# i a m v fnetext dene total momentum

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Unformatted text preview: = = mi ￿ i ￿ dm ￿ Fnet,ext = M mi ￿ i a i Momentum............. i ￿ ￿ ￿ ￿ =a m v Fnet,ext Deﬁne total momentum : = P mi ￿ i￿ i￿i Deﬁne total momentum :P = i mi￿i v i￿ i ￿ ￿ dP ￿ ￿ Deﬁne total momentum : dPP = mi ￿ i v Then : Fnet,ext = ￿ ￿ Then : Fnet,ext dt = i dt ￿ ￿ dP ￿ Then ￿ F T ∝ : L/g net,ext = dt T ∝ L/g π = 3.141592653589793.... ￿ π = 3.141592653589793.... Applications of Momentum: Impulse: how much momentum does a force impart if it acts over a small time interval? Collisions with no external forces. We’ll see, momentum is conserved. Rocket propulsion: momentum conservation in a continuous fashion. ￿ Fnet,ext = ￿ mi ￿ i a Impulse i ￿ A useful concept when an external force￿cts on an object over a a= Deﬁne total momentum : P mi ￿ i v short time interval Δt. Example: bat hitting a baseball. Refer to i the external force as Fimp . ￿ dP for the change of From Fext = d p/dt , we￿ have a simple formula Then : Fnet,ext = dt momentum Δp: ￿ Fimp ∆t = ∆p ￿ Impulsive Forces: strong deformations in short time intervals. Impulse video Ex. A tennis ball (m = 0.060 kg) strikes a tennis racket with velocity 30 m/s (→) and rebounds with velocity 40 m/s (←) in the opposite direction. (a) What are the magnitude and direction of the ball's change in momentum ? DEMO (1/A) 0.60 kg-m/s → (2/B) 0.60 kg-m/s ← (3/C) 4.2 kg-m/s → (4/D) 4.2 kg-m/s ← (5/E) Other v p Look here !! v p f o +x: → v Δp Δp = p x fx − p ox = m v fx − m v ox = (0.060 kg)(- 40 m/s - 30 m/s) ( = m v fx − v ox ) = - 4.2 kg-m/s v Δp = 4.2 kg-m / s ← (b) If the ball is in contact with the racket for 6 ms (= 0.006 s), what is the average impact force on the ball due to the racket during this time? impulsive force — acts for only a “brief” time Δt average force during impact (Δt): v F avg = v Δp Δt Same area as under actual F (t) vs. t graph F(t) Favg t 0 v F avg = 4.2 kg-m / s ← 0.006 s = 700 N ← Impact time Δt...
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## This note was uploaded on 09/29/2012 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).

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