A ball with a mass of $2 k g$ $2 kg$ moving at $14 \frac{m}{s}$ $14 m/s$ hits a still ball with a mass of $21 k g$ $21 kg$ . If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

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A ball with a mass of $2 k g$ $2 kg$ moving at $14 \frac{m}{s}$ $14 m/s$ hits a still ball with a mass of $21 k g$ $21 kg$ . If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

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Answer 1 · 2016-02-22T21:30:54

The speed of the second ball is $1.3 \frac{m}{s}$ $1.3m/s$
The kinetic energy lost in as heat was $177.3 J$ $177.3J$

Explanation:

The momentum is conserved, then

$p_{1} = m_{1} \cdot v_{1} = p_{2} = m_{2} \cdot v_{2}$ $p_1 = m_1*v_1 = p_2 = m_2*v_2$

$v_{2} = v_{1} \cdot \frac{m_{1}}{m_{2}}$ $v_2 = v_1*m_1/m_2$ and replacing for the problems figures
$v_{2} = 14 \frac{m}{s} \cdot \frac{2}{21} = 1.3 \frac{m}{s}$ $v_2 = 14m/s*2/21 = 1.3m/s$

The energy also is conserved

$E = m_{1} \cdot \frac{v_{1}^{2}}{2} = m_{2} \cdot \frac{v_{2}^{2}}{2} + Q$ $E= m_1*v_1^2/2 = m_2*v_2^2/2 + Q$ where Q is the kinetic energy

lost in the impact, then

$Q = m_{1} \cdot \frac{v_{1}^{2}}{2} \cdot [1 - \frac{m_{1}}{m_{2}}]$ $Q = m_1*v_1^2/2*[1-m_1/m_2]$ and replacing for the problems figures

$Q = \frac{2}{2} k g \cdot 14^{2} \frac{m^{2}}{s^{2}} \cdot [1 - \frac{2}{21}] = 177.3 J$ $Q= 2/2kg*14^2 m^2/s^2*[1-2/21]=177.3J$

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A ball with a mass of $2 k g$ $2 kg$ moving at $14 \frac{m}{s}$ $14 m/s$ hits a still ball with a mass of $21 k g$ $21 kg$ . If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A ball with a mass of 2kg2 kg moving at 14ms14 m/s hits a still ball with a mass of 21kg21 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?

1 Answer

Explanation:

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A ball with a mass of $2 k g$ $2 kg$ moving at $14 \frac{m}{s}$ $14 m/s$ hits a still ball with a mass of $21 k g$ $21 kg$ . If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?