Can p be related to F? dv dmy dp ∑ F=ma=m ∑F dP (6-2) dt Any conditions for existence of above Eq. The equivalence of∑h=mand∑F= depends on the mass being a constan
F ma d P F dt The equivalence of and depends on the mass being a constant. Any conditions for existence of above Eq.? Can P be related to ? dv dmv dP F ma m dt dt dt dP F dt (6-2) F
6-3 Impulse(冲量) and momentum(动量 Fig 6-6 In this section we consider the relationship between the force that acts on a F(t) body during a collision and the change in the momentum of that body. IF Fig 6-6 shows how the magnitude of the force 0 might change with time during a co∥sio冂
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 i t f 0 t
From Eq 6-2), we can write the change in momentum as dp=>Fdt entire collision, we integrate over the time of e To find the total change in momentum during the collision, starting at time t, (the momentum is Pi and ending at time t (the momentum isPr): 「dF=∫∑h(63)
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) dP Fdt i t f t f f i i P t t P d P Fdt P f Pi
The left side of eq 6-3)is the change in momentum AP=Pf-Pi The right side defines a new quantity called the impulse. For any arbitrary force p, the impulse I is defined as J=「Fdt(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 △P=Pr-P (6-5)
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 “ ” : (6-5) P P f Pi f i t t J F d t F J J P Pf Pi
Notes 1. Eq 6-5)is just as general as Newtons second law 2. Average impulsive force F J=Fa△t=Pr-P f 3. The external force may be negligible, compared to the impulsive force
Notes: 1. Eq(6-5) is just as general as Newton’s second law 2. Average impulsive force J Favt P f Pi F av 3. The external force may be negligible, compared to the impulsive force