Essential University Physics, 3e (Wolfson) Chapter 9 Systems of Particles
9 . 1 Conc e p t ua lQue s t i o ns 1) Consider two less-than-desirable options. In the first you are driving 30 mph and crash headon into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce bou nce off the thing it hits and the collision time is the same in both cases. !hich of these two situations would result in the greatest impact force" #) hitting the other car $) hitting the brick wall C) %he force would be the same in both cases. &) !e cannot answer this 'uestion without more information. () one of these is true. #nswer* C +ar* 1
,) #s a tile falls from the roof of a building to the ground its momentum is conserved. #) %rue $) alse #nswer* $ +ar* 1
3) ou ou are standing on a skateboard initially at rest. # friend throws a very heavy ball towards you. ou ou can either catch the ob/ect or deflect the ob /ect back towards your friend such that it moves away from you with the same speed as it was originally thrown). !hat should you do in order to III2( your speed on the skateboard" #) Catch the ball. $) &eflect the ball. C) our our final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball. #nswer* # +ar* 1
) 4n a smooth hori5ontal floor an ob/ect slides into a spring which is attached to another mass that is initially stationary. !hen the spring is most compressed both ob/ects are moving at the same speed. Ignoring friction what is conserved during this interaction" #) momentum and mechanical energy $) momentum only C) kinetic energy only &) momentum and kinetic energy () momentum and potential energy #nswer* # +ar* 1
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9) # baseball is thrown vertically upward and feels no air resistance. #s it is rising #) both its momentum and its mechanical energy are conserved. $) its momentum is not conserved but its mechanical energy is conserved. C) both its momentum and its kinetic energy are conserved. &) its kinetic energy is conserved but its momentum is not conserved. () its gravitational potential energy is not conserved buts its momentum is conserved. #nswer* $ +ar* 1
7) # small glider is coasting hori5ontally when suddenly a v ery heavy piece of cargo falls out of the bottom of the plane. ou can neglect air resistance. :ust after the cargo has fallen out #) the plane speeds up and the cargo slows down. $) the plane speeds up but the cargo does not change speed. C) neither the cargo nor the plane change speed. &) the cargo slows down but the plane does not change speed. () both the cargo and the plane speed up. #nswer* C +ar* 1
;) # small car has a head-on collision with a large truck. !hich of the following statements concerning the magnitude of the average force due to the collision is correct" #) %he truck e
=) In a collision between two ob/ects having une'ual masses how does magnitude of the impulse imparted to the lighter ob/ect by the heavier one compare with the magnitude of the impulse imparted to the heavier ob/ect by the lighter one" #) %he lighter ob/ect receives a larger impulse. $) %he heavier ob/ect receives a larger impulse. C) $oth ob/ects receive the same impulse. &) %he answer depends on the ratio of the masses. () %he answer depends on the ratio of the speeds. #nswer* C +ar* 1
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>) In a perfectly (?#@%IC collision between two perfectly rigid ob/ects #) the momentum of each ob/ect is conserved. $) the kinetic energy of each ob/ect is conserved. C) the momentum of the system is conserved but the kinetic energy of the system is not conserved. &) both the momentum and the kinetic energy of the system are conserved. () the kinetic energy of the system is conserved bu t the momentum of the system is not conserved. #nswer* & +ar* 1
10) In an I(?#@%IC collision between two ob/ects #) the momentum of each ob/ect is conserved. $) the kinetic energy of each ob/ect is conserved. C) the momentum of the system is conserved but the kinetic energy of the system is not conserved. &) both the momentum and the kinetic energy of the system are conserved. () the kinetic energy of the system is conserved bu t the momentum of the system is not conserved. #nswer* C +ar* 1
11) # shell e
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1,) :ac'ues and Aeorge meet in the middle of a lake while paddling in their canoes. %hey come to a complete stop and talk for a while. !hen they are ready to leave :ac'ues pushes AeorgeBs canoe with a force
to separate the two canoes. !hat is correct to say about the final
momentum and kinetic energy of the system if we can neglect any resistance due to the water" #) %he final momentum is in the direction of
but the final kinetic energy is 5ero.
$) %he final momentum is in the direction opposite of C) %he final momentum is in the direction of
but the final kinetic energy is 5ero.
and the final kinetic energy is positive.
&) %he final momentum is 5ero and the final kinetic energy is 5ero. () %he final momentum is 5ero but the final kinetic en ergy is positive. #nswer* $ +ar* 1
13) # 1.0-kg block and a ,.0-kg block are pressed together on a hori5ontal frictionless surface with a compressed very light spring between them. %hey are not attached to the spring. #fter they are released and have both moved free of the spring #) the lighter block will have more kinetic energy than the heavier block. $) the heavier block will have more kinetic energy than the lighter block. C) both blocks will both have the same amount of kinetic energy. &) both blocks will have e'ual speeds. () the magnitude of the momentum of the heavier block will be greater than the magnitude of the momentum of the lighter block. #nswer* # +ar* 1
1) %here must be e'ual amounts of mass on both side of the center of mass of an ob/ect. #) %rue $) alse #nswer* $ +ar* 1
9 . 2 Pr o bl e ms 1) # time-varying hori5ontal force F t ) At D Bt , acts for 0.900 s on a 1,.,9-kg ob/ect starting at time t 1.00 s. In the @I system A has the numerical value .90 and B has the numerical value =.;9. a) !hat are the @I units of A and B" b) !hat impulse does this force impart to the ob/ect" #nswer* a) A* Es kg F mEs 7 B* Es, kg F mEs b) 1,.> F s hori5ontally +ar* 1
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,) # ,.90-kg stone is dropped from rest at a height of 3.;9 m. !hat impulse does gravity impart to this stone from the instant it is dropped until it hits the g round assuming negligible air resistance" #nswer* ,1. F s +ar* 1
3) # firecracker breaks up into several pieces one of which has a mass of ,00 g and flies off along the x-a3.9 kgFmEs at ,=.=G from the x-a.9G from the x-a=3G from the x-a
) # stationary 1.7;-kg ob/ect is struck by a stick. %he ob/ect e
9) &uring a collision with a wall the velocity of a 0.,00-kg ball changes from ,0.0 mEs toward the wall to 1,.0 mEs away from the wall. If the time the ball was in contact with the wall was 70.0 ms what was the magnitude of the average force applied to the ball" #) 0.0 $) 10; C) 17.; &) ,7.; () 13.3 #nswer* $ +ar* 1
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7) # 0.900-kg ball traveling hori5ontally on a frictionless surface approaches a very massive stone at ,0.0 mEs perpendicular to wall and rebounds with ;0.0H of its initial kinetic energy. !hat is the magnitude of the change in momentum of the stone" #) 1=. kgFmEs $) 1.0 kgFmEs C) 3.00 kgFmEs &) 1.73 kgFmEs () 0.000 kgFmEs #nswer* # +ar* 9
;) # 7,0-g ob/ect traveling at ,.1 mEs collides head-on with a 3,0-g ob/ect traveling in the opposite direction at 3.= mEs. If the collision is perfectly elastic what is the change in the kinetic energy of the 7,0-g ob/ect" #) It loses 0.,3 :. $) It gains 0.7> :. C) It loses 0.; :. &) It loses 1. :. () It doesnt lose any kinetic energy because the collision is elastic. #nswer* # +ar* 1
=) # ,.3-kg ob/ect traveling at 7.1 mEs collides head-on with a 3.9-kg ob/ect traveling in the opposite direction at .= mEs. If the collision is perfectly elastic what is the final speed of the ,.3-kg ob/ect" #) 0.= mEs $) ;.1 mEs C) 3.= mEs &) .3 mEs () 7.7 mEs #nswer* $ +ar* 1
>) # car of mass 17=> kg collides head-on with a parked truck of mass ,000 kg. @pring mounted bumpers ensure that the collision is essentially elastic. If the velocity of the truck is 1; kmEh in the same direction as the carBs initial velocity) after the collision what was the initial speed of the car" #) 1> kmEh $) 3= kmEh C) ,> kmEh &) 10 kmEh #nswer* # +ar* 90D
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10) # block of mass m =.0 kg moving on a hori5ontal frictionless surface with a speed .,0 mEs makes a perfectly elastic collision with a block of mass M at rest. #fter the collision the =.0 block recoils with a speed of 0.00 mEs. In the figure the blocks are in contact for 0.,00 s. %he magnitude of the average force on the =.0-kg block while the two blocks are in contact is closest to
#) 1>3 $) 1=9 C) 1;7 &) 17= () 170 #nswer* # +ar* 1
11) # billiard ball traveling at 3.00 mEs collides perfectly elastically with an identical billiard ball initially at rest on the level table. %he initially moving billiard ball deflects 30.0G from its original direction. !hat is the speed of the initially stationary billiard ball after the collision" #) ,.00 mEs $) 0.=77 mEs C) 1.90 mEs &) ,.9> mEs () 0.;90 mEs #nswer* C +ar* 1
1,) # pool player is attempting a fancy shot. Je hits the cue ball giving it a speed of 9.9; mEs and directs its center on a path tangent to the surface of the target ball having the same mass as the cue ball. #fter the collision on a frictionless table) the initially-stationary ball moves with a speed of .=, mEs. #fter the collision the new speed of the cue ball and the relative direction of the balls are closest to #) ,.;> mEs at >0G to each other. $) ,.;> mEs at 70G to each other. C) =.3 mEs at >0G to each other. &) =.3 mEs at 70G to each other. #nswer* # +ar* 1
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13) # =0-kg car moving at 1. mEs hits from behind a 9;0-kg car moving at 13.3 mEs in the same direction. If the new speed of the heavier car is 1.0 mEs what is the speed of the lighter car after the collision assuming that any unbalanced forces on the system are negligibly small" #) 13.7 mEs $) 10.9 mEs C) 1>.> mEs &) 9., mEs #nswer* # +ar* 1
1) # ,.00-kg ob/ect traveling east at ,0.0 mEs collides with a 3.00-kg ob/ect traveling west at 10.0 mEs. #fter the collision the ,.00-kg ob/ect has a velocity 9.00 mEs to the west. Jow much kinetic energy was lost during the collision" #) 0.000 : $) 9= : C) 917 : &) >1.; : () 1;9 : #nswer* $ +ar* 1
19) # 19-g bullet is shot vertically into an ,-kg block. %he block lifts upward =.0 mm see the figure). %he bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s. #ssume the force on the bullet is constant during penetration and that air resistance is negligible. %he initial kinetic energy of the bullet is closest to
#) ,1 : $) 1 : C) 10 : &) 0.001, : () 0.17 : #nswer* # +ar* 90D
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17) %wo ob/ects of the same mass move along the same line in opposite directions. %he first mass is moving with speed v. %he ob/ects collide stick together and move with speed 0.100v in the direction of the velocity of the first mass before the collision. !hat was the speed of the second mass before the collision" #) 1.,0v $) 10.0v C) 0.>00v &) 0.=00v () 0.00v #nswer* & +ar* 1
1;) #n =.0-g bullet is shot into a .0-kg block at rest on a frictionless hori5ontal surface see the figure). %he bullet remains lodged in the block. %he b lock moves into an ideal massless spring and compresses it by =.; cm. %he spring constant of the spring is ,00 Em. %he initial velocity of the bullet is closest to
#) 1100 mEs. $) 1,00 mEs. C) >00 mEs. &) 1300 mEs. () 1000 mEs. #nswer* # +ar* 1
1=) In the figure determine the character of the collision. %he masses of the blocks and the velocities before and after are given. %he co llision is
#) perfectly elastic. $) partially inelastic. C) completely inelastic. &) characteri5ed by an increase in kinetic energy. () not possible because momentum is not conserved. #nswer* # +ar* 1
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1>) In the figure determine the character of the collision. %he masses of the blocks and the velocities before and after are given and no other unbalanced forces act on these blocks. %he collision is
#) perfectly elastic. $) partially inelastic. C) completely inelastic. &) characteri5ed by an increase in kinetic energy. () not possible because momentum is not conserved. #nswer* ( +ar* 1
,0) # 9.00-kg ball is hanging from a long but very light fle3 m. &) ,.,0 m. () 3.7> m. #nswer* C +ar* 1
,1) # 1000-kg car approaches an intersection traveling north at ,0.0 mEs. # 1,00-kg car approaches the same intersection traveling east at ,,.0 mEs. %he two cars collide at the intersection and lock together. Ignoring any e.; mEs in a direction ;.;G east of north $) ,1.1 mEs in a direction ;.;G west of south C) 19.1 mEs in a direction 9,.=G east of north &) ,1.1 mEs in a direction 9,.=G east of north () ,1.1 mEs in a direction ;.;G east of north #nswer* C +ar* 1
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,,) %wo automobiles traveling at right angles to each other collide and stick together. Car A has a mass of 1,00 kg and had a speed of ,9 mEs before the collision. Car B has a mass of 1700 kg. %he skid marks show that immediately after the collision the wreckage was moving in a direction making an angle of 0G with the original direction of car A. !hat was the speed of car B before the collision assuming that any other unbalanced forces are negligible" #) 17 mEs $) 1= mEs C) 11 mEs &) ,1 mEs () 1 mEs #nswer* # +ar* 1
,3) # >00-kg car traveling east at 19.0 mEs collides with a ;90-kg car traveling north at ,0.0 mEs. %he cars stick together. #ssume that any other unbalanced forces are negligible. a) !hat is the speed of the wreckage /ust after the collision" b) In what direction does the wreckage move /ust after the collision" #nswer* a) 1,., mEs b) =.0G of ( +ar* 1
,) # car heading north collides at an intersection with a truck of the same mass as the car heading east. If they lock together and travel at ,= mEs at 7G north of east /ust after the collision how fast was the car initially traveling" #ssume that any other unbalanced forces are negligible. #) 0 mEs $) ,0 mEs C) =0 mEs &) 30 mEs #nswer* # +ar* 1
,9) %wo ice skaters push off against one another starting from a stationary position. %he 9.0-kg skater ac'uires a speed of 0.3;9 mEs. !hat speed does the 70.0-kg skater ac'uire" #ssume that any other unbalanced forces during the collision are negligible. #) 0.900 mEs $) 0.,=1 mEs C) 0.3;9 mEs &) 0.;90 mEs () 0.000 mEs #nswer* $ +ar* 1
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,7) 4n a frictionless hori5ontal table two blocks A of mass ,.00 kg and B of mass 3.00 kg) are pressed together against an ideal massless spring that stores ;9.0 : of elastic potential energy. %he blocks are not attached to the spring and are free to move free of it once they are released from rest. %he ma
,;) # 10.0-kg shell is traveling hori5ontally to the right at ,9.0 mEs relative to the ground when it e
,=) # plate falls vertically to the floor and breaks up into three pieces which slide along the floor. Immediately after the impact a 3,0-g piece moves along the x-aG from the x-a.=G from the x-aG from the x-a.>G from the x-a.=G from the x-a
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,>) # 1.,-kg spring-activated toy bomb slides on a smooth surface along the x-a0 mEs along the negative y-a
#) 31G. $) 3;G. C) 3=G. &) 93G. () 9>G. #nswer* # +ar* 1
30) # 1.,-kg spring-activated toy bomb slides on a smooth surface along the x-a0 mEs along the negative y-a
#) 0.,0 :. $) 0., :. C) 0.,= :. &) 0.3, :. () 0.37 :. #nswer* & +ar* 1
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31) # ,.00-m rod of negligible mass connects two very small ob/ects at its ends. %he mass of one ob/ect is 1.00 kg and the mass of the other is unknown. %he center of mass of this system is on the rod a distance 1.70 m from the 1.00-kg mass ob/ect. !hat is the mass of the other ob/ect" #) .11 kg $) 3.,, kg C) .00 kg &) 0.,90 kg () 0.=00 kg #nswer* C +ar* 9
3,) # uniform piece of wire ,0 cm long is bent in a right angle in the center to give it an ?shape. Jow far from the bend is the center of mass of the bent wire" #) ,.9 cm $) 3.9 cm C) .9 cm &) 9.0 cm () ;.1 cm #nswer* $ +ar* 1
33) # long thin rod of length L has a linear density λ x) Ax where x is the distance from the left end of the rod. a) Jow far is the center of mass of the rod from the left end of the rod" b) !hat is the mass of the rod" #nswer* a) , LE3 b) AL,E, +ar* 1
3) In the figure four point masses are placed as shown. %he x and y coordinates of the center of mass are closest to
#) ,., m ,.7 m). $) ,., m ,.; m). C) ,.3 m ,.7 m). &) ,.3 m ,.; m). () ,.3 m ,.= m). #nswer* ( +ar* 1
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39) In the figure a 70-cm length of uniform wire of 70 g mass and negligible thickness is bent into a right triangle. %he x and y coordinates of the center of mass in cm are closest to
#) = 3). $) = 9). C) > ). &) 10 3). () 10 9). #nswer* & +ar* 1
37) # 310-g air track cart is traveling at 1.,9 mEs and a ,70-g cart traveling in the opposite direction at 1.33 mEs. !hat is the speed of the center of mass of the two carts" #) ,.=0 mEs $) 0.0;3, mEs C) 0.131 mEs &) 1.; mEs () 1.,> mEs #nswer* $ +ar* 9
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