exxxs01 - Exam 1 1. Two blocks of mass m and 2m are on a...

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Unformatted text preview: Exam 1 1. Two blocks of mass m and 2m are on a horizontal frictionless surface and are attached together by a spring with spring constant k and unstretched length 60. The heavier block is initially at rest, and the lighter block is given an initial speed 13 toward the heavier block. The spring is initially unstretched. At a later time, the lighter block is instantaneously at rest while the heavier block is moving away from the lighter block. (a) (13 points) W hat is the speed of the heavier block at this instant? (b) (20 points) What is the compression of the spring at this instant? 7‘ \solqitefli 90" X mo “M (—31“- lgi % 94“?“ mv‘ =. (film) V.[: =5 m A1: oxwxovmn‘l? gq‘nriv‘f) cow/x (N‘e SS Coi 2. (33 points) A block of mass m. and a block of mass 277‘: are ('(')l]ll(.‘(‘t(,‘(l by a string over a pulley of mass M , radius R, and moment of inertia. @1111”. The lighter block is on an inclined plane at an angle 6 above the horizontal, while the heavier block hangs down. The system is released from rest. A constant li'ictitfmal force. f acts on the lighter block. What is the final speed of the heavier block after it has (,lroymod a distance Ii? What is the condition on the frictional force so that the system actually moves after it is released? "Fche 0“: [J lqme ov‘ m \ ..L. (no gv‘fcbi‘om) 'Z '1 E- "'- l<§+V{ = 0 +0 ‘ W- Atfinc V;-O a. z ‘Q’anbv: + it“); + mal’u Jéflslnz ‘ .- E’F = imv‘e + 2 W W 5f):er commtgfid L07 SfV'CmS ‘ MW: mat + ‘3 taw/ lg’élLJ'WBW'4‘MJ 2. same ok= o/M‘S'éowigc \MOV-QJ W = lnl %‘ A \A‘ 1L: shoe =3 \“i z okc’lv“ e 0* = \AZSime 3. Two identical moons of mass M and radius R have a center—to—centcr distance d > 2B. A rock of mass m is launched from the surface of one moon toward the other. The moons have 110 atmosphere, so neglect air resistance. (a) (10 points) Consider the potential energy of the system consisting of the two planets and the rock. With the positions of the moons held fixed, sketch a graph of the potential energy of the system as a function of the position of the rock. Your graph need only be valid for positions of the rock between the two moons. (b) (23 points) What is the minimum speed the rock must be launched in order to make it to the other moon? Assume that the moons do not move. x=w. (‘0) M‘ got—'3 x/‘ocla low/1J7 molccs It £0 K— a m Sr): - WOOV‘S ’rV‘Ocic -. {$0l%&<0’( ,_= E z t' {L c,vi C3 0H2 ...
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exxxs01 - Exam 1 1. Two blocks of mass m and 2m are on a...

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