A ball with a mass of $2 k g$ $2 kg$ is rolling at $25 \frac{m}{s}$ $25 m/s$ and elastically collides with a resting ball with a mass of $2 k g$ $2 kg$ . What are the post-collision velocities of the balls?

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A ball with a mass of $2 k g$ $2 kg$ is rolling at $25 \frac{m}{s}$ $25 m/s$ and elastically collides with a resting ball with a mass of $2 k g$ $2 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2017-11-11T06:59:41

The velocities of the balls are $= 0 m s^{- 1}$ $=0ms^-1$ and $= 25 m s^{- 1}$ $=25ms^-1$

Explanation:

As the collision is elastic, there is conservation of linear momentum and conservation of kinetic energy

Let the velocity before collision be $u_{1} m s^{- 1}$ $u_1ms^-1$ and $u_{2} m s^{- 1}$ $u_2ms^-1$

Let the velocity after collision be $v_{1} m s^{- 1}$ $v_1ms^-1$ and $v_{2} m s^{- 1}$ $v_2ms^-1$

$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$ $m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2}$ $1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2$

Here, we have

$m_{1} = m_{2} = 2 k g$ $m_1=m_2=2kg$

$u_{1} = 25 m s^{- 1}$ $u_1=25ms^-1$

$u_{2} = 0 m s^{- 1}$ $u_2=0ms^-1$

Therefore,

$v_{1} + v_{2} = 25$ $v_1+v_2=25$

$v_{1}^{2} + v_{2}^{2} = 25^{2} = 625$ $v_1^2+v_2^2=25^2=625$

$v_{1} = 25 - v_{2}$ $v_1=25-v_2$

${(25 - v_{2})}_{2}^{2} + v_{2}^{2} = 625$ $(25-v_2)^2+v_2^2=625$

$625 - 50 v_{2} + v^{2} + v^{2} = 625$ $625-50v_2+v^2+v^2=625$

$2 v_{2}^{2} - 50 v_{2} = 0$ $2v_2^2-50v_2=0$

$2 v_{2} (v_{2} - 25) = 0$ $2v_2(v_2-25)=0$

$v_{2} = 25$ $v_2=25$ and $v_{1} = 0$ $v_1=0$

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A ball with a mass of $2 k g$ $2 kg$ is rolling at $25 \frac{m}{s}$ $25 m/s$ and elastically collides with a resting ball with a mass of $2 k g$ $2 kg$ . What are the post-collision velocities of the balls?

1 Answer

Explanation:

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A ball with a mass of 2 kg2kg 2 kg is rolling at 25 m/s25ms25 m/s and elastically collides with a resting ball with a mass of 2 kg2kg 2 kg. What are the post-collision velocities of the balls?

1 Answer

Explanation:

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A ball with a mass of $2 k g$ $2 kg$ is rolling at $25 \frac{m}{s}$ $25 m/s$ and elastically collides with a resting ball with a mass of $2 k g$ $2 kg$ . What are the post-collision velocities of the balls?