Mathematics, 11.06.2020 17:57 smn43713
The energy, E, of a body of mass m moving with speed v is given by the formula below. The speed is nonnegative and less than the speed of light, c which is constant. Use lower case letters here. E = mc^2 (1/Squareroot1 - v^2/c^2 - 1)
(a) Find E/m = c^2Squareroot1 - v^2/c^2 - c^2/1 - v^2/c^2 what is the sign of this partial? Positive negative
(b) Find E/v =?
Answers: 1
![\frac{\delta E}{\delta m}= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ]](/tpl/images/0682/9970/d6bf3.png)
![E = mc^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } }- 1 ]](/tpl/images/0682/9970/33d81.png)
![\frac{\delta E}{\delta m} = \frac{\delta }{\delta m} [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 )]](/tpl/images/0682/9970/b9a67.png)
![= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2 } } } -1 ] \frac{\delta m}{\delta m}](/tpl/images/0682/9970/7431b.png)
![= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ]](/tpl/images/0682/9970/6d2e4.png)
![\frac{\delta E}{\delta V} = \frac{\delta }{\delta v } [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } - 1 )]](/tpl/images/0682/9970/465ae.png)
![\frac{\delta E}{\delta V} = mc^2 [\frac{\delta }{\delta v} (\frac{c}{\sqrt{c^2 -v^2} } - 1 )]](/tpl/images/0682/9970/2b0e4.png)
![= mc^2 [c* [\frac{\delta }{\delta v} (c^2 - v^2 )^{-\frac{1}{2} }] - 0]](/tpl/images/0682/9970/fbe09.png)
![= mc^3 [- \frac{1}{2} (c^2 - v^2 )^{-\frac{3}{2} } * (-2v)]](/tpl/images/0682/9970/e085d.png)
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The energy, E, of a body of mass m moving with speed v is given by the formula below. The speed is n...
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