magnitude and direction

Question

Two forces F₁ and F₂ are applied to an object whose mass is 11.1 kg. The magnitude of F₁ is larger than that of F₂. When two forces point due east, the object has an acceleration whose magnitude is 0.889 m/s². On the other hand, when F₁ points due east and F₂ points due west, the magnitude of the acceleration is 0.756 m/s^{2 }

Answer 1

This is a clever question. We will end up with two formulas and we have two unknowns, which means that we will be able to solve for the unknowns.

Let's take our first scenario -- both forces pushing the same direction:

1) F₁ + F₂ = F_n = m x a = 11.1kg x 0.889 m/s² = 9.87N

Let's consider our second scenario now, in which the forces are opposed:

2) F₁ - F₂ = F_n = m x a = 11.1kg x 0.756m/s² = 8.39N

There are a couple ways of taking this next step. One that I like in simple situations like this is to just add the formulas together so that one of the unknowns cancels out:

1) F₁ + F₂ = 9.87N

2) F₁ - F₂ = 8.39N

-------------------------

2F₁ = 18.26N

Therefore, F₁ = 18.26 / 2 = 9.13N

And we then just solve for F₂ using simple algebra:

9.13N + F₂ = 9.87N

F₂ = 9.87 - 9.13 = 0.74N