Question

A body of mass 3.6 kg makes an elastic collision with another body at rest and continues to move in the original direction but with 1/6 of its original speed. (a) What is the mass of the other body

Answer 1

The mass of the other body is 2.57 kg.

Step-by-step explanation:

The expression of the velocity of an object in an elastic collision is as follows;

`v_1=((m_1-m_2)/(m_1+m_2))u_1+((2m_2)/(m_1+m_2))u_2`

Here,
`m_1`,
`m_2` are the masses of the objects,
`u_1`,
`u_2` are the initial speed of the objects and
`v_1` is the final speed.

According to the given problem, a body of mass 3.6 kg makes an elastic collision with another body at rest and continues to move in the original direction but with 1/6 of its original speed.

`v_1=(1)/(6)u_1`

Calculate the mass,
`m_2`.

`v_1=((m_1-m_2)/(m_1+m_2))u_1+((2m_2)/(m_1+m_2))u_2`

Put
`v_1=(1)/(6)u_1`,
`u_2=0` and
`m_1=3.6 kg`.

`(1)/(6)u_1=((m_1-m_2)/(m_1+m_2))u_1+((2m_2)/(m_1+m_2))(0)`

`(1)/(6)u_1=((m_1-m_2)/(m_1+m_2))u_1`

`(1)/(6)=((3.6-m_2)/(3.6+m_2))`

`m_2=2.57 kg`

Therefore, the mass of the other body is 2.57 kg.