What is the central value of the x-component of the net force on this system, in

Question

What is the central value of the x-component of the net force on this system, in N? Answer= 128N

**For both forces and for both angles, the uncertainty is F = 15N and theta = 1 degree. Find the corresponding error in the x-component of the net force on this system, in N.

Hints: Propagate the uncertainty for the x-component of each force first. Then, propagate through the subtraction. Keep at least 3 decimals in all the intermediate steps

Note: The answer is not -125.83, which is what I thought it was.

Explanation / Answer

given F1 = 325 +- 15 N
F2 = 421 +- 15 N
theta1 = 57 +- 1 deg
theta2 = 44+- 1 deg

so net x component of force = F1cos(theta1) - F2cos(theta2)
Fx = 325cos(57) - 421cos(44) = -125.83 N
now, d(Fx)/Fx = sqroot((dF/F1)^2 + (sin(theta1)*d(theta)/cos(theta1))^2) + sqroot((dF/F2)^2 + (sin(theta2)*d(theta)/cos(theta2))^2)
d(Fx)/125.83 = sqroot((15/325)^2 + (tan(57)*1)^2) + sqroot((15/421)^2 + (tan(44)))^2)
d(Fx)/125.83 = 1.54 + 0.966
d(Fx) = 315.373 N [ which is really high]

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