A ball with a mass of #5 kg# moving at #12 m/s# hits a still ball with a mass of #9 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 #5 kg# moving at #12 m/s# hits a still ball with a mass of #9 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?

Emily Abbate · Accepted Answer

I found: #6.6m/s# and #164J# lost.

Have a look:

Axel Acevedo · Answer

undefined To find the velocity of the second ball after the collision, you can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

The initial momentum is given by the formula: $ p = mv $ where $ p $ is momentum, $ m $ is mass, and $ v $ is velocity.

The total initial momentum before the collision is $ p_{\text{initial}} = m_1 \cdot v_1 + m_2 \cdot v_2 $.

After the collision, the first ball stops moving, so its final velocity $ v_1' = 0 $.

The total momentum after the collision is $ p_{\text{final}} = m_1 \cdot v_1' + m_2 \cdot v_2' $.

Using the conservation of momentum, we have $ p_{\text{initial}} = p_{\text{final}} $, which gives:

$ m_1 \cdot v_1 + m_2 \cdot v_2 = m_1 \cdot v_1' + m_2 \cdot v_2' $.

Solving for $ v_2' $, the velocity of the second ball after the collision, we get:

$ v_2' = \frac{m_1 \cdot v_1 + m_2 \cdot v_2 - m_1 \cdot v_1'}{m_2} $.

Plugging in the given values, $ m_1 = 5 $ kg, $ v_1 = 12 $ m/s, $ m_2 = 9 $ kg, and $ v_1' = 0 $ m/s, we can calculate $ v_2' $.

$ v_2' = \frac{5 \cdot 12 + 9 \cdot 0 - 5 \cdot 0}{9} $  
$ v_2' = \frac{60}{9} $  
$ v_2' \approx 6.67 $ m/s

To find the kinetic energy lost as heat in the collision, you can use the formula for kinetic energy: $ KE = \frac{1}{2}mv^2 $, where $ KE $ is kinetic energy, $ m $ is mass, and $ v $ is velocity.

The initial kinetic energy before the collision is the sum of the kinetic energies of both balls, and the final kinetic energy after the collision is the sum of the kinetic energies of both balls.

The kinetic energy lost as heat in the collision is the difference between the initial and final kinetic energies.

Plugging in the given values, we can calculate the initial and final kinetic energies, then find the difference to determine the kinetic energy lost as heat.