Question

A 10.0 kg and a 2.0 kg cart approach each other on a horizontal frictionless air track. Their

total kinetic energy before collision is 96 ). Assume their collision is elastic. What is the
final speed in m/s of the 10.0 kg mass if that of the 2.0 kg mass is 8.0 m/s? (Hint: There are
2 conditions for elastic collisions.)

Answer 1

the final speed in m/s of the 10.0 kg is 2.53 m/s .

Explanation:

Here we have , A 10.0 kg and a 2.0 kg cart approach each other on a horizontal friction less air track. Their total kinetic energy before collision is 96 ). Assume their collision is elastic. We need to find What is the final speed in m/s of the 10.0 kg mass if that of the 2.0 kg mass is 8.0 m/s . Let's find out:

We know that in an elastic collision :

⇒ Total kinetic energy before collision = Total kinetic energy after collision

⇒
`96 = (1)/(2)M_1(v_1)^2 + (1)/(2)M_2(v_2)^2`

⇒
`96 = (1)/(2)(10)(v_1)^2 + (1)/(2)(2)(8)^2`

⇒
`96=5(v_1)^2 + 64`

⇒
`5(v_1)^2 =32`

⇒
`(v_1)^2 =6.4`

⇒
`v_1 =2.53 m/s`

Therefore , the final speed in m/s of the 10.0 kg is 2.53 m/s .