Question

(25 Points) A 10.0 kg ball, moving to the right at a velocity of 4.00m/s on a frictionless table, collides head-on with a 5.00kg ball at rest. Find velocities of the balls is the collision is (a) (15 points) elastic and (b) (10 points) completely inelastic

Answer 1

4)

here,

mass of ball 1 , m1 = 10 kg

initial velocity of 1 ,u1 = 4 m/s

mass of ball 2 ,m2 = 5 kg

a)

let the final velocities of balls be v1 and v2

for elastic collison

using conservation of momentum

m1 * u1 = m1 * v1 + m2 * v2

10 * 4 = 10 * v1 + 5 * v2 ...(1)

and

using conservation of kinetic energy

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

10 * 4^2 = 10 * v1^2 + 5 * v2^2 ...(2)

from (1) and (2)

v1 = 1.33 m/s

v2 = 5.33 m/s

the final velocity of 1 is 1.33 m/s

the final velocity of 2 is 5.33 m/s

b)

for completely inelastic collison

let the final velocity of combination be v

using conservation of momentum

m1 *u1 = (m1 + m2 ) * v

10 * 4 = (10 + 5) * v

v = 2.67 m/s

the final velocity of combination is 2.67 m/s