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PHYS2001_Ch. 7

# PHYS2001_Ch. 7 - Ch 7 Momentum 7.1 Impulse and Momentum Up...

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Ch. 7 Momentum 7.1 Impulse and Momentum Up to now, we have been dealing only with constant forces. But, in many instances the force on an object is not constant in time. Take collisions, for example. In a collision the forces are very complicated. In a collision, the forces involved may be very large, but only act for a very short period of time. These type of forces are called Impulse Forces. A car crashing into a wall would be an example of an impulse force. Typically, the impulse force is so large that it is the only significant force of the collision. Friction and gravity are insignificant. We define a quantity associated with the impulse force, called the Impulse : t F I = I is the impulse. It is equal to the average force times the time over which the force acts. It is a vector quantity.

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o f t t t - = Before t o , the force is zero. After t f the force is zero. Between t o and t f the force is large. Units? s] [N Time] [Force = × There are two ways to generate a large impulse. Apply a large force for a very short time, or apply a small force for a very long time. In this chapter, we will only consider the former. As an example of an impulse force, let’s consider a crash test of a Mercedes.
Example : If the time-averaged force acting on the Mercedes is -2.0 × 10 5 N. What is the impulse delivered to the car by the wall? t F I = s N 10 4 . 2 ) 120 . 0 )( 10 2 ( 4 5 × - = × - =

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Momentum and the Impulse – Momentum Theorem By Newton’s 2 nd Law, we know that: ma F = t v m = This assumes that we keep the mass of the object constant. But what if the mass can vary too?? Then we can write the force this way: t mv F = ) ( In the parentheses we have the product mv . Let’s define this new quantity as the momentum , p . v m p F F = So momentum is proportional to both mass and velocity. A heavy truck moving fast has a large momentum. My cat does not. Momentum is a vector. It points in the same direction as the velocity. Units? = × s m kg Velocity] [Mass
Assume the space shuttle, or any rocket, is heading toward space at constant speed. Is its momentum constant? Yes No 50% 50% 1. Yes 2. No Clicker Question As it moves, it burns fuel, so its mass is not constant, and thus its momentum must change if the speed stays constant.

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ma F = t v m = If mass is not constant, then we bring it inside the delta. t mv F = ) ( t p = Rearrange this: t F p = I = p I = The impulse on a object is equal to its change in momentum! This is the Impulse – Momentum Theorem. Example : A 0.14-kg baseball has a KE = 142 J. What is the ball’s momentum? What is the ball’s speed? 2 2 1 KE mv = m mv 2 ) ( 2 = m p 2 2 = m p 2 KE 2 = KE) )( 2 ( 2 m p = 40 ) 142 )( 14 . 0 ( 2 = = m/s kg 3 . 6 = p m p v / = m/s 45 ) 14 . 0 /( ) 3 . 6 ( = =
7.2 Conservation of Linear Momentum We talked last time how Newton’s Laws naturally show up in our discussions of momentum.

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PHYS2001_Ch. 7 - Ch 7 Momentum 7.1 Impulse and Momentum Up...

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