- #1
omoplata
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Homework Statement
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A particle of rest mass ##m_0## is is caused to move along a line in such a way that its postion is $$x = \sqrt{b^2 + c^2 t^2} -b$$What force must be applied to the particle to produce this motion?
2. Homework Equations
The velocity of the particle as seen from the rest frame is ##v = \frac{dx}{dt}## and the acceleration is ##a = \frac{dv}{dt}##.
The mass of the particle as seen in the rest frame is ##m = \gamma m_0##, where ##\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}##.
Then the force should be ##F = m a##.
The Attempt at a Solution
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Differentiating ##x##, I get ##v = \frac{c^2 t}{\sqrt{b^2 + c^2 t^2}}##.
So, ##\gamma = \frac{\sqrt{b^2 + c^2 t^2}}{b}##.
Differentiating ##v##, I get ##a = \frac{b^2 c^2}{(b^2 + c^2 t^2)^{\frac{3}{2}}}##.
So, ##F = \frac{m_0 b c^2}{b^2 + c^2 t^2}##.
The answer given in the book is ##F = \frac{m_0 c^2}{b}##. What did I do wrong?