A steel ball of radius 2cm is initially at rest.It is struck head on by another steel ball of radius 4cm travelling with a velocity of 81cm/s.If the collision is elastic their respective final velocities are?
Answers
Answer:
144 m/s - 2 cm Ball
63 m/s - 4 cm Ball
Explanation:
Volume of Sphere = (4/3)π Radius³
Mass = Volume * Density
Both Balls are of same Material so same density
Mass of 2 cm Ball = Density * (4/3)π 2³ =8 * Density * (4/3)π = M
Mass of 4 cm Ball = Density * (4/3)π 4³ = 64 * Density * (4/3)π = 8 * 8 * Density * (4/3)π = 8M
As per Conservation of Momentum
M * 0 + 8M * 81 = MV₁ + 8MV₂
=> V₁ + 8V₂ = 648
=> V₁ = 648 - 8V₂
As per Energy conversation
(1/2)M*0² + (1/2)8(81)² = (1/2)MV₁² + (1/2)8MV₂²
=> V₁² + 8V₂² = 52488
=> (648 - 8V₂)² + 8V₂² = 52488
=> 64V₂² + 419904 - 10368V₂ + 8V₂² = 52488
=> 72V₂² - 10368V₂ + 367416 = 0
=> V₂² - 144V₂ + 5103 = 0
=> V₂² - 81V₂ - 63V₂ + 5103 = 0
=> (V₂ - 81)(V₂ - 63) = 0
=> V₂ = 63 m/s
V₁ = 648 - 8*63 = 144 m/s
144 m/s - 2 cm Ball
63 m/s - 4 cm Ball
Answer:
v1= 144m/s, for 2cm
v2 = 63m/s, for 4cm.