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Momentum Newton’s 2nd Law tells us that F ma From here we get ... F ma F ma v F m t F ma v F m t F t mv Imagine trying to throw a tennis ball and a bowling ball at the same speed. Since F t mv , the product F t would have to be greater for the bowling ball to get the same v . (The bowling ball has the greater mass.) To get the same speed we would have to throw harder (more force) or longer (more time). Either way, the product F t is important. It is called the impulse of the force. Imagine this time that we give the tennis ball and the bowling ball the same impulse. Since the mass of the bowling ball is greater, its velocity will be less. So the product mv is quite different from just v on its own. We call this product momentum. p mv Velocity tells us how fast and in which direction an object moves, it tell us nothing about the effort required to get it moving or to get it to stop. Momentum tells us the impulse required to get it moving or to get it to stop, but does not tell us the speed of the object. Two people on ice skates are at rest. Two people on ice skates are at rest. The boy pushes the man. The boy pushes the man. They move off in opposite directions, but their speeds are inversely proportional to their masses. If the 50 kg boy pushes the 80 kg man so that he moves off at 0.25 m/s, we find that the boy moves off at - 0.40 m/s. The momentum of the man is mv 80 0.25 20 kgm/s The momentum of the man is mv 80 0.25 20 kgm/s The momentum of the boy is mv 50 0.40 20 kgm/s This shows that momentum is conserved. This shows that momentum is conserved. We can express this as This shows that momentum is conserved. We can express this as m1v1 m2 v2 (m1 m2 )v3 This shows that momentum is conserved. We can express this as m1v1 m2 v2 (m1 m2 )v3 or ptotal p1 p2 p3 .... This shows that momentum is conserved. We can express this as m1v1 m2 v2 (m1 m2 )v3 or ptotal p1 p2 p3 .... or p 0 In a 60km/hr zone, a volvo skids 14.3 m before colliding with a parked BMW. The cars become locked together and skid another 6.6 m before stopping. The coefficient of friction between the road and the tyres is 0.75. The mass of the volvo (and driver) is 1470 kg and the mass of the BMW is 1260 kg. In a 60km/hr zone, a volvo skids 14.3 m before colliding with a parked BMW. The cars become locked together and skid another 6.6 m before stopping. The coefficient of friction between the road and the tyres is 0.75. The mass of the volvo (and driver) is 1470 kg and the mass of the BMW is 1260 kg. Was the volvo speeding? When the two cars became locked together and skidded for 6.6 m, the only horizontal force on the cars was due to friction. Balancing forces gives us When the two cars became locked together and skidded for 6.6 m, the only horizontal force on the cars was due to friction. Balancing forces gives us ma mg When the two cars became locked together and skidded for 6.6 m, the only horizontal force on the cars was due to friction. Balancing forces gives us ma mg is the coefficient a g of friction. It is negative because friction is in the opposite direction to the movement of the car. When the two cars became locked together and skidded for 6.6 m, the only horizontal force on the cars was due to friction. Balancing forces gives us ma mg is the coefficient a g of friction. It is negative because a 0.75 9.8 friction is in the opposite direction to the 7.35 m/s 2 movement of the car. When the two cars became locked together and skidded for 6.6 m, the only horizontal force on the cars was due to friction. Balancing forces gives us ma mg is the coefficient a g of friction. It is negative because a 0.75 9.8 friction is in the opposite direction to the 7.35 m/s 2 movement of the car. The deceleration of the two cars is -7.35 m/s2 When the two cars became locked together and skidded for 6.6 m, the only horizontal force on the cars was due to friction. Balancing forces gives us ma mg is the coefficient a g of friction. It is negative because a 0.75 9.8 friction is in the opposite direction to the 7.35 m/s 2 movement of the car. The deceleration of the two cars is -7.35 m/s2 v u 2as 2 2 u v 2as 2 2 0 2 7.35 6.6 97.02 u 97.02 9.85 m/s v u 2as 2 2 u v 2as 2 2 0 2 7.35 6.6 97.02 u 97.02 9.85 m/s The initial velocity of the two cars is 9.85 m/s The momentum of the two cars, after the collision, is given by pvolvo& BMW mvolvo& BMW vvolvo& BMW The momentum of the two cars, after the collision, is given by pvolvo& BMW mvolvo& BMW vvolvo& BMW pvolvo&BMW 2730 9.85 26890.5 kgm/s The momentum of the two cars, after the collision, is given by pvolvo& BMW mvolvo& BMW vvolvo& BMW pvolvo&BMW 2730 9.85 26890.5 kgm/s The momentum of the two cars, before the collision, is given by The momentum of the two cars, after the collision, is given by pvolvo& BMW mvolvo& BMW vvolvo& BMW pvolvo&BMW 2730 9.85 26890.5 kgm/s The momentum of the two cars, before the collision, is given by pvolvo pBMW mvolvo vvolvo mBMW vBMW pvolvo pBMW mvolvo vvolvo mBMW vBMW pvolvo 0 1470 vvolvo 1260 0 pvolvo 1470vvolvo pvolvo pBMW mvolvo vvolvo mBMW vBMW pvolvo 0 1470 vvolvo 1260 0 pvolvo 1470vvolvo Since momentum is conserved, pvolvo pBMW mvolvo vvolvo mBMW vBMW pvolvo 0 1470 vvolvo 1260 0 pvolvo 1470vvolvo Since momentum is conserved, pvolvo (before) pvolvo& BMW (after) 1470vvolvo 26890.5 26890.5 vvolvo 1470 vvolvo 18.3 m/s v u 2as 2 2 u v 2as 2 2 18.3 2 7.35 14.3 2 545.1 u 545.1 23.4 m/s 23.4 3.6 km/h 84.0 km/h Yes, the volvo was speeding.

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posted: | 11/19/2011 |

language: | English |

pages: | 42 |

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