical cart passes through the lower photogate, the traveling time mechanical cart moving downward on the inclined plane is displayed in the photogate timer. Since the mechanical cart strongly collides with the lower end inclined plane, a method that decreases the shock mechanical cart s collision should be prepared. 5) Change the angle inclined plane to and measure the acceleration and the velocity mechanical cart for various angles inclined plane. Draw the vs. sin graph by using a proper program and evaluate the gravitational acceleration from the slope of this graph. Finally, compare the experimental value gravitational acceleration with the reference value.

8 PAGE 8/14 6) Calculate the change of kinetic from the velocity mechanical cart. Calculate the change of potential from the angle inclined plane and the traveling distance mechanical cart moving downward on the inclined plane. Finally, calculate the change of mechanical and investigate the motion mechanical cart in terms conservation law of mechanical. (2) Measurement motion of a steel bead 1) Control the height photogates where the steel bead passes through the signal detection lines photogates. The height photogates should be sufficiently low due to the small size steel bead. 6) Calculate the change of kinetic due to the translational motion and the change of kinetic due to the rotational motion respectively from the velocity and the angular speed steel bead. Calculate the change of potential from the angle inclined plane and the traveling distance steel bead moving downward on the inclined plane. Finally, calculate the change of mechanical and investigate the motion steel bead in terms conservation law of mechanical. 7) If the measurement is finished, turn off the photogate timer and clean up the experimental instruments according to the suggested method. 2) Measure the mass and the radius steel bead by using an electric balance and a vernier calipers, respectively. Measure the distance between the two photogates placed on the inclined plane by using a scale attached to the inclined plane. This distance corresponds to the traveling distance steel bead moving downward on the inclined plane. 3) In order to set the initial velocity steal bead to zero, place the steel bead to the upper photogate as close as possible. After clearing the data stored in the photogate timer by pressing the CLEAR button photogate timer, let go steel bead on the inclined plane. 4) When the steel bead passes through the lower photogate, the traveling time steel bead moving downward on the inclined plane is displayed in the photogate timer. 5) Change the angle inclined plane to and measure the acceleration and velocity steel bead for various angles inclined plane. Draw the vs. sin graph by using a proper program and evaluate the gravitational acceleration from the slope of this graph. Finally, compare the experimental value gravitational acceleration with the reference value.

9 PAGE 9/14 5. Experimental Values (1) Measurement motion of a mechanical cart 1) Measurement acceleration and the velocity mechanical cart for various angles inclined plane Traveling distance mechanical cart moving downward on the inclined plane (cm) Angle inclined plane sin Traveling time mechanical cart moving downward on the inclined plane (s) #1 #2 #3 #4 #5 Average Acceleration Velocity mechanical cart mechanical cart (ms ) (ms) Slope ms -intercept -intercept ms Gravitational acceleration Reference value (ms ) Experimental value (ms ) Error (%)

10 PAGE 10/14 2) Consideration conservation law of mechanical for the mechanical cart moving on the inclined plane Mass mechanical cart (g) Traveling distance mechanical cart moving downward on the inclined plane (cm) Gravitational acceleration (ms ) Angle inclined plane Velocity mechanical cart (ms) height mechanical cart sin (m ) kinetic (J ) potential (J ) mechanical (J ) Change rate of mechanical (%)

11 PAGE 11/14 (2) Measurement Motion of a steel bead 1) Measurement acceleration and the velocity steel bead for various angles inclined plane Traveling distance steel bead moving downward on the inclined plane (cm) Angle inclined plane sin Traveling time steel bead moving downward on the inclined plane (s) #1 #2 #3 #4 #5 Average Acceleration steel bead (ms ) Velocity steel bead (ms) Slope ms -intercept -intercept ms Gravitational acceleration Reference value (ms ) Experimental value (ms ) Error (%)

12 PAGE 12/14 2) Consideration conservation law of mechanical for the steel bead moving on the inclined plane Mass steel bead (g) Radius steel bead (mm) Rotational inertia steel bead (kg m ) Traveling distance steel bead moving downward on the inclined plane (cm) Gravitational acceleration (ms ) Angle inclined plane Velocity steel bead (ms) Angular speed steel bead (rads) height steel bead sin (m ) kinetic due to the translational motion (J ) kinetic due to the rotational motion (J ) potential (J ) mechanical (J ) Change rate of mechanical (%)

13 PAGE 13/14 6. Results and Discussions (This page should be used as the first page 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 following key points. 1. Explain the relation between the acceleration object and the angle inclined plane when the mass object is constant. 2. As the cause of error, calculate the angle inclined plane, the initial position or the initial speed object quantitatively. 3. Discuss the case that the object moves downward on the curved plane with variable slope instead flat plane with constant slope.

14 PAGE 14/14 7. Solution of Problems (This page should be used as the first page 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. #2-9 : Measurement of Planck Constant through the Photoelectric Effect

PAGE 1/13 Exp. #2-9 : Measurement of Planck Constant through the Photoelectric Effect Student ID Major Name Team No. Experiment Lecturer Student's Mentioned Items Experiment Class Date Submission Time