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Nmne _ _____________________ P hysics D epartment
Duquesne University . "" PH211-01 GAP I , , Exam 3 'December 9, 2008
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S HOW Y OUR W ORK O N A LL P ROBLEMS, I NCLUDING M ULTIPLE C HOICE.
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TIris test covers Chapters 8 - 10. There are 5 multiple-choice questions worth 5 points-each, and 5 long-answer questions worth 15 points each. There are 100 points possible. Partial credit will be given, but only i f you. S~ow your work and yourreasomng is clear!!!
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Moments o f inertia 1. solid disk (about an axis through its center and perpendicular to the plane o f the
disk): 1 = Y, MR'
2, r od ( about a n a xis t hrough its 'center a nd p erpendicular t o i t) 1=1/12 MR'
1. Two particles interact by conservative forces and-no other forces act. They complete round . trips, endinS,at t he p oints -where t hey started, OV, , this t rip : e
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$~ A i<-=-" , - t he t otal k inetic e nergy m ight h ave a d ifferent v alue a t t he beginning a nd e nd
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B)
C)
D
E)
the total potential energy might have a differnt value at the beginning and end the total mechtmical energy might bave a diff~~eDt value at the beginning and end the total linear momenturi:l might have different'values at the beginning and end none o f the above
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2. A s a particle moves aloilg the x axis i t)s acted 0 0 by a conservative force. Tb,e potential . energy is shown below as a function o f the coordinate x o f the particle. Rank the labeled tegions accon;iuw to.,t.he tI}agnitude o f the force,least to ~est . ,:, I
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3. The ftrst graph (parabola) shows the potential energy U(x) for a particle moving on t hex axis. Which o f the following four graphs correctly gives the force F exerted on the particle? Please circle your choice.
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4. The x,y coordinates in meters o f the center o f mass o f the three-particle system shown
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1.9 m ,2.5 m
1.4 m, 2.5 m
5. A wheel starts from rest and has an angular acceleration o f 4.0 rad/s 2 . The time it takes to make 10 revolutions is: t> . (O/\.LI/ ~ 2.DIT ~
A)" 0.50 s
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6. The thin uniform rod in the figure below has mass 1.6 k g and length 2.3 m long and can pivot about a horizontal, frictionless pin through one end. I t is initially at an angle o f 25 above the horizontal. U se t he principle of conservation o f energy to determine the INITIAL a ngular speed o f t he rod i f it has angular speed w = 2 .6 rad/s when it passes through the horizontal position.
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7. A system o f t wo s mall spheres o f identical mass m collid e ob li quely as sho-wn in the figure. T he co ll ision is inelastic. Initiall y one o flhe masses is al rest. After the collision, the two go o ff with velocities v; and v ; , each at an angle o f P12 = 25 relative to the initial direction . I f the initial speed is VIO = 25 mis, find the fi nal speeds of the two spheres.
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After collision
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8 . A 4S-kg brick is suspended by a li ght s tring from a ~-kg pulley. T he b rick is re leased from rest and fa ll s to ward the floor below as the pulley rotates. T he pulley may be considered a solid disk o f radius 1.5 m. Find both (a) the a cce leration o f the block and (b) the tension in the string.
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9. An 80.0 kg student stands inside a 20.0 kg canoe that can slide freel y on a frictionless surface o f water. Both are initial ly at rest relative to the ground. On a dare (considering h e's in a canoe), the student runs as fast as he can along the canoe, Ius speed being "re1 = 3 .0 m ls relative to the cano e.
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(a) (5 points) What is the velocity (relative to the water) o f the center o f mass of t h e studentcanoe system as the student is running?
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(b) (10 points) R ecalling that the student's velocity relative to the canoe is Vrel = Ystuden t Vcanoe find the velocities Vstudent o f the student and v canoe o f the canoe (these will b.e as measured relative to the water; i f you c an't figure out the <1Swer to part a, preij::nd it is I mls for this part o f the-prb blem). : ',' . . . : ~
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10. A 60.0 k g block is held at rest against the spring o n the left (k = 4 000 N /m) w hile th at spring is compressed b y a di s tance o f 150 m from its equi li briwn length. The block is released from rest and s li des back and fo rth across the surface. most o f which is fiict ionless. bu t in the center there is a 2.00 m stretch Ihal has a kinetic c oe ffici ent o f friction j.!k = 0.200. The spring on the right has a spring cons~~n l k' = 3000 N /m .
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l' So' (a) What is the maximum compression o f the left-hand spring. the first lime the bioCk ()oy-t. t~va..J. returns after rebounding o ff the spring on the right? 1IQ'A.$,it.call ,
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, i, ", ! , , (b) What is the total dit'tance the block travels on the rough part o f the suiface before coming to rest? (Do nOl include the distance traveled on the s mooth part o f the surface. ) C ontinue on back o,flthis page i f you need m ore sp~c~. ,
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