A pink ball of mass 0.30 kg is sliding along a frictionless surface at 14.0 m/s

Question

A pink ball of mass 0.30 kg is sliding along a frictionless surface at 14.0 m/s in the +x direction. It collides with a ball of mass 1.60 kg, which is initially at rest. After the collision, the-yeen ball is travelling at 4.00 m/s in the opposite direction, (a) Find the final speed and direction of the ted ball, (b) Find the change in the total kinetic energy of the system which results from the collision, (c) If instead, the green and red balls stuck together after collision, how mu Ch kinetic energy would be lost?

Explanation / Answer

a. total momentum before collission =0.3 x 14 + 1.6 x 0

total momentum after collission= -0.3x4 +1.6 xv

as momentum is conserved,

0.3 x 14 + 1.6 x 0 = -0.3x4 +1.6 xv

so, v= speed of black ball = 3.375 m/s

b. change in kinetic energy= final kinetic energy - initial kinetic energy = [1/2 x 1.6 x 3.375^2 + 1/2 x 0.3 x (-4)^2 ] - [ 1/2 x 0.3 x 14^2]

= 9.1125 +2.4 - 29.4= -17.8875 (-ve sign means kinetic energy lost)

c. if both balls stuck together, then final momentum= (1.6 +0.3) Vf

as momentum is conserved,

0.3 x 14 + 1.6 x 0= (1.6 +0.3)vf

so vf= 2.21 m/s

change in kinetic energy= final kinetic energy - initial kinetic energy = [1/2 x 1.9 x 2.21^2 ] - [ 1/2 x 0.3 x 14^2]

= 4.64 - 29.4= -24.76 (-ve sign means kinetic energy lost)

so kinetic energy lost =24.76 J

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