Modern Physics (S. Theory of relativity) problem

AI Thread Summary
To determine the force required to accelerate a proton at 1.0 x 10^19 m/s², the relationship between momentum (p), mass (m), and the gamma factor (λ) is crucial. The user derived the equation F = mλa but encountered issues with the school software rejecting their answers. It is emphasized that the gamma factor λ is dependent on the proton's velocity (u), necessitating the use of the product rule when differentiating. The correct approach involves calculating the derivative of momentum with respect to velocity, incorporating both λ and u. Proper application of these principles should resolve the discrepancies with the software.
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Homework Statement



Find the force necessary to give a proton an acceleration of 1.0 10e19 m/s2 when the proton has the following velocities (along the same direction as the force).

Homework Equations


P=mλu


The Attempt at a Solution


Found the derivative of the above equation and got F=mλa, but my answers are been rejected by the school software. I don't know what I did wrong please help.
 
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The gamma factor λ depends on u. Since p is proportional to the product of λ and u, you'll need to use the product rule when taking the derivative dp/du in the expression F = dp/dt = (dp/du)(du/dt)
 
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