Method 1: Impulse Method
This is the east method mathematically.
I = Delta p
-- Impulse causes momentum to change --
Where I = Impulse = barFDeltat
p= momentum = mv
Delta p = Change of momentum = mv_f-mv_i
m = mass of the bullet = 5.5 xx10^-3 kg
v_f = final velocity = 0
v_i = initial velocity = 325 m/s
rArr barFDeltat= 0 - mv_i = mv_i
Deltat= (mv_i)/barF
Method 2. Work-energy theorem
W_"net" = DeltaK rArr vecF_"net"*vecd = 1/2mv_f^2 - 1/2mv_i^2
--Work causes kinetic energy to change --
where
d = stopping distance
F = frictional force
- Fd = 0 - 1/2mv^2
d = 1/(2F)(mv_i^2)
Deltat = d/barv =(mv_i^2)/(2Fbarv)
Because barv = ½(v_i + v_f) = ½v_i
Deltat = (mv_i)/(F)
Method 3 Kinematics and Newton's 2nd Law
a = F/m
v_f^2 = v_i^2 - 2ad
rArr 0 =v_i^2 - 2(F/m)d
d =(mv_i^2)/(2F)
Deltat = d/barv =(mv_i^2)/(2Fbarv) = (mv_i^cancel(2))/(cancel(2)F*cancel(v_i)/cancel(2))
Deltat = (mv_i)/F
