A ball with a mass of #4 kg# moving at #6 m/s# hits a still ball with a mass of #10 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

Question

A ball with a mass of #4 kg# moving at #6 m/s# hits a still ball with a mass of #10 kg#.  If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

William Audy · Accepted Answer

This is a conservation of momentum problem; find the speed of the second by computing the system momentum before and after: #m_1v_1 + m_2v_2 =m_1v_ 1^'+ + m_2v_2^' =#
Where #m_1=4kg; m_2=10kg; v_ 1=6m/s; v_2 =0#; Replace and solve it; I'll let you see it through to the end. for kinetic information find the energy before the collision:
#KE_i=1/2m_1v_1^2;  KE_f=1/2m_2v_2^2;#
The difference: #KE_i-  KE_f#
#1/2m_1v_1^2 - 1/2m_2v_2^2;# Is the loss of energy Wishing you luck, Yonas

Carson Alexander · Answer

undefined To find the velocity of the second ball after the collision, we can use the principle of conservation of momentum:

$$ m_1 \cdot v_1 + m_2 \cdot v_2 = m_1 \cdot u_1 + m_2 \cdot u_2 $$

Where:
- $ m_1 $ = mass of the first ball (4 kg)
- $ m_2 $ = mass of the second ball (10 kg)
- $ v_1 $ = final velocity of the first ball (0 m/s, as it stops moving)
- $ v_2 $ = final velocity of the second ball (unknown)
- $ u_1 $ = initial velocity of the first ball (6 m/s)
- $ u_2 $ = initial velocity of the second ball (0 m/s, as it is still)

Once we find the final velocity of the second ball, we can calculate the kinetic energy lost as heat using the principle of conservation of energy:

$$ \text{Kinetic energy lost} = \frac{1}{2} m_1 (u_1^2 - v_1^2) $$

Where:
- $ m_1 $ = mass of the first ball (4 kg)
- $ u_1 $ = initial velocity of the first ball (6 m/s)
- $ v_1 $ = final velocity of the first ball (0 m/s)