Question

A 4.38 kg sphere makes a perfectly inelastic collision with a second sphere that is initially at rest. The composite system moves with a speed equal to one third the original speed of the 4.38 kg sphere. What is the mass of the second sphere?

Answer 1

Answer: The mass of the second sphere is 8.76 kg

Step-by-step explanation:

The equation for a perfectly inelastic collision follows:

`m_1u_1+m_2u_2=(m_1+m_2)v`

where,

`m_1\text{ and }u_1` are the mass and initial velocity of first sphere

`m_2\text{ and }u_2` are the mass and initial velocity of second sphere

v = final velocity of the system

We are given:

`m_1=4.38kg\\u_2=0m/s\\v=(u_1)/(3)`

Rearranging the above equation, we get:

`m_1u_1-m_1v=m_2v\\\\m_2=m_1(u_1-v)/(v)\\\\m_2=m_1((u_1)/(v)-1)`

Plugging values in the above equation, we get:

`m_2=4.38((3u_1)/(u_1)-1)\\\\m_2=(4.38* 2)=8.76kg`

Hence, the mass of the second sphere is 8.76 kg