A ball with a mass of $5 k g$ $5 kg$ is rolling at $9 \frac{m}{s}$ $9 m/s$ 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?

Question

A ball with a mass of $5 k g$ $5 kg$ is rolling at $9 \frac{m}{s}$ $9 m/s$ 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

Impact of this question

1775 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-08T09:16:19

The velocity of the first ball is $= 3.86 m s^{- 1}$ $=3.86ms^-1$
The velocity of the second ball is $= 12.86 m s^{- 1}$ $=12.86ms^-1$

Explanation:

In an elastic collision, we have conservation of momentum and conservation of kinetic energy,

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

and

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

Solving the above 2 equations for $v_{1}$ $v_1$ and $v_{2}$ $v_2$ , we get

$v_{1} = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \cdot u_{1} + \frac{2 m_{2}}{m_{1} + m_{2}} \cdot u_{2}$ $v_1=(m_1-m_2)/(m_1+m_2)*u_1+(2m_2)/(m_1+m_2)*u_2$

and

$v_{2} = \frac{2 m_{1}}{m_{1} + m_{2}} \cdot u_{1} + \frac{m_{2} - m_{1}}{m_{1} + m_{2}} \cdot u_{2}$ $v_2=(2m_1)/(m_1+m_2)*u_1+(m_2-m_1)/(m_1+m_2)*u_2$

$m_{1} = 5 k g$ $m_1=5kg$

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

$u_{1} = 9 m s^{- 1}$ $u_1=9ms^-1$

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

Therefore,

$v_{1} = \frac{3}{7} \cdot 9 + \frac{4}{7} \cdot (0) = \frac{27}{7} = 3.86 m s^{- 1}$ $v_1=3/7*9+4/7*(0)=27/7=3.86ms^-1$

$v_{2} = \frac{10}{7} \cdot 9 - \frac{3}{7} \cdot (0) = \frac{90}{7} = 12.86 m s^{- 1}$ $v_2=10/7*9-3/7*(0)=90/7=12.86ms^-1$

Verificaition

$m_{1} u_{1} + m_{2} u_{2} = 5 \cdot 9 + 2 \cdot 0 = 45$ $m_1u_1+m_2u_2=5*9+2*0=45$

$m_{1} v_{1} + m_{2} v_{2} = 5 \cdot 3.86 + 2 \cdot 12.86 = 45$ $m_1v_1+m_2v_2=5*3.86+2*12.86=45$

Science

Math

Humanities

... and beyond

A ball with a mass of $5 k g$ $5 kg$ is rolling at $9 \frac{m}{s}$ $9 m/s$ 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:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A ball with a mass of 5 kg5kg 5 kg is rolling at 9 m/s9ms9 m/s and elastically collides with a resting ball with a mass of 2 kg2kg2 kg. What are the post-collision velocities of the balls?

1 Answer

Explanation:

Related questions

Impact of this question

A ball with a mass of $5 k g$ $5 kg$ is rolling at $9 \frac{m}{s}$ $9 m/s$ 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?