Two pool balls collide on the pool table. The first ball is moving at 10 m/s bef

Question

Two pool balls collide on the pool table. The first ball is moving at 10 m/s before it strikes the second ball which is at rest on the table. After the collision, the second ball is moving with a velocity of 4 m/s. Assume the pool balls move only in one dimension and the balls have the same mass.

a.) What is final velocity of the first ball?

b.) Is kinetic energy conserved? To show whether it is or is not, you must calculate ?KE.

c.) Using your answer to part b.), what type of collision is this?

d.) If mechanical energy is not conserved, what happened to it? If it is conserved, write N/A as your answer to this part of the question.

Explanation / Answer

from conservation of momentum,

m1*u1 = m1*v1 + m2*v2

all the balls have same mass, so m1 = m2

u1 = (v1+v2)
10 = v1 + 4
v1 = 6 m/s

a) final velocity of the first ball = v1 = 6 m/s

b) Initial K.E = 0.5*m1*u1^2 = 0.5*m1*(10^2) = 50 * m1

Final K.E = (0.5*m1*v1^2) + (0.5*m1*v2^2) = (0.5*m1*6^2 ) + (0.5*m1*4^2) = 18*m1 + 8*m1 = 26*m1
so, Initial K.E is not equal to final K.E
Kinetic energy is not conserved.

c)
It is an inelastic collision

d) the remaining mechanical energy = Initial K.E - Final K.E = (50*m1) - (26*m1) = (24*m1)
the remaining mechanical energy is dissipated in form of heat.

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