Newton's Second Law of Motion, week 3 lab 3

Title of the Experiment: Newton's Second Law of Motion Student's name: Naeim Naeirni Section SLN: PHY 122-7 6056 TAts Name: .itxli: i't:i't-'it'it. ALrlrtsircl< Yaclar'. A-vLtsh l(L.rnrar Sitrgh Week of the experiment: Week 3,Lab 3

Objectives: (3 points) The objectives of this lab are to apply Newton's Second Law of Motion to tnovitlg systerrs of different configuratiops and to confirm these laws of motion in several ways, by detemining the nlass of the system, measuring the acceleration of gravity, and keeping the system tnotionless on a tilted trach. Experimental Data (3 points): PART l. Horizontal, frictionless track and a moving system of constant mass State oll values with appropriote units Mass of the cart, M = 0.80K9 Mass of the hanger, mr = 0.05K9 Total mass of the system tnsystem = 0.85Kg ?. Time (s) Fig. I 0515D.; 0.0001:rO -!029+000C7137 la..-.----_1 IAutohr(.' ?oorPo.eon I ----\l P: ^'I"2.EI;C I I e o lo re -r. o oooroqg I ls oroanr-o.ooooogr I I" o.rrn.,.ooooarto I lcor"ttn'r oo I I R[tsE o ooo222Bn I 2

PART 2. Two-way motion with friction on a horizontal track Lrnear Fitlor 12091 velocity v : mT.b r(5lopB) i.066 frvsls lY-lnlercePu. -4.455 ffLs 1 Lrneattrt tor: /u0 | Ye$cty v : mlrb m(Slope}0.2966 m/sis b (Y-lfllercepl): -0 8580 rr3 L'near Fllfor:7og I veloclt/ v ! mf+b m (Slopel 1.379 m/srs b ff-lnlsrcsDl): -3.985 mrs I -i I j e 813-i I .l s.aL r -.i I S09-"1 I l 1 ; g 807-l i t. f-- t L s 805-t - 9.805 (AT 1.56 4y 0.18) N I E o Lrnear Fn lor. 909 | Yelodty ,r = nlTrb m(Slopel 0 5222 mjs/s b rY lnt4rccptl t.{17 d5 (AT 2 09 Ay:o t 4) Starrn6 lur oala 5q I t mn I 806ot g 806 mar. g 614 al 9.814 meani S.S l 0medlan: I 810 std dsr'0 00431,1 $amPte! 3 I 9 807 I 9 809 I 981 1 Fig.4 4 I ,l I eJ r-1 I (;'11.5"2

Mass of the cart, M -- 750g Mass of the hanger, m6 = 70g,90g, 1209 Table 2 Mean value of g: 9.801 m/s2 standard deviation 0.015 m/s2 number of runs 3 Note: The uncertainty in the experimental gravitational acceleration equals the standard deviation in the average g value as determined by Graphical Analysis' PART 3. Cart on frictionless tilted track Calculated critical angle: 5.74" Experimental critical angle: 5.74" Data Analvsis (10 points): Be sure to include equations! PART 1. Horizontal, frictionless track and a moving system of constant mass * Equation and 1 sample calculation of the force applied to the system that was calculated by Logger Pro (Fg: lnnanging*g )! Fnet:1Tl*g F,'.1(50g): (509/1000) * 9.81 m/s2 F,,"t (509) = 0.49 N Run Mass on the hanger Acceleration 1(system moves towards motion sensor) Acceleration 2 (sYstem moves away from motion sensor) ?aver L los 1.379 mls2 0.2966 mls2 0.8378 m/s2 2 9og 1.519 nlsz 0.5222 mls2 1.0506 m/s2 3 120g 1.866 m/s2 0.8402 m/s2 1.3531 rr/s2

o/od"iscrepancy --lM'v1-: m'v't'*l x 1000/o msystem - Discrepanr, : Eiffigql * loo : 0.59% PART 2. Two-way motion with friction on a horizontal track * Show one sample calculation of the gravitational acceleration for one of the runs, using equation (6): - For each run separately the value of the acceleration due to gravity was determined as shown in the exatnple below: e: u*gp - r.506 <'##l : e.8056 {. Calculate the discrepancy between the average value of the experimental and the theoretical value of gravitational acceleration (9.81m/s2) is: - The discrepancy between the experimental and the theoretical (expected) value of gravitational acceleration is: Discrepancy :*#*rn"o* lo0% xlooyo:oo/o PART 3. Cart on frictionless tilted track * Include the free body diagrams for the cart on the tilted track and the hanger, derive the equation for the "critical" angle at which the cart stays still on tilted track. Calculate its value. 7

{r"* a'l'; dl^*f"" *[ \\ ,,.t \4' lr , ,? i r\ _.11 -,t' \ ,,' { .,.i 't ^(0 | _.1 I .v ft 0 f *o+ 3. rr'r -/ arl 6 l.c ,,! [ - {t' 1' "1. t*'r [:, .i)fi, *.;,/ , ""1'r .4 /t '- I /{) ,il' 94 r' il ll *)'/ t ; 0 s otrcl'\f' ,, /,6,n,:l $ ,' otn I \' ' --j" /'I ). T-*,i' 'T't *i t-f 0 : arcssin (rn/M) 0 : arcsin(50/500) 0:5.1"

Results (3 points) MASS OF SYSTEM (Part 1) GRAVITATIONAL ACCELERATION (Part 2) "CRITICAL ANGLE" (Part 3) EXPERIMENTAL VALUE 855g 9.81 m/s2 )./ EXPECTED VALUE 8509 9.81 rn/s2 ).tJ DISCREPANCY 0.59% 0% u.t Discussion and Conclusion (10 points): The purpose of this lab was to test the principles of Newton's second Law of Motion in various ways to determine thevaiidity of the law. Newton's second law of Motion states that the acceleration of an object is the sum of the net forces acting on that object, divided by the mass of the object, written as Q : F,,,r / m' ln part 1 of the lab, this theory is tested by applying a force to acart on a frictionless track. The acceleration of the cart was measured and plotted on a graph to obtain acceleration vs. force graph. Mass is the inverse of the slope of this graph. Mass : 1/sloPe : 111.169 : 855g The discrepancy of the experimental weight of the system and the actual weight of the carl was calculated AS: Discrepancy * 100%:-0.59% The discrepancy in this case is because the slope is the average ofall forces acting on an object which is equal to the acceleration multiplied by its mass. ln part 2 of this lab friction is added. The cart had a mass and friction acting against its movement. When the cart was released, it overcame the friction force, resulting in a higher velocity of the car.t moving towards the rnotion sensor. As it moved, the mass of the system and the kinetic friction of the track resulted in slowing down the velocity of the cart. Using the average acceleration of the two parts of the motion and the mass of the system the experirnental force of gravity was determinedJo be: e : oo" *#:1'0506 e*#5 : e'80s6 This result is statistically the same as the theoretical value for the acceleration due to gravity , again confirming the principles of Newton's Second Law of Motion. The last section of the lab was to test the calculated angle that would allow the caft to remain motionless on a tilted track. The angle was calculated as: 10

XFn.,:T-Mg(sin(o)):o T: Mg (sin(O)) sin(o)=ffi:#:# arcsin (0.1) : 5.7q critical angle: 5.7{ At this angle, the cart should remain motionless. However, due to the lirnitation of the track angle, it was not possible to achieve the goal without the brakes engaged. Testing the cart at the angle of 5.8" resulted in negative acceleration. Testing the cai at the angle of 5.7" resulted in positive acceleration. These results indicate that the theoretical angle of 5.74" would in fact result in a motionless caft. This means that the net forces acting on the cart were zero. By conducting the first and second part of this lab Newton's Second Law of Motion is confirmed' The experimenial rnass of the weighted carl deteimined by the acceleration vs. force graph was well within the range of any uncertainties allowed. Th"e experimental force ofgravity determined by the average velocities multiplied by the mass;thevalueswereidentical totheacceptedvalueofthe'accelerationduetogravityofg.8l m/s2. The third part of the lab indicates that the calculated value of the angle of the track would hold the cat steady. Thus, regarding all these results of all sections of this lab, the principle of Newton's Second Law of Motion is confirmed. 11