Question

Two blocks of mass 0.30g and 0.20g are moving towards each other along a horizontal frictionless surface with velocities of 0.500m/s and 1.000m/s respectively.

c. Find the final velocity of each block if the collision is completely elastic.

Answer 1

here,

mass of block 1 , m1 = 0.3 g

mass of block 2 , m2 = 0.2 g

initial speed of 1 , u1 = - 0.5 m/s

initial speed of 2 , u2 = 1 m/s

let the final velocity of each block be v1 and v2

using conservation of momentum

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

0.3 * (-0.5) + 0.2 * 1 = 0.3 * v1 + 0.2 * v2 ....(1)

and

using conservation of energy

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

0.3 * (-0.5)^2 + 0.2 * 1^2 = 0.3 * v1^2 + 0.2 * v2^2 ....(2)

from (1) and (2)

v1 = 0.7 m/s

v2 = - 0.8 m/s

the final speed of 1 is 0.7 m/s in opposite direction

the final speed of 2 is 0.8 m/s in opposite direction