Homework answers / question archive / ATWOOD’S MACHINE OBJECTIVE To calculate the acceleration of the Atwood’s Machine experimentally by using the kinematic equations of motion and to compare to the expected value obtained from applying Newton’s 2nd Law to the Atwood’s Machine

ATWOOD’S MACHINE OBJECTIVE To calculate the acceleration of the Atwood’s Machine experimentally by using the kinematic equations of motion and to compare to the expected value obtained from applying Newton’s 2nd Law to the Atwood’s Machine

Sociology

Share With

ATWOOD’S MACHINE OBJECTIVE To calculate the acceleration of the Atwood’s Machine experimentally by using the kinematic equations of motion and to compare to the expected value obtained from applying Newton’s 2nd Law to the Atwood’s Machine. EQUIPMENT 1. 2. 3. 4. 5. 6. pulley rod stop watch pan balance masses 2-meter stick pulley M1 rod H M2 THEORY Using Newton’s 2nd Law 1. Draw a free-body diagram of mass M1 and mass M2. 2. Select an appropriate coordinate system for each mass. 3. Apply Newton’s 2nd Law to each mass by using the corresponding coordinate system. 4. Obtain an expression for the acceleration of the blocks in terms of M1, M2, and g. That is a = a (M1, M2, g). This expression will give the theoretical (expected) value for the acceleration. 1 Using the Kinematic Equations of Motion 1. Using one of the kinematic equations derive and expression for the acceleration of the blocks when they have moved a distance H starting from rest in a time t. Your expression will be in terms of H and t. That is a = a(H, t). This expression will give the experimental acceleration. The PROCEDURE 1. 2. 3. 4. 5. 6. 7. Setup apparatus as shown on equipment section. Choose M1 = 180g and M2 =150g. Adjust M1 and M2 so that M1 falls through a height H ≈ 130 cm. Release M1 from rest and measure the time of fall t for a total of 5 runs. Repeat steps (2) and (3) for M1 = 230g and M2 =200g. Calculate aexp and atheo for each set of data. Construct a data table like the following: H(cm) M1 M2 t1 a1 t2 a2 t3 a3 t4 a4 t5 a5 aave atheo %error 130 130 2 Lab Report Format Physics 2A, 4A-D 1. TITLE Place the title of the lab experiment at the top of the first page. 2. OBJECTIVE State the objective of the experiment clearly. The objective of the experiment is what you’re trying to prove or accomplish. 3. THEORY Explain relevant concepts and provide any appropriate definitions. Pertinent equations should be derived in a clear, logical manner. Any relevant background information may also be included in this section. 4. APPARATUS Record a list of the equipment being used. Write down the serial number, model, and make of the equipment. You will need this information for reference in case you need to repeat the experiment or collect additional data. Describe the equipment being used and draw a diagram or picture of the equipment. 5. PROCEDURE This section includes your plan for performing the experiment. The experimental plan should be written in a step-by-step, orderly fashioned method. It describes in detail your procedure for performing the lab such that you or anyone else could re-create the experiment exactly as it was performed. The experiments in the lab manual/handouts already have a step-by-step written procedure. You may cut and paste the written procedure from your lab manual into your lab notebook. Keep in mind that you may need to repeat an experimental procedure during the lab final. (The lab handouts have the TITLE, OBJECTIVE, THEORY, APPARATUS, and PROCEDURE sections already written out, so you may cut and paste these sections into your lab notebook.) 6. DATA Your data should be well organized and easy to read. Label each set of data with the appropriate quantity being measured along with the trial/run number. Use ‘table’ format for easier reading. Your data should have the correct number of significant figures and appropriate units. If your data is represented by graphical methods, make sure your graph has been appropriately labeled with the correct axis, units, and scale. Any work that is printed out from the computer must be attached securely (taped, glued, stapled ....)to your lab notebook. DO NOT FOLD PRINTOUTS AND SLIP INTO NOTEBOOK! Any work that is done on the computer should not be saved on the hard drive! Once finished with your work, delete it and empty Recycle Bin. 7. CALCULATIONS Write down equations being used to do calculations. The calculations should be clear and readable. Show and label calculations in complete detail for any quantity. If you are repeating a calculation several times, you only need to show one sample calculation. The calculation for % error between experiment and theory should be included here. 8. CONCLUSION & RESULTS Include a discussion of the results and their significance. Address the experimental objective and state whether it was accomplished. Comment on the % error between theory and experiment. Identify at least two sources of experimental error (systematic or random) to account for the percentage error involved in the experiment. Explain how these errors effected the outcome of the experiment? Was the experimental result greater than or less than the theoretical value? Was this what you had anticipated? Explain why or why not? You may also discuss methods to eliminate or minimize these experimental errors. PHYSICS SAMPLE LAB WRITE-UP Title - Newton’s 2nd Law Objective In this experiment we will attempt to confirm the validity of Newton’s 2nd Law by analyzing the motion of two objects (glider and hanging mass) on a horizontal air-track. First, we will calculate the theoretical acceleration by applying Newton’s 2nd Law (Fnet = MA), neglecting friction, to the glider and hanging mass. Next, we will calculate the experimental acceleration of the glider by applying the kinematic equations of motion as it moves between two markers (photogates) on the track. We will then compare the experimental acceleration to the theoretical acceleration. Theory a) Acceleration using Newton’s 2nd Law Apparatus Setup V1 Photogates V2 glider M1 d +X Airtrack M2 +Y hanging mass Free-Body Diagram N T T M1 M1g M2 M2g Apply Newton’s 2nd Law to mass M1 and M2. Mass ‘M1’ ΣFx = T = M1a Mass ‘M2’ 1 ΣFY = M2g - T = M2a Adding both equations gives: M2g = M1a + M2a atheo = M2g/(M1 + M2) b) Acceleration using Kinematic Equations Using the kinematic equation V22 = V12 + 2a ( x − x0 ) we will calculate the experimental acceleration of the glider as it moves between the two photogates. We will take the origin of our coordinate system at the first photogate. d = distance between photogates V1 = (s/t1) velocity of the glider through photogate 1 V2 = (s /t2) velocity of the glider through photogate 2 s = diameter of small flag on glider t1 = time for small flag to go trough photogate 1 t2 = time for small flag to go trough photogate 2 a exp = V22 − V12 2d Apparatus Refer to theory section for apparatus setup One air track(#21), blower(#2), blower hose and power supply One digital photogate(#2C) and one accessory photogate(#2A) One glider(#1B) One flat accessory box(#22A) String Electronic pan balance(#1) Vernier Calypers (#12c) Procedure 1. 2. 3. 4. 5. Measure the mass of the glider and hanging mass. Setup the air track and blower as indicated by instructor. Measure the distance between photogates. Measure the diameter of the small flag on glider with vernier calipers. Release glider 10 cm away from photogate 1 and record times trough both photogates. 6. Repeat step (5) four more times. 2 Data M1= 4750 g M2=50.00 g g = 9.80 m/s2 d = 60.65 cm s = 1.01 cm Run # t1 t2 1 2 3 4 5 0.039 0.043 0.044 0.041 0.038 0.023 0.024 0.023 0.023 0.032 V1 (cm/s) 25.5 23.0 22.5 24.5 26.0 V2 (cm/s) d (cm) 43.0 41.5 42.5 42.5 43.5 60.65 60.65 60.65 60.65 60.65 aexp (cm/s2) 9.91 9.86 10.7 9.97 10.1 Calculations Theoretical Acceleration: atheo = M2g/(M1 + M2) = 50.00 g*980 cm/s2/(4750g + 50.00 g) atheo = 10.2 cm/s2 Experimental Acceleration: a exp = V22 − V12 = (43.5 cm/s)2 - (26.0 cm/s)2 /(2*60.65 cm) (sample calculation Run #5) 2d aexp = (9.91 +9.86+10.7+9.97+10.1)/5 = 10.1 cm/s2 (average experimental acceleration) % error = exp− theo % error = ? theo 10.1−10.2 10.2 × 100 ? X 100 = 0.98 % 3 Conclusion 1. The theoretical acceleration using Newton’s 2nd Law was 10.21 cm/s2 and the average experiment acceleration using the kinematic equations was 10.10 cm/s2. The percent error between experiment and theory was only 1%. Although the percent error was small, there were still systematic and random errors present. 2. Based on the relative small % error of 0.98% we can conclude that the objective of confirming Newton’s 2nd Law was accomplished. 3. In measuring the velocity of the gliders through the photogates we used the average velocity instead of the instantaneous velocity. This resulted in the average velocity always being smaller than the instantaneous velocity. This will V 2 − V12 then cause a exp = 2 to be consistently smaller than atheo which resulted in a 2d systematic error. A second systematic error was that in applying Newton’s 2nd Law to derive atheo of the glider we neglected the frictional force. The resulting equation should have been atheo = (M2g – fk)/(M1 + M2). Neglecting friction on the atheo equation should result in atheo being consistently larger than aexp. The data shows this to be true with the exception of one data point. 4. In addition to the random errors involved due to the uncertainty of the measuring devices, other random errors involved in the experiment include: a) Not releasing the glider from same initial point every run. b) Trying to balance the air track. c) Having the hanging mass M2 swinging when releasing M1 from rest. All these random errors contributed to the uncertainty in the final results for the accelerations. These random errors also contributed to the 0.98% error in the final results. 4 LAB REPORT GRADING RUBRIC TITLE: b Section PARNERS NAMES TITLE OBJECTIVE THEORY EQUIPMENT PROCEDURE THEORY Description of Section 1. Partners names at the upper right-hand corner of the first page of the lab report. 1. Includes handout containing these components stapled to lab report or each component is explicitly written. Possible Points 1 2 1. The theory/principle/law associated with the lab is clearly stated. 2. Explained how the theory will be used to accomplish the objective of the lab. 3. Derivation/proof of equations are done clearly and logically. 1. All data is labeled, organized, and easy to read. 2. Used table-format whenever appropriate 3. Data measurements taken correctly. 4. Used appropriate significant figures and units. 5. Graphs have correct axis labeled, units, and scale. 2 CALCULATIONS 1. Calculations are labeled with equations shown. 2. Calculations are clear and legible. 3. Calculations are done correctly 4. Calculations have correct number of significant figures and units. 5. % error calculation shown. 5 CONCLUSION 1. Includes a summary of the results of the experiment and the % error involved. 2. Addresses the experimental objective and EXPLAINS if it was accomplished or not based on experimental results. 3. Provides and explains one systematic error involved in the experiment and explains how it affected the outcome of the experiment and the % error involved. 4. Provides and explains one random error involved in the experiment and explains how it affected the outcome of the experiment and the % error involved. 5 DATA Write the conclusion in outline-number form to obtain credit! SCORE 5 20 Your Score LabAtwoods Machine.pdf - Adobe Acrobat Pro DC (32-bit) File Edit View Sign Window Help Home Tools 3. Motion in 2D(2A... Newton's Laws of ... 4A N2L hw proble... LabAtwoodsMachi... x 1 / 2 106% Mio Me pulley M M, Vo=0 lice aches = Athos (M., Mz, g) X g=980 cm / y=x yarat x rod 2 M, 2 THEORY H= bat la= 24 sing Newton's 2nd Law Eye ?? Drew a free body juga ? LabAtwoodsMachine.pdf - Adobe Acrobat Pro DC (32-bit) File Edit View Sign Window Help Home Tools 3. Motion in 2D(2A... Newton's Laws of ... 4A N2L hw proble... LabAtwoodsMachi... X DD 106% 1 / 2 y a do ?· alue=authoo (m., m2, g) M, Vo=0 rod K to better g=980 cm 2 2 Ht le Y=X4 yst at M2 co THEORY 2 H = hat la= 2H exp t², Using Newton's 2nd Law 1. Draw a free body diagram of mass M, and mass M2. 2. Select an appropriate coordinate system for each mass. 3. Apply Newton's 2nd Law to each mass by using the corresponding coordinare system. 4. Obtain an expression for the acceleration of the blocks in terms of M1, M2, and g. That is a = a (M.2 PPIU W moment (expected)