Finding Ratios of Forces in a Two-Force System | Homework Question

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The discussion revolves around solving a physics problem involving two forces, Fa and Fb, applied to an object, with the goal of finding the ratio of their magnitudes. The object experiences different accelerations depending on the direction of the forces, specifically 0.50 m/s² when both forces act east and 0.40 m/s² when Fa acts east and Fb acts west. The user initially struggles with applying the equations of motion but eventually arrives at the correct ratio of Fa to Fb, which is 9. This solution confirms the user's understanding of how to manipulate the equations to find force ratios. The discussion concludes with the user expressing satisfaction in learning how to solve such problems.
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Homework Statement



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

Homework Equations



F = ma ?
d = Vt + 1/2at^2 ?

The Attempt at a Solution



I've tried manipulating the F = ma equation to no avail. Maybe it has something to do with d = Vt + 1/2at^2 but I think maybe I'd have to use Fa + Fb = sigmaF.
But to be honest, I have no idea where to start, especially with finding ratios. I just need a little help forward. Thanks :smile:
 
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Fa + Fb = ma1...(1)
Fa - Fb = ma2...(2)
take the ratio of 1 and 2 and solve for Fa and Fb
 
I've tried something like that, but the book says that the answer is 9. Does that change anything?
 
Nevermind my last post, I've gotten the answer to be 9. Thanks! I'll know how to do ratios now :approve:
 
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