9.2 Conservation of Momentum

Transcription

1 Worksheet 9. Conservation of Momentum 1. Mya and Kengo are both at rest and facing each other on roller skates. Mya has a mass of 65 kg and Kengo has a mass of 40 kg. When they push against each other Mya moves at a speed of 6 m/s. a) How fast does Kengo move? b) How much work did they do pushing against each other?. A loaded freight car whose mass is kg rolls along a level track at a speed of 1.5 m/s toward an empty freight car. When the two cars collide, they couple and proceed at 1 m/s. a) Determine the mass of the empty freight car. b) What are the initial and final kinetic energies of the system and what percent of the energy was lost (energy lost / initial energy). 3. A 6 kg mass moving at 10 m/s has a head-on collision with a 4 kg mass that is initially at rest. Following the collision, the 6 kg mass moves at a speed of m/s. a) Find the final speed of the 4 kg mass. b) Is this collision elastic, inelastic, or something in between? Justify your answer. 4. A baseball (m.149 kg) is pitched at a speed of 36 m/s. The batter swings a bat (m.85 kg) at a speed of 15 m/s. After the collision, the baseball is moving in straight toward the pitcher at a speed of 4 m/s. a) What is the speed of the bat after the collision? b) How much heat was generated in this collision? 5. A 3. kg handgun fires a 35 g bullet. The bullet leaves the handgun with a velocity of 80 m/s. What is the velocity of recoil of the handgun? 6. A 7 Th nucleus (m = 7 u, don t worry about the units, they will cancel out) decays into a 3 Ra nucleus by α emission (an α particle is the same as a 4 He nucleus). When a 7 Th nucleus at rest decays, the a particle has a final speed of m/s. What is the final speed of the recoiling 3 Ra nucleus? 7. An open railroad with a mass of kg roll at a speed of 3 m/s when it starts raining. What is the velocity of the car when kg of water has accumulated in it? 8. A football running back with a mass of 110 kg runs at 4 m/s. A stationary free safety with a mass of 85 kg grabs him and the two continue to move together. What is their new combined speed? 9. A VW Beetle with a mass of 850 kg travels at a speed of 5 m/s when it has a head on collision with a pick up with a mass of 080 kg. Both vehicles come to a rest as a result of the collision. a) What was the speed of the pick up? b) How much kinetic energy was lost in the collision? 10. An astronaut with a mass of 140 kg working in space accidently pushes off from his spacecraft and begins drifting away at a speed of 0.5 m/s. To get back he throws his 5 kg tool bag at a speed of 16 m/s. At what speed will he be moving back toward the spacecraft?

2 1a. Before After Kengo moves backward at 9.8 m/s. p M +p K m M v M + m K = m v M M m K = 65$kg 40$kg = 9.8$m/s ( )( 6$m/s) 1b. W = ΔKE M + ΔKE K W = 1 m v + 1 m v M M K K W = 1 65%kg ( ) 6%m/s W = 1170%J%+%1900%J W = 3100%J %kg ( )( 9.8%m/s) They do 3100 J of work. a. Before After ( )( 1.5#m/s) p = 16#000#kg p = 4#000#kg m/s = 4#000#kg m/s p = 4#000#kg m/s m = p v m = 4#000#kg m/s 1#m/s m = 4#000#kg The mass of both cars is kg. The second car must have a mass of kg.

3 b. Before After before = 1 16$000$kg ( ) 1.5$m/s = 18$000$J energy&lost initial&energy = 18&000&J&1&1&000&J 18&000&J.33 =&33% = J, = J, resulting in a 33% loss. after = 1 4$000$kg ( ) 1$m/s = 1$000$J 3a. Before After = m 1 v 1 = 6#kg ( )( 10#m/s) = 60#kg m/s = m v = 4#kg = 60#kg m/s ( )( 0#m/s) = 60#kg m/s = 48#kg m/s After the collision the 4 kg mass is moving at 1 m/s. = m 1 v 1 = 6#kg ( )( #m/s) = 1#kg m/s v = m v = 48#kg m/s 4#kg v = 1#m/s 3b. Before After 1 = 1 6$kg ( ) 10$m/s = 300$J = 300#J = 1 4$kg ( ) 0$m/s $J 1 = 1 6$kg $m/s = 1$J = 1#J#+#88#J = 300#J = 1 4$kg ( ) 1$m/s = 88$J Since the total kinetic energy before the collision is equal to the total kinetic energy after the collision, the collision is elastic.

4 4a. Before After = m ball v ball.149&kg ( )()36&m/s) = )5.364&kg m/s = m bat.85%kg = 7.386&kg m/s ( )( 15%m/s) = 1.75%kg m/s = 7.386&kg m/s = 1.18%kg m/s The final speed of the bat is 1.3 m/s. = m ball v ball.149&kg ( )( 4&m/s) = 6.58&kg m/s = m bat = 1.18%kg m/s 0.85%kg = 1.3%m/s 4b. Before After ball ( )( 36'm/s) = 'kg = 96.6'J bat ( )( 15'm/s) = 'kg = 95.6'J = 96.6$J$+$95.6$J = 19.$J Q = ΔKE Q = 61.1%J There was 61.1 J of heat generated in the collision. ball ( )( 4'm/s) = 'kg = 131.4'J Q = 19.%J%'%131.1%J bat ( )( 1.3'm/s) = 'kg.7'J = 131.4%J%+%0.7%J = 13.1%J 5. Before After The gun moves backward at 3.1 m/s. p b +p g m b v b + m g = m b v b m g ( )( 80%m/s) = 0.035%kg 3.%kg = 3.1%m/s

5 6. Before After The radium nucleus recoils backward at m/s. p Ra +p He m Ra + m He v He = m He v He m Th ( )( 1.4# #10 7 #m/s) = 4#u 3#u =.5# #10 5 #m/s 7. Before After p car = m car v car p car = 1#000#kg ( )( 3#m/s) p car = 36#000#kg m/s = 36#000#kg m/s p rain = m rain v rain p rain = 36#000#kg m/s v = p m 4#000#kg m/s v = 1#000#kg#+#6#000#kg v = #m/s The velocity after the car is full of rain is m/s. 8. Before After p rb = m rb v rb p rb = 110#kg ( )( 4#m/s) p rb = 440#kg m/s = 440#kg m/s p fs = m fs v fs p fs = 440#kg m/s v = p m v = 440#kg m/s 110#kg#+#85#kg v =.3#m/s The velocity after the collision is.3 m/s.

6 9a. Before After p VW +p truck m VW v VW + m truck = m v VW VW m truck = 850$kg 080$kg = 10.$m/s ( )( 5$m/s) The truck was moving in the opposite direction at 10. m/s. 9b. Before After KE VW = 1 m v VW VW KE VW = 1 800%kg 5%m/s KE VW = 66%000%J = 66#000#J#+#109#000#J = 374#000#J KE truck = 1 m v truck truck KE truck = 1 080%kg ( ) 10.%m/s KE truck = 109%000%J There were J of kinetic energy lost. ΔKE =!+! ΔKE!J 374!000!J ΔKE = 374!000!J 10. Before After ( )( 0.5$m/s) = 140$kg$+$5$kg = 7.5$kg m/s p tool = m tool v tool p tool = 5"kg ( )( 16"m/s) p tool = 80"kg m/s The astronaut moves backwards at a speed of 0.05 m/s. = 7.386&kg m/s p astronaut = 7.5%kg m/s%+%80%kg m/s p astronaut = +7.5%kg m/s v astronaut = p astronaut m astronaut v astronaut = +7.5%kg m/s 140%kg v astronaut = +0.05%m/s

7