Part 1 Question 1, Part 2 Questions 1 and 2

Lab 4: Newton's Second Law - Fall 2022 1 Purpose Newton's Second Law is one of the most fundamental laws of physics encountered in the study of the mechanical world. In this laboratory exercise you will make measurements of the motion of masses in a very Simple physical system and test the predictions of the law. When you are done with this lab you should: 0 Know how to apply Newton's second law to simple systems 0 Know how to draw and interpret free body diagrams for simple systems 0 See how equations of motion are derived for systems and how to apply them 0 See the overlap between simulation and experiment 2 Theory The equation that governs acceleration in simple systems is remarkably succinct: Z l5 2 mi. Your goal in this exercise is to apply the law to a mechanical system that you almost certainly have encountered in homework problems or classroom examples. The problem: A block of mass m1 slides on a horizontal, frictionless surface. It is connected to a second mass [Hg by a massless string which passes over a massless, frictionless pulley. Calculate the acceleration of the masses and the tension in the string. N' 1') l I $ _> 2? as: I' m 0:7273M m3 MI+MZ You should solve the problem just stated before going to the laboratory. In the laboratory, you will be able to measure the acceleration but not the tension. The predicted acceleration is given by: "12 a = g. ml + mz Huv.' rim things change if the surface is not totally frictionless? This is an important question since the laboramrv equipment is not perfect and some friction will remain despite your best effort to eliminate it. \"'9 will return to this question later in the exercise. * percent error for part 2 lower than part 1 a = (a' + a") = m28 m1 + m2 4. You can now use the curve-fitting tool to deduce a' and a" from your measurements. You could then compare your measurements to predictions by using Equation 3. You do not have to know the friction force explicitly since it does not appear in the equation. 5. There is space on the worksheet at Q3 to make and record four measurements. Use the curve- itting tool to deduce a' and a" in each case. You need not plot any data; just record the constants and deduce a' and a". Finally, find the average value of a' and a" to obtain a. Compare the predicted and measured values. 6. There are some questions on the worksheet for your consideration (Q4 and Q5). Feel free to discuss them with your classmates. These questions are not there so much to test you as to provoke thought about the physics of what you have been doing. Your answers should be brief. 5 Data and Calculations 5.1 Part 1 1. Record Fits coefficients and Equation of motion. Ensure you state what the acceleration is. equation of motion : A+ 2 + B+ + C A 0. 1526 the acceleration would B : 0 06123 be coefficient A C: 0 . 3596 (0. 1526 m/s 2 ) - 2 9= 2 A 0. 1526 + 2 + 0. 06123+ + 0.3596 weight of cart : 510 9 Correlation : 0 99 9 756 RMSE : 0. 001 8 12 63 5.2 Part 2 1. Derive the equations for the acceleration of the cart here. (For a' and a"). a = f + mn 2 8 -70 152 for a " = - f + mag mitmz each object SFX = ma Fr + Fue = ma EFX= ma FT - FK = ma FT + Fx = ( rni + mz ) a FT - FK = (mitz ) a" = FT - FK FT = m 2 8 a = FT + Fu FT : mag (mitmz ) a = mag - Fe mitma2. Solve for the averaged acceleration here. Be sure to compare your answer from Logger Pro and the theoretical value using percent error. a= . Scata" ) ! im zg 20g ( 9. 8 me = . 3702 m(8 2 ; qexp mi+m 2 209 + 510g Utheo PERCENT ERROR I PERCENT ERROR 2 the cart weighs 5 510 g 0. 1526 - 0. 3702 = 01703 - 0 37021 + 100 O. 3702 RICO 0 . 3702 58.78 . 1. = 53.99% (part ! ) ( part 2 ) 3. Is a level track necessary for accurate measurements in Procedure 4? Explain. yes, a level track is necessary , because the / cart needs to remain only under the Influence of the tension force and friction force Whereas if the cart was an incline the acceleration (force of gravity ) would act on the cart. PART 2 4. Estimate the size of the friction force in Procedure 3. Show your work. Be quantitative. To estimate does not mean to guess. a = mzg+tu rn, + m2 a (mitma ) = mag + FK a (m . - mz ) - m z g = Fe - 2 0. 370 2 m / 5 2 ( 20 g + 5lag ) - ( 20 . 9. 81 m /s 2 ) = 0.206N convert g-7 kg