A ball with a mass of $2 k g$ $2 kg$ is rolling at $1 \frac{m}{s}$ $1 m/s$ and elastically collides with a resting ball with a mass of $3 k g$ $3 kg$ . 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 $1 \frac{m}{s}$ $1 m/s$ and elastically collides with a resting ball with a mass of $3 k g$ $3 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2016-04-25T12:30:34

$u_{1} = - \frac{1}{5} \frac{m}{s}$ $u_1=-1/5 m/s$
$u_{2} = \frac{4}{5} \frac{m}{s}$ $u_2=4/5 m/s$

Explanation:

$given data:$ $"given data:"$
$m_{1} = 2 k g$ $m_1=2kg$
$v_{1} = 1 \frac{m}{s}$ $v_1=1m/s$
$Momentum before collision for the first ball:$ $"Momentum before collision for the first ball:"$
${\to P}_{1} = m_{1} \cdot v_{1} = 2 \cdot 1 = 2 k g \cdot \frac{m}{s}$ $vec P_1=m_1*v_1=2*1=2 kg*m/s$

$m_{2} = 3 k g$ $m_2=3 kg$
$v_{2} = 0$ $v_2=0$
$momentum before collision for the second ball:$ $"momentum before collision for the second ball:"$
${\to P}_{2} = 3 \cdot 0 = 0$ $vec P_2=3*0=0$

$Total momentum before collision:$ $"Total momentum before collision:"$
${\to P}_{b} = {\to P}_{1} + {\to P}_{2}$ $vec P_b=vec P_1+vec P_2$
${\to P}_{b} = 2 + 0 = 2 k g \cdot \frac{m}{s}$ $vecP_b=2+0=2 kg*m/s$

$Velocities for post collision :$ $"Velocities for post collision :"$

$u_{1} : Post collision velocity of the first ball$ $u_1:"Post collision velocity of the first ball"$

$u_{1} = \frac{2 \cdot {\to P}_{b}}{m_{1} + m_{2}} - v_{1}$ $u_1=(2*vec P_b)/(m_1+m_2)-v_1$

$u_{1} = \frac{2 \cdot 2}{2 + 3} - 1$ $u_1=(2*2)/(2+3)-1$

$u_{1} = \frac{4}{5} - 1$ $u_1=4/5-1$

$u_{1} = - \frac{1}{5} \frac{m}{s}$ $u_1=-1/5 m/s$

$u_{2} : Post collision velocity of the second ball$ $u_2:"Post collision velocity of the second ball"$

$u_{2} = \frac{2 \cdot {\to P}_{b}}{m_{1} + m_{2}} - v_{2}$ $u_2=(2*vec P_b)/(m_1+m_2)-v_2$

$u_{2} = \frac{2 \cdot 2}{2 + 3} - 0$ $u_2=(2*2)/(2+3)-0$

$u_{2} = \frac{4}{5} \frac{m}{s}$ $u_2=4/5 m/s$

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A ball with a mass of $2 k g$ $2 kg$ is rolling at $1 \frac{m}{s}$ $1 m/s$ and elastically collides with a resting ball with a mass of $3 k g$ $3 kg$ . What are the post-collision velocities of the balls?

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A ball with a mass of 2 kg2kg2 kg is rolling at 1 m/s1ms1 m/s and elastically collides with a resting ball with a mass of 3 kg3kg3 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 $1 \frac{m}{s}$ $1 m/s$ and elastically collides with a resting ball with a mass of $3 k g$ $3 kg$ . What are the post-collision velocities of the balls?