A ball of mass m moving at a speed v makes a head-on collision with an

1.	A ball of mass m moving at a speed v makes a head-on collision with an identical ball at rest. The kinetic energy of the balls after the collision is three fourths of the original. Find the coefficient of restitution.
Answer» Thanks for asking the question! ANSWER:: Mass of FIRST ball = m Speed of first ball = v Mass of SECOND ball = m Let final velocities of first and second ball are v₁ and v₂ respectively. Using law of conservation of momentum, m(v₁ + v₂) = mv v₁ + v₂ = v Equation 1 And , v₁ - v₂ = ev Equation 2 Given:- Final KINETIC Energy = 3/4 Initial Kinetic Energy (1/2)mv₁² + (1/2)mv₂² = (3/4) x 1/2 mv² v₁² + v₂² = (3/4) v² [(v₁ + v₂)² + (v₁ - v₂)² ] / 2 = 3v² / 4 (1 + e²)v² / 2 = 3v² / 4 1 + e² = 3/2 e² = 1/2 e = 1 / √2 Hope it helps!

A ball of mass m moving at a speed v makes a head-on collision with an identical ball at rest. The kinetic energy of the balls after the collision is three fourths of the original. Find the coefficient of restitution.

Answer»

Thanks for asking the question!

ANSWER::

Mass of FIRST ball = m

Speed of first ball = v

Mass of SECOND ball = m

Let final velocities of first and second ball are v₁ and v₂ respectively.

Using law of conservation of momentum,

m(v₁ + v₂) = mv

v₁ + v₂ = v Equation 1

And , v₁ - v₂ = ev Equation 2

Given:-

Final KINETIC Energy = 3/4 Initial Kinetic Energy

(1/2)mv₁² + (1/2)mv₂² = (3/4) x 1/2 mv²

v₁² + v₂² = (3/4) v²

[(v₁ + v₂)² + (v₁ - v₂)² ] / 2 = 3v² / 4

(1 + e²)v² / 2 = 3v² / 4

1 + e² = 3/2

e² = 1/2

e = 1 / √2

Hope it helps!

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