A ball with a mass of $2 k g$ $2 kg$ moving at $16 \frac{m}{s}$ $16 m/s$ 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 $16 \frac{m}{s}$ $16 m/s$ 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 · 2016-10-28T14:13:51

In the first scenario, momentum conservation law will be applied.

Explanation:

from the law,
$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$ $m_1u_1+m_2u_2=m_1v_1+m_2v_2$

here,
$m_{1} = 2 k g$ $m_1=2kg$
$m_{2} = 21 k g$ $m_2=21kg$
$u_{1} = 16 m s^{- 1}$ $u_1=16ms^(-1)$
$u_{2} = 0 m s^{- 1}$ $u_2=0ms^(-1)$
$v_{1} = 0 m s^{- 1}$ $v_1=0ms^(-1)$
we have to find $v_{2}$ $v_2$
if we put all the values in the equation, we will find,

$2 \cdot 16 + 21 \cdot 0 = 2 \cdot 0 + 21 \cdot v_{2}$ $2*16+21*0=2*0+21*v_2$
$or, 32 = 21 v_{2}$ $or, 32=21v_2$
$or, v_{2} = \frac{32}{21}$ $or, v_2=32/21$
$or, v_{2} = 1.524 m s^{- 1}$ $or, v_2=1.524ms^(-1)$

for the energy loss,
$E_{i} = \frac{1}{2} \cdot 2 \cdot 16^{2} + \frac{1}{2} \cdot 21 \cdot 0^{2}$ $E_(i)=1/2*2*16^2+1/2*21*0^2$
$= 256 j$ $=256j$

$E_{f} = \frac{1}{2} \cdot 2 \cdot 0^{2} + \frac{1}{2} \cdot 21 \cdot {1.524}^{2}$ $E_(f)=1/2*2*0^2+1/2*21*1.524^2$
$= 24.387 j$ $=24.387j$

so, $Delta E=E_(i)-E_f$
$=256j-24.387j$
$=231.613j$

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A ball with a mass of $2 k g$ $2 kg$ moving at $16 \frac{m}{s}$ $16 m/s$ 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 kg2kg2 kg moving at 16 m/s16ms16 m/s hits a still ball with a mass of 21 kg21kg21 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 $16 \frac{m}{s}$ $16 m/s$ 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?