A 3.0 kg mass is released from rest at point A of a circular frictionless track

Question

A 3.0 kg mass is released from rest at point A of a circular frictionless track of radius 0.40 m as shown in the adjacent Figure. The mass slides down the track and collides with a 1.4-kg mass that is initially at rest on a horizontal frictionless surface. If the masses stick together, what is their speed after the collision? (b) If this collision lasts milliseconds and the magnitude and direction of the average force exerted by car B on car A. Calculate and compare the kinetic energies of the two-car system before and after the collision. Explain your result.

Explanation / Answer

a) at the bottom 3 kg block has a velocity

u1= sqrt(2gh) = 2.8 m/s

u2 = 0

after the collision

from conservation of momentum

m1u1 = (m1+m2)v

v = 3*2.8/4.4 = 1.91 m/s

b) f = chaneg in monetum/t = 3(2.8-1.91)/5*10^-3 = 534 N

c) k1 = 1/2*3*2.8^2 = 11.76 J

k2 = 1/2(m1+m2)v^2 = 8.03 J

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