Newton's 2'id Law Purpose: To investigate Newton's 2\"d Law and to examine the factors affecting the acceleration of a system. Theory: Newton's 2'\" Law basically states that the net force on a given object is equal to the product of the mass and acceleration of the object. In effect for a constant mass the force then will be proportional to the acceleration. "'2 Consider the mass of the cart as me and the hanging mass as an as shown in the figure above. We can set up equations of motion using Newton's 2\" law for each of m1 and me (for simplicity we will take the rotational inertia of the smart pulley and the friction on the table as negligible, and the tensions in the string to be the same). Thus, we obtain: T = mm (1) mg T = mm (2) where T is the tension in the string, a is the acceleration of the system, and g the acceleration due to gravity. Adding up equations (1) and (2), we obtain m1g = (m1+ m2) 0 (3) Part 3: The gravity g from the graph of m1 vs. a mi + m2 = ............... l-Repeat part 1 for 5 different m1 values to obtain the acceleration a, while keeping m1 + m2 constant, that is, when m1 is increased, m2 is decreased by the same about, and vice versa. 2- Record the values of mi and a in the data table below; 3- Select and copy the data and paste in the data table in Graphical Analysis. 4-Using Graphical Analysis, do a linear t. Compare the linear fit equation with the equation m1 : ((mi + m2)/ g) a. From the comparison, determine the acceleration due to gravity g. Copy and paste your plots here. 5- Compare the acceleration due to gravity g obtained from the graph and the actual value of g to nd the percentage error between them. Part 3: The gravity 9 from the graph of m: vs. a m1+ m2 =.............. I-Repeat part 1 for 5 different m1 values to obtain the acceleration a, while keeping m1 + m2 constant, that is, when m1 is increased, m2 is decreased by the same about, and vice versa. 2- Record the values of m1 and a in the data table below: 3- Select and copy the data and paste in the data table in Graphical Analysis. 4-Using Graphical Analysis, do a linear fit. Compare the linear fit equation with the equation m1 = ((m1 + m2)/g) a. From the comparison, determine the acceleration due to gravity 9 5- Compare the acceleration due to gravity 9 obtained from the graph and the actual value of g to find the percentage error between them. Questions: 1-(a) What happens if the friction is not negligible on the cart? (b) Draw the free body diagram for mmnd m2 (c) Rewrite the equation (1) and (2) including the force of friction. 2- A cart at mass 1.2 kg is placed on a track and connected to a mass on a pulley hanging over the edge. It the hanging mass is 0.4 kg, what would the acceleration of the cart be? m1 = ((m1 + m2)/g) a (4) Thus, if NewTon's 2\":I law holds as applied in This caSe, a ploT of m: vs. a for consTanT (m1+ me) should resulT in a sTraighT line, wiTh The slope being equal To (m1+ m2)/g. Thus knowing (m1 + me), you can obTain The acceleraTion due To graviTy and compare wiTh The expecTed value. VirTual Lab: We will use a virTual seTup in The link below To collecT daTa. There are Three parTs of This experimenT. In parT 1, we will calculaTe The acceleraTion of The carT using The graph of x vs. T. In parT 2, The acceleraTion of The carT will be obTained from The NewTon's 2\" law using The equaTion (3). In parT 3, we will invesTigaTe The graviTy 9 using The graph of m1vs. a. hTTp://www.'rhegh_vsicsaviary.com/Physics/Programs/Labs/NewTonsLawLab/index.hTml Procedure / DaTa Analysis ParT 1: The acceleraTion of The carT from The graph of x vs. T m1 =.............. m2 =............ I-Run The program aT The link above To obTain daTa of The posiTion of The carT m2 as a funcTion of Time in The spreadsheeT. 2- Copy The daTa, and Type inTo a Table in Graphical Analysis. (NoTe: ConverT The uniT of Time from millisecond To second). 3-Using Graphical Analysis, do a quadraTic curve fiT. Compare The curve fiT equaTion wiTh The kinemaTic equaTion x = x0 + 5,595+ 1/2 at? From The compariSOn, deTer'mine The acceleraTion 'a' of The carT. ParT 2: The acceleraTion of The carT from The Theory 1- Using The equaTion (3), calculaTe The acceleraTion 'a' of The carT. 2- Compare The acceleraTion values obTained from parT 1 and parT 2 To find The percenTage difference beTween Them. Lab 6 Newton's 2\"d Law Data Sheet Name: Date: htt ://www.the h sicsaviar .com/Ph sics/ProJrams/Labs/NewtonsLaWLab/indexhtml Procedure / Data Analysis Part 1: The acceleration of the cart from the graph of x vs. t m1 i .............. m2: ............ l-Run the program at the link above to obtain data of the position of the cart mg as a function of time in the spreadsheet. 2- Copy the data, and type into a table in Graphical Analysis. (Note: Convert the unit of time from millisecond to second). Copy and paste your plot here. 3-Using Graphical Analysis, do a quadratic curve fit. Compare the curve fit equation With the kinematic equation X : X0 + X93? + 1/2 atz. From the comparison, determine the acceleration 'a' of the cart. Part 2: The acceleration of the cart from the theory 1- Using the equation (3), calculate the acceleration 'a' of the cart. 2- Compare the acceleration values obtained from part 1 and part 2 to nd the percentage difference between them. Conclusion: In the conclusion part, mention about the following questions: - Is your graph of mi vs. a linear? - Why was it necessary to keep (mi + mz) constant? -What is the effect of varying the mass mi on the whole system?Questions: l-(a) What happens if the friction is not negligible on the cart? (b) Draw the free body diagram for m1 and m2 (c) Rewrite the equation (1) and (2) including the force of friction. 2- A cart of mass 1.2 kg is placed on a track and connected to a mass on a pulley hanging over the edge. If the hanging mass is 0.4 kg, what would the acceleration of the cart be? Conclusion: In the conclusion part, mention about the following questions: - Is your graph of m1 VS. a linear? - Why was it necessary to keep (m1 + m2) constant? -What is the effect of varying the mass m1 on the whole system