Question

Bucket?

A 4kg ball moving at 8m/s collides with a stationary ball of mass 12 kg, and they stick and
move together, calculate the final velocity and kinetic energy lost on impact.​

Answer 1

Final velocity=2m/s

kinetic energy lost = 96J

Step-by-step explanation:

This question is an example for total inelastic collision.

For this type of collision, the equation is,

Step1: Finding the velocity

m1v1+m2v2 =(m1+m2) vf
`m_1v_1+m_2v_2 =(m_1+m_2) v_f`

4*8+12*0 = (4+12)v

32 = 16v

`v= frac{32}{16}` = 2m/s

Step 2:Finding the kinetic energy

`Kinetic energy = (1)/(2)* mv^2`

`\text{Kinetic Energy before collision} = (1)/(2) m_1v_1^2+(1)/(2)m_2v_2^2`

Kinetic Energy before collision=
`(1)/(2)*4*8^2+(1)/(2)*12*0^2`

Kinetic Energy before collision= 128J

`\text{Kinetic Energy after collision} = (1)/(2) m_1v_1^2+(1)/(2)m_2v_2^2`

`\text{ Kinetic Energy after collision}= (1)/(2)*4*2^2+(1)/(2)*1**2^2`

Kinetic Energy after collison= 32J

Step 3: Finding the kinetic energy lost

Kinetic Energy lost = Kinetic Energy after collision – Kinetic Energy before collision

Kinetic energy lost=128 -32

Kinetic energy lost=96J