Question

A 2kg mass is moving on a frictionless airtrack. It collides into a motionless 1.5 kg mass.

What is the combined speed of the two masses if they stick together on impact

Answer 1

`0.57v_1`

Step-by-step explanation:

From the law of conservation of momentum, the sum of initial momentum equals the sum of final momentum

Momentum, p=mv where m is the mass and v is the velocity

`m_1v_1+m_2v_2=(m_1+m_2)v_c` where
`v_c` is the common velocity,
`v_1` and
`v_2` are velocities of 2 Kg moving mass and motionless 1.5 kg mass respectively,
`m_1` and
`m_2` are masses of 2 Kg moving mass and motionless 1.5 kg mass .

Since the 1.5 Kg mass is motionless, it's velocity is zero hence

`m_1v_1=(m_1+m_2)v_c`

By substitution

`2v_1=(2+1.5)v_c`

`2v_1=3.5v_c`

`v_c=\frac {2v_1}{3.5}=0.571428571v_1\approx 0.57v_1`