answer to question 11: 0.0194 0.0553 0.0381 0.1147 q11 y = 4.2125x - 0.0298 0.0479 0.1466 0.6 0.0672 0.2093 0.08537 0.4992 0.1115 0.3525 0.5 0.4 0.3 0.2 0.1 0 0 0.02 0.04 0.06 0.08 0.1 0.12 answer to question 13: 5.241 0.3126 4.1528 0.246 q13 y = 0.0579x + 0.0087 3.4387 0.2139 0.35 2.9342 0.1757 0.3 2.5588 0.1567 0.25 0.2 0.15 0.1 0.05 5Physics 195: Newton's Method Page 1 of8 Newton's 'Laws' Objective: To understand the relationship between force, mass and acceleration; To create and interpret graphs of these relationships; To evaluate the validity of Newton's Second Law. Hypothesis: An object accelerates when it experiences a net force. We assume a net force is present if an object accelerates while observed from an inertial reference frame. We assume that the effects of the earth's curvature, atmosphere and rotation are minimal. Mathematical Models and Reference Values Used: Newton's 'Laws' state that acceleration of an object is proportional to the net external force acting on it, but F m inertia (resistance to velocity changes). Large masses accelerate less than small masses for the same net external force. Forces are vector quantities. Forces acting on an object can be graphically represented by a 'Free Body Diagram'. A force of one Newton has been defined to cause a 1 kg object to change its velocity at the rate of 1 m/s'. Overview A constant mass glider will be subjected to increasing forces and a variable mass glider will be subjected to a constant force. Acceleration data will be used to investigate Newton's Laws of motion for constant acceleration systems. inversely proportional to the mass.: :6 . The mass of the object is a measure of its Equipment List: Air Track Et Blower, Glider, Glider Accessory Kit, Photogate, 1&2 Meter Sticks. Setup and Procedure Do not slide the glider along the track unless the blower is running. 1. Place the glider in the middle of the track and turn on the blower. If the track is level, the glider should remain motionless or slowly drift back and forth near the middle of the track. If the glider moves towards one end of the track, level the air track by adjusting the screws in the horizontal support. Once the track is leveled, turn off the blower. 2. Measure and record the length of the glider flag in Data Table One as Lf. 3. Insert the flag into the glider and determine the mass of the glider-flag combination using the electronic balance. Record the result in Data Table One as 'Mo'. 4. Place a 'SO-gram' mass on each peg on the side of the glider. Record the mass of the glider, flag and masses in Data Table One as 'M1'. Use the electronic balance to measure the value of the empty mass hanger, and record it in Data Table One as 'mh'. 5. Make sure the glider flag can pass under/ through the photogate without hitting it. Insert a pulley into the lower opening of the stop at the end of the track. Position the glider about 25 cm from the pulley. Cut a length of string that will reach from the floor, over the pulley and to about the middle of the track. 6. Attach the mass hanger to the end of the string near the floor. With the hanger touching the floor, run the string over the pulley and along the track. Attach it to the stem of the glider flag. Lift and position the glider on the track until the string is taut, but the hanger Physics 195: Newton's Method Page 2 of 8 is still resting on the floor. The string should be parallel to the track and the glider should still be about 20 -25 cm from the pulley. Use the scale on the side of the air track to determine the position of the leading edge of the glider. Once you are satisfied, record this 'end position' in Data Table One. Trim excess string. 7. Position the photogate just beyond the end of the glider flag. This ensures the glider reaches maximum speed before it enters the photogate. 8. Turn on the blower and pull the glider back until the hanging mass is just below the pulley. You may want to adjust this position to obtain a convenient value. The 'start' and 'end' positions should be 60 to 80 cm apart. Once you are satisfied, turn off the blower and record this 'start position' in Data Table One. 1. Acceleration as a function of Applied Force 1. Move the sliding switch on the photogate to the 'GATE' position and press the 'Reset' button. The display should read all zeros. If it does not, notify the instructor. 2. Measure the values of the large and small metal and black plastic masses. Record the values in Data Table Two. 3. Hold the glider, turn on the blower and allow the air to circulate for several seconds. Make sure that the mass hanger is stationary then release the glider from your chosen start position. Have one of your lab partners catch the glider after it passes through the photogate and before it hits the pulley. 4. Record the number on the photogate in Data Table Three as t1. Push the reset button and repeat the procedure. Record this value as t;. Take the average of these times and record it as well. Repeat steps 3 and 4 with different amounts of mass on the mass hanger until Data Table Three is complete. Q1. Show a sample calculation of the final speed and average acceleration of the glider. Show all work with units then complete Data Table Four. Q2. Draw a free body diagram for the glider (M1) and one for the mass hanger (mh). Show that the net external force acting on the glider is the force of tension in the string between the glider and the hanging mass and that it is equal to the mhM19 [mh+M1) Q3. Show that when M is much larger than m, the value of FTension approaches mhg. Q4. Use the values for M1 and m, from Data Table One and the expression from Q2 to calculate the tension in the string. Show your work, with units. Q5. Calculate the value of FTension = mg. Show your work with units. Q6. Calculate the percent difference or error (as appropriate) between Q4 and Q5. Show your work with units. Q7. Is it acceptable to use the approximate value for the tension in the string instead of the actual value? Answer using complete sentences. Q8. Use whichever m - - - sion in the string. Show one sample calculat Page Ile Five. Transfer the tension from 'Hange exprESSion: IIFTensiorIHZIIZ Fiddler\": Physws 195: Newton's Method Page 5 01 5 2. Acceleration as a function of Glider Mass 1. Place 'mass C' on the mass hanger. Remove both '50-gram' masses from the glider and place the glider at your start position. Reset the photogate, then release the glider. Record the time on the photogate in Data Table Six as t1 then repeat the procedure. Record the second time as t: then calculate the average time. 2. Add a single '50-gram' mass to the glider. - l Place the mass as shown in the diagram. Measure and record the value of this mass in k and take two data runs. Record all data in Data a Table Six. Q9. Show a sample calculation for the final speed and the average acceleration of the glider, then complete Data Table Seven. Show work with units. Q10. Calculate the reciprocal of the glider mass in Data Table Eight. Data Table Six. 3. For each of the mass configurations shown, measure and record the value of the masses 3. Graphical Analysis: Acceleration as a function of Applied Force Read the graphing instructions from the syllabus or course resources before you begin. Q11. Construct a Cartesian graph of the glider acceleration as a function of the net applied force. Draw a best-fit line then calculate the slope on the graph, with units. Transfer the result to Data Table Nine. Q12. What physical quantity in the experiment does the slope represent? Answer using complete sentences. 4. Graphical Analysis: Acceleration as a function of Glider Mass Read the graphing instructions from the syllabus or course resources before you begin. Q13. Construct a Cartesian graph of the glider acceleration as a function of reciprocal glider mass. Draw a best-fit line and calculate the slope on the graph, with units. Transfer your result to Data Table Nine. Q14. What physical quantity in the experiment does the slope represent? Answer using complete sentences. 5. Results @m 5. Use the Q11 slope value from Data Table Nine to determine the effective mass of the glider, masses and flag (AM). Show your work with units. __9Q16. Calculate the percent difference (or error, as appropriate) between the two values you obtained for the mass of M1. Show your work with units. %Q17. Use the Q13 slope value to determine the external force acting on M. Show your work with units. '77 Q18. Calculate the percent difference (or error, as appropriate) between the two values you obtained for the external force acting on M,. Show your work with units. Q19. What do the results of Q16 and Q18 tell you about the validity of the theoretical model? Answer using complete sentences. MacBook Pro Physics 195: Newton's Method bortoMano Page 8 of 8 Q15. fife cele mass = mass MI 6 : 1291 keg 15:98kg Q16. Percent A Man amere COM option OFO Q18. 41065 7814 thereData Table One Length of Glider Flag: Lf = Mass of Glider & Flag: Mo = 10. 1908 kg Mo & 2, '50 g' masses: M1 = 029100kg Mass of hanger: mr = 1902 kg End' position: Xf = 02820 m 'Start' position: X. = 1. 12 4 Displacement = |4x]| = 01868 m imu ajiwenow world syse aldel old older Data Table Two Mass Description Label Mass (kg) Small black plastic A Large black plastic B Small metal C 6. 005 03 ks Large metal D 0. 609 85 kof 8 Physics 195: Newton's Method How Page 7 of 8 Data Table Seven Initial speed: Mass Description Final speed: Acceleration: V 1 7 t average a = _ Vi-Vom 2AX 6 7367 Mis Mo + '50 grams' O Mo + '100 grams' 01:24 610 m / s 2 Mo+ '150 grams' 01 6095 mls 6 . 2 139 MIS O 0.5524 on's Mo+ '200 grams' 0.17 5 7is 2 O 0: 5 217 ml 0 . 153 7 Mis 2 Q10. Data Table Eight Mass description Reciprocal Mass (kg-') mo's 5, 2410 kg Mo + '50 grams' 4 . 15 28 kgl Mo + '100 grams' 3 . 4 38 7 kgil Mo+ '150 grams' 2 93 42 kg7 Mo+ '200 grams' 2. 5 58 8 kg- 1 3. Graphical Analysis: Acceleration as a function of Applied Force Q12. Is hows the relationship betwen these two mysocal quantities, and slop shows the mass OF the slider . 4. Graphical Analysis: Acceleration as a function of Glider Mass Q14. shows the relationship between the glider accelertion reciprocal glider ) and slope shows the acceleration of the slider per vite fret force applike to it . 5. Results Data Table Nine Quantity Value Units Q11 slope 4: 2125 2 Mass of M, from balance 0.2910 Q13 slope Tension from 'Hanger + C' 01 06 72 rev 01/20