Ch 07 Impulse and Momentum

Ch 07 Impulse and Momentum - LECTURE NOTES 7 Impulse and...

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Definition of Linear Momentum The linear momentum p of an object is the product of the object’s mass m and velocity v : p = m v Linear momentum is a vector quantity that points in the same direction as the velocity. SI units of momentum : kilogram.meters/second kg.m/s LECTURE NOTES 7 Impulse and Momentum Goals To study momentum. To understand conservation of momentum. To study momentum changes during collisions. To add time and study impulse. To understand center of mass and how forces act on it. Definition of Impulse The impulse J of a force is the product of the average force F av and the time interval t during which the force acts: Impulse J = F av t Impulse is a vector quantity and has the same direction as the average force. SI units of Impulse: N.s
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Impulse-Momentum Theorem When a net force acts on an object, the impulse of the net force is equal to the change in momentum of the object: f o J F t m v m v p     Impulse = Final momentum Initial momentum = Change in momentum f o f o av v v mv mv F m t t The Impulse-Momentum Theorem f o av v v a t N2 states that the cause of the average acceleration is an average net force F av = m a av . Thus: Note : During a collision, it is often difficult to measure the average net force F av , so it is not easy to determine the impulse J directly. Example 1: + 1 v o 2 F av 3 v f When a bat (or racket) hits a ball, an average force F av is applied to the ball. As a result, the ball’s velocity changes from an initial value of v o to a final value v f . Given: m = 0.14 kg, v o = 38 m/s, v f = +58 m/s, and the time of contact t = 1.6 10 3 s. Note that p is a vector (magnitude and direction). Indicate the direction by assigning a plus and minus sign to it. a. Impulse = m v f m v o = (0.14kg)(+58m/s) (0.14kg)( 38m/s) = +13.4kg.m/s b. Average force can be calculated from the contact time : F av = J / t = +13.4 kg.m/s / 1.6 10 3 s = +8400 N
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f o o mv mv m F v t t   Example 2: + A raindrop falling on a car roof has an initial velocity of v o just before striking the roof. The final velocity of the raindrop is v f =0, because it comes to rest on the roof. The average force F av needed to reduce the rain’s velocity from v o to v f = 0 m/s is: The term m / t is the mass of rain per second that strikes the roof.
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