6-3 Impulse(冲量)and Momentum(动量)Fig 6-6In this section, we considerthe relationship betweenFthe force that acts on aF(t)body during a collision andthe change inthemomentum of that bodyFavFig6-6showshowthemagnitude of the forcemight change with timeti0tftduring a collision
6-3 Impulse(冲量) and Momentum(动量) In this section, we consider the relationship between the force that acts on a body during a collision and the change in the momentum of that body. Fig 6-6 shows how the magnitude of the force might change with time during a collision. t F F(t) Fig 6-6 𝐹av 𝑡𝑖 0 𝑡𝑓
From Eg(6-2), we can write the change inmomentum asdP-ZFdtTo find the total change in momentum during theentire collision, we integrate over the time ofcollision, starting at time t; (the momentum iss):)and ending at time(the momentum is Pi(6-3)P,DdP-JFdttiP
From Eq(6-2), we can write the change in momentum as To find the total change in momentum during the entire collision, we integrate over the time of collision, starting at time (the momentum is )and ending at time (the momentum is ): (6-3) d P Fdt = 𝑡𝑖 𝑡𝑓 f f i i P t t P d P Fdt → → = P f Pi
The left side of Eg(6-3) is the change in momentum,The right side deniRes nevPquantity called theimpulse.Forany arbitraryforcethe impulseis defined as(6-4)JFdtId dimensions.asA impulsehas thesJ6-3),weobtainthemomentum.Fromimpulse-momentu(6-5)J=△P-Pr-Pi
The left side of Eq(6-3) is the change in momentum, The right side defines a new quantity called the impulse. For any arbitrary force , the impulse is defined as (6-4) A impulse has the same units and dimensions as momentum. From Eq(6-4) and (6-3), we obtain the “impulse-momentum theorem” : (6-5) = − P P P f i f i t t J Fdt = 𝐹 → J J P P P = = −f i
Notes:1. Eq(6-5) is just as general as Newton's secondlaw2.Average impulsiveforceF。J=FAt=Pf-P3. The external force may be negligible, comparedto the impulsive force
Notes: 1. Eq(6-5) is just as general as Newton’s second law 2. Average impulsive force J F t P P = = − av f i Fav 3. The external force may be negligible, compared to the impulsive force
Sample problem 6-1A baseball(棒球) of mass 0.14 kg is movinghorizontally at a speed of 42m/s when it is struckby the bat it leaves the bat in a direction atparB5°angle above its incident path and with a speedof 50m/s(a) find the impulse of the force exerted on the ball(b) assuming the collision lasts for 1.5ms what isthe average force.(c) find the change in the momentum of the bat
Sample problem 6-1 A baseball(棒球) of mass 0.14 kg is moving horizontally at a speed of 42m/s when it is struck by the bat it leaves the bat in a direction at an angle above its incident path and with a speed of 50m/s (a) find the impulse of the force exerted on the ball. (b) assuming the collision lasts for 1.5ms what is the average force. (c) find the change in the momentum of the bat. 𝜑 = 35∘