8A-midterm1-solutions - 1(30 points Two blocks Two blocks...

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Unformatted text preview: 1) (30 points) Two blocks Two blocks sit on a table. They are connected T T by a string as shown. Another string leads off ‘ 7" to the left. Note that the tension in each string @ has been labeled as T l and T2; please use that / / / / notation. The two blocks have equal masses M. Somebody pulls on the left string with a force FE. Until told otherwise in part d, ignore frictiOn. a) Find the acceleration of the blocks. b) Is the tension in T2 larger, the same as, or less than tension T1? Explain your reasoning clearly. (You can do this after part c if you want to, but you don’t have to) c) Find an expression for T2 in terms of M and T]. d) Now we want to add friction with the table to one of the blocks until T l and T2 are equal. To which block do we have to add the friction, and why? 6) Find the coefficient of friction needed for part d. clmwwég MM; M flew/Avrwé/ 41cc :4 7’, 4., y. 3 WM, 7.»qu *7 w 7%; xiv/1% b) ’1: m g,“ awn/M 2M rum/Ad. 7; “rev/5‘44 Mv‘f (wepé‘q 5.1qu fl Met/(MW OVC (sum 4/“? a, amt MK), in! 6) Mfzfi/‘épzfl‘iflaitwi 5-)M_Mflrm; N"’¢[email protected]~' Tz=fll0x flaws fiavckCa) {L‘MEL— : 7/; LM / 4’ 2) (30 points) Atwood’s lesser machine Two blocks are connected by a string, as shown at the left. Ignore friction. Note that the blocks do not have equal masses. a) Does mass M2 fall faster, slower or equal than when it’s in free-fall? Be sure to explain your reasoning. b) How are the pull of the string on M] and the pull of the string on M2 related? Please comment on both direction and magnitude. c) Is the total momentum of M1 and M2 conserved? Why or why not? (1) Find an expressionfor the acceleration of M1 in terms of M1, M2 and g. Be sure to explain your conventions, and describe how you’ve checked your result. © [41 VQ/CQ M CmLfl> Muff at "Cong Marge" 4) 44W. 0’1 ® {£949. fl'g} a €ro~ ’47 M— ML) M; W flvce «A 4.; fl flak “7ij W on J /&k flat “2% MIL) T; (“‘0‘ U21". T’HLj '7 q"""17. , T:"€(L +ML3 ML : +4.M,+ Mt) ,. -. 6 6 9(41 '~’ "Hat‘ij 36? 3) (15 points) Bouncing a ball You throw a ball of mass 0.1kg with speed 4 m/s at a toy car of mass 0.7 kg. a) If the ball sticks to the car, what will be their combined speed afterwards? b) If the ball bounces back instead of sticking, will the car be moving faster or slower? P/fivb = @WW/«M O = (9.9L pg;— .— a (mmwg) gills—CC fl‘ve M, M 94/Cez/ pmon a; I {/C' : §:S &.0 4) (25 points) The leg bone is connected to... WT @ Consider a simple model of your leg while riding in an elevator. The ML mass of the leg is mL, the mass of your upper body is m8, and the elevator is accelerating upward with constant acceleration a. //// a) Identify all the forces acting on the leg by drawing and £10m» clearly labeling a free—body diagram. b) Identify all the forces acting on your upper body by drawing and clearly labeling another free—body diagram. c) Which forces in (a) and (b) are related, and how? d) In terms of the variables given, find the force that your leg is exerting on the floor. CK / g mm m WAM/ ’ fe?$ P (9“ v-L My,“ Lea/e L0 My,» M [i M an Wyn/(,3) 2 ' gw zwr V60 (4’- W M “fflk r50 W‘r C 0 ~ 3 ")0 G>C9 /Q W % a- ) / ...
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