Chapt 6 - Linear Momentum and Collisions Chapter 6 Linear...

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1 Linear Momentum and Collisions Chapter 6 Linear Momentum Defined c The linear momentum of an object of mass “m” moving with a velocity “ v ” is defined as the product of the mass and the velocity p = m v c SI Units are kg·m/s c It is a vector quantity. The direction of the momentum is the same as the velocity c Momentum has components p x = mv x and p y = mv y Example 6-3
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2 Momentum and Force c In order to change the momentum of an object, a force must be applied. (Proof follows) c Newton’s Second Law of Motion : F net = m a c But p = m v b p = m v c Thus, the time rate of change is p / t = m v / t c Recall a = v / t b p / t = m a c Comparing with F net = m a we have F net = p / t Momentum and Force (Cont) c The time rate of change of momentum of an object is equal to the net force acting on it F net = p / t c Alternative form of Newton’s Second Law c The rate of change of the momentum of an object is equal to the net force acting on the object. Momentum Change in Projectile Motion c F net = m g c Δ p / Δ t = m g c Δ v / Δ t = g c a = g
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3 Conservation of Linear Momentum c We have F net = p / t c What happens if F net = 0 Then Δ p = 0 And p f - p i = 0 Thus p f = p i c i.e. They are the same vector!! Connection Between Momentum and Kinetic Energy c K = ½ mv 2 but p = m v thus v = p /m c Thus we have v 2 = p 2 /m 2 Therefore we can write K = p 2 /2m Definition of an Impulsive Force c When an average force acts for a short time on an object we can write F ave = p / t b p = F ave t c F ave t is defined as the impulse c It is a vector quantity, whose direction is the same as the direction of the force c The impulse acting on the object is equal to the change in momentum of the object Impulse = F ave t = p = p f - p i
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4 Impulsive Force c Usually the impulse forces are very strong, but short-lived. c
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Chapt 6 - Linear Momentum and Collisions Chapter 6 Linear...

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