Question

An object with a mass of 8.00 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 21.0 cm/s. If the collision is elastic, determine the speed of each object after the collision.

27.0-g object	cm/s
8.00-g object	cm/s

Answer 1

momentum will be conserved

=> initial momentum = final momentum

=> 8*14 + 27*21 = 8*vf1 + 27*vf2

=> 8*vf1 + 27*vf2 = (8*14 + 27*21) = 679 .........eq1

now for elastic collision energy conservation

=> KEi = KEf

=> (1/2)*8*(14)^2 + (1/2)*27*(21)^2 = (1/2)*8*vf1^2 + (1/2)*27*vf2^2

=> 8*vf1^2 + 27*vf2^2 = 13475

now using eq (1)

13475 = 8*((679 - 27*vf2)/8)^2 + 27*vf2^2

=> 13475 = 57623.2 - 4576.19*vf2 + 90.85*vf2^2 + 27*vf2^2

=> 117.85*vf2^2 - 4576.19*vf2 + 44148.2 = 0

=> vf2^2 - 38.83*vf2 + 374.61 = 0

=> vf2 = 20.94 cm/s , vf2 = 17.89 cm/s

now vf1 = (679 -27*20.94)/8 = 15.215 cm/s

and also vf1 = (679 -27*17.89)/8 = 24.49 cm/s