Momentum problems

Question

1) a 200 kg cannon fires a 3 kg shell forward. If the cannon recoilds at 5.1 m/s, how fast is the shell fired?

2) a 2000 kg rail car traveling east at 15 m/s collides inelastically with a 500 kg car travelling west at 24 m/s. What direction and speed do they travel after colliding?

Answer 1

(a)

Use conservation of momentum.

M = mass of cannon = 200 kg

m = mass of shell = 3 kg

u = recoil velocity of cannon = -5.1 m/s (Note the negative sign.)

v = speed of shell = ?

Initial momentum is zero, so final momentum must also be zero.

Mu + mv = 0 ⇒

v = -Mu/m = -(200)(-5.1)/(3) m/s = (200)(5.1)/3 m/s = ? m/s

(b)

Assume the two are stuck together as one body and use conservation of momentum.

M = mass of rail car = 2000 kg

u = initial speed of car = 15 m/s

m = mass of car = 500 kg

v = initial velocity of car = -24 m/s (Note the negative sign.)

w = final speed of combined mass = ?

Mu + mv = (M + m)w ⇒

w = (Mu + mv) / (M + m)

Plug in the numbers. Be careful with signs. If w is positive, it ravels east. If w is negative, it travels west. You can finish from here.