PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 6 HOMEWORK PROBLEMS Chapter 6 MOMENTUM AND COLLISIONS PART A Hand in your answers in class on scantron on Wednesday 22 September 2010 The questions have been numbered so you can use the back side of an older scantron Write your name class 1401 and HW 6 on the scantron 1 A 57 0 g tennis ball is traveling straight at a player at 21 0 m s The player volleys the ball straight back at 25 0 m s If the ball remains in contact with the racket for 0 060 s what average force acts on the ball a 22 6 kg m s2 b 32 5 kg m s2 c 43 7 kg m s2 d 72 1 kg m s2 e 102 kg m s2 The impulse given to the ball is I Fav Dt mv fi mv m v fi v Choosing the direction of the final velocity of the ball as the positive direction this gives Fav m v fi v Dt 57 0 10 3 kg 25 0 m s 21 0 m s 43 7 kg m s2 43 7 N 0 060 s and the correct choice is c 2 A car of mass m traveling at speed v crashes into the rear of a truck of mass 2m that is at rest and in neutral at an intersection If the collision is perfectly inelastic what is the speed of the combined car and truck after the collision a v b v 2 c v 3 d 2v e None of these Assuming that the collision was head on so that after impact the wreckage moves in original direction of the car s motion conservation of momentum during the impact gives mc mt v f mc v0c mt v0t mc v mt 0 or mc v m vf v v m 2m 3 mc mt showing that c is the correct choice 3 A small china bowl having kinetic energy E is sliding along a frictionless countertop when a server with perfect timing places a rice ball into the bowl as it passes him If the bowl and rice ball have the same mass what is the kinetic energy of the system thereafter a 2E b E c E 2 d E 4 e E 8 The mass in motion after the rice ball is added to the bowl is twice the original moving mass Therefore to conserve momentum the speed of the rice ball bowl after the event must be one half of the initial speed of the bowl i e f i 2 The final kinetic energy is then 2 KE f v 1 1 1 1 E mball mbowl v2 2mbowl i mbowl v2 2 2 2 2 2 2 and the correct choice is c PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 6 4 In a game of billiards a red billiard ball is traveling in the positive x direction with speed v and the cue ball is traveling in the negative x direction with speed 3v when the two balls collide head on Which statement is true concerning their velocities subsequent to the collision Neglect any effects of spin a red ball v cue ball 3v b red ball v cue ball 2v c red ball 3v cue ball v d red ball v cue ball 3v e The velocities can t be determined without knowing the mass of each ball Billiard balls all have the same mass and collisions between them may be considered to be elastic The dual requirements of conservation of kinetic energy and conservation of momentum in a one dimensional elastic collision are summarized by the two relations m1v1i m2 v2 i m1v1 f m2 v2 1 and v1i v2i v1 f v2 2 In this case m1 m2 and the masses cancel out of the first equation Call the cue ball 1 and the red ball 2 so that 1i 3 2i 1f cue and 2f red Then the two equations become 3v v vcue vred vcue vred 2v or 1 and 3v v vcue vred or vcue vred 4v 2 Adding the final versions of these equations yields 2 cue 2 or cue Substituting this result into either 1 or 2 above then yields red 3 Thus the correct response for this question is c 5 A 5 kg cart moving to the right with a speed of 6 m s collides with a concrete wall and rebounds with a speed of 2 m s Is the change in momentum of the cart a 0 b 40 kg m s c 240 kg m s d 230 kg m s or e 210 kg m s We choose the original direction of motion of the cart as the positive direction Then i 6 m s and f 2 m s The change in the momentum of the cart is Dp mv fi mv m v fi v and choice c is the correct answer 5 kg 2 m s 6 m s 40 kg m s PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 6 6 A 0 10 kg object moving initially with a velocity of 0 20 m s eastward makes an elastic head on collision with a 0 15 kg object initially at rest What is the final velocity of the 0 10 kg object after the collision a 0 16 m s eastward b 0 16 m s westward c 0 040 m s eastward d 0 040 m s westward e None of these Requirements of conserving both momentum and kinetic energy in this one dimensional elastic collision are summarized by the equations m1v1i m2 v2 i m1v1 f m2 v2 1 and v1i v2 i v1 f v2 2 Choosing eastward as the positive direction we have m1 0 10 kg 1i 0 20 m s m2 0 15 kg and 2i 0 The general equations then become 0 10 kg 0 20 m s 0 15 kg 0 0 10 kg 1f 0 15 kg 2f or after simplifying 1f 1 50 2f 0 20 m s 1 and 0 20 m s 0 1f 2f or 2f 1f 0 20 m s 2 Substitute the final version of 2 into the final version of 1 to obtain 2 50v1f 0 10 m s yielding 1f 0 040 m s or 1f 0 040 m s westward This means that d the correct choice for this question 7 A 0 004 kg bullet is fired into a 0 200 kg block of wood at rest on a horizontal surface After impact the block with the embedded bullet slides 8 00 m before coming to rest If the coefficient of friction is 0 400 what is the speed of the bullet before impact a 96 m s b 112 m s c 286 m s d 404 m s e 812 m s First consider the motion of the block with embedded bullet from just after impact until it comes to rest During this time the only force doing …