• roadjester
Two forces F1 and F2 act on a 5.00 kg object. Taking F1=20.0N and F2=15.00N, find the acceleration of the object for the configurations: a) mass m with F1 acting in the positive x direction and F2 acting perpendicular in the positive y direction b) mass m with F1 acting in the positive x direction and F2 acting on the object at 60 degrees above the horizontal.
  • Stacey Warren - Expert
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  • chestercat
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  • roadjester
  • anonymous
First, find the acceleration that each force causes in each orthogonal direction (X and Y). Then, add the accelerations in X and in Y together. To find the magnitude of the acceleration use Pythagorean's Theorem, \(M = \sqrt{X^2 + Y^2}\) I'll do the second case as an example. \[a_x = {1 \over m} \left ( F_1 + F_2 \cos(60) \right)\] \[a_y = {1 \over m} \left( F_2 \sin(60) \right)\] I obtained the above equations from Newton's Second Law\[\sum F = m \cdot a ~\therefore a = {1 \over m} \cdot F \]

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