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# MT1 S04 - PROBLEM 1(25 points A specially designed...

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Unformatted text preview: PROBLEM 1 (25 points). A specially designed parachute suddenly de- ploys at time t = i}, and starts to decelerate a racing car, to which it is attached at the rear. Observers stationed on the side of the racetrack make measurements of the position of the racing car as a function of time slit}. Their data ﬁt the following equation: 1: (r) = ﬂit? + or — C's—m {1) with A = 1131) mfsgI B = lﬂﬂmf's, C = lilﬂ In, and D = 1.00 if“. {CAVEAT Do not aslume that :c (t = G) = :0 = U.) (a) What is the instantaneous velocity of the racing car immediately.r after the deployment of the parachute at t = D? (b) What is the instantaneous velocity of the racing car after a time t = 1 second? {c} What is the average velocity of the racing car in the interval tram t = U to t = 1 second? (d) What is the instantaneous acceleration of the racing car immediately after the deployment of the parachute at t = 0? (e) What is the instantaneous acceleration of the racing car after a time t m 1 second? (f) What is the average acceleration of the racing car in the interval from t=ﬂtot=1 second? PROBLEM 2 {16 points). A swimmer can swim at a leisurely, steady speed of {1.500 refs in still water. She is trying to swim at her usual leisurely, steady speed directly.r across a. 4ﬂﬂ-meter-wide river whose steady current is 0.300 mfs, so that she can arrive at a point directly across the river on the opposite bank. {3.) At what upstream angle must she aim her swimming so that she can arrive at this point? [b] How long would it take her to reach the other side? PROBLEM 3 (15 points}. An Olmpic long jumper makm a jump of a distance 9.30 In. His horizontal speed is measured to be 9.53 mfs, as he leaves the ground at t s 0. Assume that air resistance is negligible, and that he leaves the ground, and also lands, standing upright. (a) At what time does he reach his maximum height? [b] 1What is the maximum height he reached? {c} At what hutial angle did he push away from the ground at t: 0‘? PROBLEM 4 (25 points). Two cube-shaped masses m1 = 513G kg and m2 = 1070 kg are attached to each other by means of a string stretched over a pulley, but these two masses are on opposite sides of the polls}r which is rigidly attached to the top of a double incline. The two inclines on the two aid. of the pulley have oppositer signed slopes, but the same inclination angle 3 = 30.0“ with respect to horizontal; see Figure 1. The pulley is frictionless and massless, Figure 1: Figure for Problem 4. and the string is nonelastic and meealess; the masses slide frictionlessly on the incline: (i.e.. airtracks). (3.) Draw separate freebody diagrams for the two messes. Label all forces acting on the masses. (b) What is the common magnitude of the acceleration of the two masses? (c) What is the tension in the string? PROBLEM 5 (25 points). Two cube-shaped masses m1 and mg, with different materials glued onto their undersides, are connected together by a. maaaless, nonelastic string. They are sliding down together an inciine at an angle 8 = 300° to the horizontal (see Figure 2 below). The coefficients of kinetic friction are p1 = 0.200 for the lower mass m; = 5.00 kg, and M = 0.300 and for the upper mass m: = 5.00 kg, respectively: (a) Draw separate free-body diagrams for the two masses. Label all forca acting on the masses. (b) If there were no string to connect the two masses, what would he the two accelerations of the two masses, rmpectively? New connect the two menace by means of the string. Will the string be in tension, or will it become slack, if the the two masses are released at the same time with the string initially stretched to its maximum length? Explain. (c) What is the acceleration of the two masses when they are connected by the string? (d) What is the tension in the string, ii any? string ea.‘ Figure 2: Figure for Problem 5. ...
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MT1 S04 - PROBLEM 1(25 points A specially designed...

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