Name:

WASHINGTON UNIVERSITY

Department of Mechanical Engineering

ME 232 - Dynamics

MIDTERM EXAMINATION 1

SHOW ALL WORK:A correct answer without supporting work will not receive credit.DISTINGUISH VECTORSAND SCALARS

USE CONSISTENT, APPROPRIATE UNITS

1. (25 points). Tarzan has a mass of 100 kg and, starting from rest, swings ona vine chosen so that his center of mass is exactly 10 m from the supportinglimb (A). At the bottom of his trajectory the vine hits a limb (B), 7 m belowlimb A.

(a)(b)(c)

What is Tarzan's initial acceleration?

What is Tarzan's velocity when the vine contacts limb B?What force must Tarzan exert to hold onto the vine just before and justafter the vine strikes limb B?

NOTE: At the instant the vine strikes B Tarzan is considered to be

directly below points A and B.III' -'(I ,

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2. (25 points) A small plane flies horizontally with a speed of 180 mi/hr at analtitude of 400 ft. The pilot drops a package at A; the package has aparachute that deploys at B and allows the package to descend vertically ata constant rate of 6 ft/sec. The total time to reach the ground is 37 sec.What horizontal lead, L, is required so that the package hits the target?(Neglect air resistance between points A and B).

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3. (25 points) A WU undergraduate student designs a system to move a 50 kgwooden cart without getting off the couch, by continuously shooting the cartwith round, 0.2 kg metal balls from an air gun (Case A, below). The horizontalspeed of the ball is 45 mls as it leaves the gun. Air resistance decreases thespeed to 35 mls at impact. The coefficient of restitution is e=0.8 for theimpact.

(a) What is the increase in the speed of the cart at each impact?(b) What time between impacts will provide an average cart acceleration of

1 mls2 ?

(c) A graduate student from MIT examines the system and decides it canbe easily improved by substituting pointed bullets to decrease airresistance (Case B, below). The average drag force is reduced to 1,4ofwhat it was for the round bullets, but the bullets stick in the woodcart. Mass of the new bullets is 0.2 kg as well.

What is the increase in speed with each impact with the pointed bullet?Is the system improved?

HINT: Consider the first impact. Others are equivalent.

HINT for Part (c): Consider the work done by the drag force.

NOTE: Neglect the increase in mass due to bullets accumulating in thecart.

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