Calculating Force in Special Relativity with Proton Velocities

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Homework Statement

Find the force necessary to give a proton an acceleration of 4.0 1019 m/s2 when the proton has the following velocities (along the same direction as the force).

We're covering special relativity and due to my lack of a brain I can't figure this simple problem out.

Velocities are .09c and .4c (I have answers the homework website likes for these ones because the v/c isn't doing much to y?)

and .7c and .97c, which I can't get right.

Homework Equations

F = dp/dt
P = ymv
(y is gamma)

The Attempt at a Solution

I tried using the quotient rule for derivatives, and got an eqn that, when plugging in the given velocities, came up with answers that it marked as correct for the first 2, but not for the 2nd 2.

F = dp/dt = m*d/dt(yv)
(B is v/c) (a is acceleration)
F = m[(a*sqrt(1-B^2) + ((1-B^2)^-.5)(B^2)(A)]/(1-B^2)

There must be a better way to do this problem... if anyone can help I would appreciate it, very angry with this problem. Thanks.

 

[Doc Al]

F = dp/dt = m*d/dt(yv)
(B is v/c) (a is acceleration)

OK.

F = m[(a*sqrt(1-B^2) + ((1-B^2)^-.5)(B^2)(A)]/(1-B^2)

Not quite sure I understand that last step. Try to simplify this expression into some final form. (Express everything in terms of γ.)