The only two forces acting on a body have magnitudes F1 and F2 and directions that differ by an angle θ. If the resulting acceleration has a magnitude a, what is the mass of the body?

Answer 1

Fx = F1 + F2 cos T
Fy = F2 sin T

F = sqrt (Fx^2+Fy^2)

Fx^2 = F1^2 + 2 F1F2 cos T + F2^2 cos^2 T
Fy^2 = F2^2 sin^2 T

sum = F1^2 + 2 F1F2 cos T + F2^2(sin^2T+cos^2T)

sum = F1^2 + 2 F1 F2 cos T + F2^2
so
F = sqrt (F1^2 + 2 F1 F2 cos T + F2^2)
and
m = F/a
=(1/a)sqrt(F1^2 + 2 F1 F2 cos T + F2^2)