Question

n object with a mass of 9.00 g is moving to the right at 14.0 cm/s when it is overtaken by an object with a mass of 27.0 g moving in the same direction with a speed of 17.0 cm/s. If the collision is elastic, determine the speed of each object after the collision.

27.0-g object	(No Response) cm/s
9.00-g object	(No Response) cm/s

Answer 1

here,

m1 = 9 g has initial speed , u1 = 14 cm/s

m2 = 27 g has initial speed u2 = 17 cm/s

let the final velocity of each object be v1 and v2

using conservation of momentum

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

9 * 14 + 27 * 17 = 9 * v1 + 27 * 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

9 * 14^2 + 27 * 17^2 = 9 * v1^2 + 27 * v2^2 .....(2)

from (1) and (2)

v1 = 18.5 cm/s

v2 = 15.5 cm/s

the final speed of 9 g object is 18.5 cm/s

the final speed of 27 g object is 15.5 cm/s