At what speed v will the mass of an object be 10% greater than its rest mass?

Asked on by bwang96

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The mass-energy equivalence relation `E = mc^2` gives the energy released when an object with mass m is completely converted to energy. Alternately, as the energy of an object is increased there is a corresponding increase in its mass.

If an object with rest mass `M_o` moves at v m/s, the mass of the object is increased to `M = M_o/(sqrt(1 - v^2/c^2))` , where c is the speed of light.

Let the mass of an object be 10% greater than the rest mass at speed v,

`1.1*M_o = M_o/(sqrt(1 - v^2/c^2))`

=> `sqrt(1 - v^2/c^2) = 1/1.1`

=> `1 - v^2/c^2 = 1/1.21`

=> `v^2/c^2 = 21/121`

=> `v^2 = (21/121)*c^2`

=> `v = (sqrt(21)/11)*c`

=> `v ~~ 0.4166*c`

The mass of an object is 10% greater than the rest mass when its speed is 0.4166*c


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