Question

A 1.00-kg ball, moving to the right at a velocity of +1.35 m/s on a frictionless table, collides head-on with a stationary 8.00-kg ball. Find the final velocities of (a) the 1.00-kg ball and of (b) the 8.00-kg ball if the collision is elastic. (c) Find the magnitude and direction of the final velocity of the two balls if the collision is completely inelastic.

Answer 1

here,

mass of first ball , m1 = 1 kg

mass of seccond ball , m2 = 8 kg

initial speed of 1 , u1 = 1.25 m/s i

a)

let the final velocities be v1 and v2

using conservation of momentum

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

1 * 1.25 + 0 = 1 * v1 + 8 * v2 ....(1)

and

using conservation of kinetic energy

0.5 * m1 * u1^2 + 0.5 * m2 * u2^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

1 * 1.25^2 + 0 = 1 * v1^2 + 8 * v2^2 ....(2)

from (1) and (2)

v1 = - 0.97 m/s

v2 = 0.28 m/s

the final speed of first ball is 0.97 m/s in opposite direction

b)

the final speed of seccond ball is 0.28 m/s

c)

when the collison is inelastic

let the final speed be v

using conservation of momentum

m1 * u = (m1 + m2) * v

1 * 1.25 = ( 1 + 8) * v

solving for v

v = 0.14 m/s

the final speed of combination is 0.14 m/s