Two forces Fa and Fb are applied to an object whose mass is 8.0kg. The larger force is Fa. When both forces po?

[Johhny]

Two forces Fa and Fb are applied to an object whose mass is 8.0kg. The larger force is Fa. When both forces point due east the object's acceleration has a magnitude of 0.50m/s^2. However, when Fa points due east and Fb points due west, the acceleration is 0.40 m/s^2, due east. Find the magnitude of Fa and Fb.

[KiwiJoey]

Newton's Law: F = ma.

When they're pointing in the same direction F (which will be the sum of Fa and Fb) = 8.0 kg *0.50 m/s^2 = 4.0 N.

When they're pointing in opposite directions, the sum of the forces will be Fa - Fb, and they will equal 8.0 kg * 0.4 m/s^2 = 3.2 N.

So we have the two equations

Fa + Fb = 4.0
Fa - Fb = 3.2, which we can solve simultaneously. Adding the two equations together gives

2Fa = 7.2, so Fa = 3.6 N.
Substituting this into either one of the equations will give Fb = 0.4 N.