5AL Lab 4 Assignment

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University of California, Los Angeles *

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Mechanical Engineering

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Jan 9, 2024

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5±!%% !%%aIIFb 4 ±ssignment ±va 330Rosenthal, ==:Xian ²hen, °ane ''$guyen, 11/1/23, ³18, ´enJJGch 1 <URNK] SPVS]VSkjURNKLI ALILIVS]TQ x_nmpj jNKkjfg_]kjNKkj _] NKAJUR kj[VSLINK kjAsruNK mlURVSkj Akj A +±" SPVS[NK A]LI nmpfg[_ALI VSml ml_ x_nmpj #jALINKkjJ_fgNK AkjkjVSTQ]\NK]ml

441Slide 2: µesJJGcriIIFbe the experimental equipment and soPftware that was used, so that someone else JJGcould dupliJJGcate these results. ± photograph would IIFbe helpPful, with the diPfPferent parts laIIFbeled. JJGcart = 404g weight holder = 10g 552Trial 1 : m 2 = 60g 552Trial 2: m 2 = 159g 552The wireless aJJGcJJGcelerometer sensor was physiJJGcally JJGconneJJGcted to the JJGcart. 552The sensor was JJGconneJJGcted to a set mass with a string. 552The sensor was JJGconneJJGcted to the 00-±441S²))& soPftware via IIFbluetooth and IIFboth the PforJJGce and aJJGcJJGceleration sensor were zeroed. ¶verything was weighed IIFbePfore use to get an aJJGcJJGcurate mass. 552The Pfirst trial used a 50g weight, then the air was turned on and the JJGcart was held ready Pfor reJJGcording. ))&nJJGce the reJJGcording started we waited a Pfew seJJGconds and then released the JJGcart. 552The PforJJGce and aJJGcJJGceleration were measured, then we moved onto the IIFbigger weight oPf aIIFbout 160g. 552The same steps were Pfollowed. ·urther analysis oPf the graphs yielded the data, mean and standard deviation, Pfor eaJJGch trial IIFboth IIFbePfore and aPfter the JJGcart was released.

441Slide 3: 00-aste plots oPf the aJJGcJJGceleration and tension PforJJGce vs. time Pfor the smallest hanging mass m 2 that was used. !%%aIIFbel your axes and show the units. !%%aIIFbel with an arrow the time at whiJJGch the air JJGcart was released. ±ir JJGcart released ±ir JJGcart released

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441Slide 4: ·or the data in 441Slide 3, Pfind the average values oPf the tension IIFbePfore and aPfter the JJGcart is released, inJJGcluding standard deviation. ±lso Pfind the average value oPf the JJGcart aJJGcJJGceleration. <q]VSH^[ ﾂ ±UNZSb_gqUN qUN^[UNHrjUNS ±verage · = -0.60 ''$ 441Standard deviation = 0.01 ±verage JJGcart aJJGcJJGceleration = 0.1 441Standard deviation = 0.0 t= 0 - 1.2 s ²ZStlUNq qUN^[UNHrjUNS ±verage · = -0.49 ''$ 441Standard deviation = 0.02 ±verage JJGcart aJJGcJJGceleration = 1.3 441Standard deviation = 0.2 t=1.2 - 2.3 s ²ompare these values to the values you JJGcalJJGculate Pfrom ''$ewton’s laws Pfor these values oPf the masses. 663Use proper signiPfiJJGcant Pfigures in numeriJJGcal results. 552The JJGcalJJGculated values Pfor tension PforJJGces are almost equal to the measured values (0.59 ~ 0.60''$ and 0.49 ~ 0.51''$) ²rUNqH[TQUN < ±UNZSb_gqUN (0.060 kg)(9.80 m/s^2) = 0.59 ''$ ²rUNqH[TQUN < ²ZStlUNq ((0.060kg)(0.404 kg)(9.80 m/s^2)) / (0.060kg + 0.404 kg) = 0.51 ''$

441Slide 5: 330Repeat the analysis oPf 441Slides 3 & 4 Pfor the larger value oPf m 2 . ±verage 552T ´ePfore: (0.159 kg)(9.80 m/s^2) = 1.56 ''$ ±verage 552T ±Pfter: ((0.1590kg)(0.404 kg)(9.80 m/s^2)) / (0.159kg + 0.404 kg) = 1.12 ''$ <qH]VS^[ ﾃ ±UNZSb_gqUN qUN^[UNHrjUNS ±verage · = -1.38 ''$ 441Standard deviation = 0.28 ±verage JJGcart aJJGcJJGceleration = 0.1 441Standard deviation = 0.0 t= 0 - 1.2 s ²ZStlUNq qUN^[UNHrjUNS ±verage · = -1.20 ''$ 441Standard deviation = 0.26 ±verage JJGcart aJJGcJJGceleration = 1.8 m/s 2 441Standard deviation = 1.2 t=1.25 - 2.3 s 552The JJGcalJJGculated average tension PforJJGce IIFbePfore releasing is higher than the measured value (1.56 > 1.38''$) 552The JJGcalJJGculated average tension PforJJGce aPfter releasing is lower than the measured value (1.12 < 1.20''$ )

441Slide 6: <<9Write a thoughtPful JJGconJJGclusion here. µid you Pfind agreement with the theory Pfrom ''$ewton’s laws? ²ould you use these experiments to determine a value oPf g? <<9What aPfPfeJJGcted the aJJGcJJGcuraJJGcy oPf your measurements? ¸ow JJGcould you improve the experiment? 552The results we got Pfrom the experiments matJJGches the ''$ewton’s laws. 552The heavier the mass, the more PforJJGce the oIIFbjeJJGct has. ))&ur results show that the 159g oIIFbjeJJGct has a larger PforJJGce than the 60g oIIFbjeJJGct when they were not released (1.38 > 0.6''$). ±t the same time, the aJJGcJJGceleration oPf the heavier oIIFbjeJJGct is higher than the lighter oIIFbjeJJGct (1.8 > 1.3 m/s 2 ). 552This proves the equation ·=ma is true IIFbeJJGcause PforJJGce is proportionally related to aJJGcJJGceleration and mass. <<9When there is more mass or more aJJGcJJGceleration, there is more PforJJGce exerted on the oIIFbjeJJGct. <<9We JJGcould use these experiments to determine a value oPf g sinJJGce we JJGcan measure the PforJJGce oPf the oIIFbjeJJGcts and use the PforJJGce and mass to determine value oPf g Pfrom equation ·=ma <<9What JJGcan aPfPfeJJGct the aJJGcJJGcuraJJGcy oPf the measurement is the JJGcart goes IIFbaJJGck to the opposite direJJGction at the instant when it drops the oIIFbjeJJGct. ¹t might move too Pfast and the oIIFbjeJJGct might IIFbe vigorously dropped and that JJGcould aPfPfeJJGct the measured value oPf PforJJGce and aJJGcJJGceleration. 552The experiment JJGcan IIFbe improved IIFby switJJGching to an oIIFbjeJJGct with less mass than the one we used so the movement JJGcan IIFbe more gentle and the measurement would IIFbe smooth.

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