Question

Two forces FA and FB are applied to an object whose mass is 12.0 kg. The larger force is FA. When both forces point due east, the object's acceleration has a magnitude of 0.800 m/s2. However, when FA points due east and FB points due west, the acceleration is 0.400 m/s2, due east. Find the magnitude of FA and the magnitude of FB.

Answer 1

  Newton's Law: F = ma.

When they're pointing in the same direction F (which will be the sum of Fa and Fb) = 12.0 kg *0.800 m/s^2 = 9.6 N.
I.e FA + FB = 9.6 N....(i)
When they're pointing in opposite directions, the sum of the forces will be FA - FB, and they will equal 12.0 kg * 0.4 m/s^2 = 4.8 N.

I.e FA - FB = 4.8 N......(ii)

So we have the two equations

FA + FB = 9.6
FA - FB = 4.8, which we can solve simultaneously. Adding the two equations together gives

2FA = 14.4, so FA = 7.2 N.
Substituting this into either one of the equations will give FB = 2.4 N.

Hope this will help you.

Please rate the answer.