Question

A kid at the junior high cafeteria wants to propel an empty milk carton along a lunch table by hitting it with a 3.1 g spit ball.

If he wants the speed of the 30 g carton just after the spit ball hits it to be 0.30 m/s , at what speed should his 3.1 g spit ball hit the carton?

Answer 1

Now when spit ball collides with carton and stick together after collision, So it is completely inelastic collision, Using Momentum

conservation:

Pi = Pf

Pi = Initial momentum of mass m and M

Pi = m*v + M*0 = m*v (since initially speed of mass M(carton) is zero)

Pf = final momentum of combined mass m and M

Pf = (m + M)*V

given,

m = mass of ball = 3.1 g

M = mass of carton = 30 g

V = speed of mass m and M after collision = 0.30 m/s

So Using above expressions

m*v + M*0 = (m + M)*V

v = (m + M)*V/m

v = (3.1 + 30)*0.30/3.1

v = 3.20 m/sec. = Initial speed of 3.1 g spit ball