Physics, 21.07.2020 20:01 charismameeks

An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.8 times the mass of the other. Requried:
a. If 7230 J were released in the explosion, how much kinetic energy did the heavier piece acquire?
b. How much kinetic energy did the lighter piece acquire?

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Answer from: Coscutt

a) The heavier piece has a translational kinetic energy of 4647.857 joules, b) The lighter piece has a translational kinetic energy of 2582.143 joules.

Explanation:

a) The object breaking can be described by means of the Principle of Energy Conservation, knowing that heavier piece has 1.8 times the mass of the lighter ( $m_{h} = 1.8\cdot m_{l}$ ), both are modelled as particle due to the absence of rotation and that energy liberated by explosion is transform into kinetic energy, the equation that describes the phenomenon is:

$E_{ex} = K_{h} + K_{l}$

Where:

$E_{ex}$ - Energy liberated by the explosion, measured in joules.

$K_{h}$ , $K_{l}$ - Translational kinetic energies of the heavier and lighter piece, respectively.

This expression is expanded by using the definition of translational kinetic energy and supposing the both parts are liberated at the same initial speed ( $v_{o}$ ). Then:

$E_{ex} = \frac{1}{2}\cdot (m_{h} + m_{l})\cdot v_{o}^{2}$

As can be seen, the energy liberated by expression is directly proportional to the mass of the system. Hence, the kinetic energy can be estimated by simple rule of three:

$K_{h} = \frac{m_{h}}{m_{h}+m_{l}}\times E_{ex}$

If $m_{h} = 1.8\cdot m_{l}$ and $E_{ex} = 7230\,J$ , then:

$K_{h} =\frac{1.8\cdot m_{l}}{2.8\cdot m_{l}}\times E_{ex}$

$K_{h} = \frac{9}{14}\cdot (7230\,J)$

$K_{h} = 4647.857\,J$

The heavier piece has a translational kinetic energy of 4647.857 joules.

b) The translational kinetic energy of the lighter piece is calculated by using the equation derived from the Principle of Energy Conservation:

$K_{l} = E_{ex} - K_{h}$

Given that $E_{ex} = 7230\,J$ and $K_{h} = 4647.857\,J$ , the translational kinetic energy of the lighter piece is:

$K_{l} = 7230\,J - 4647.857\,J$

$K_{l} = 2582.143\,J$

The lighter piece has a translational kinetic energy of 2582.143 joules.

Answer from: Quest

32: from largest to smallest, this hierarchy includes eons, eras, periods, epochs, and ages.

33: answer is c

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Answer from: Quest

this means that the temperature of both substances will be equal

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