How Do You Calculate Magnitude of Acceleration from Multiple Forces in Physics?

AI Thread Summary
To calculate the magnitude of acceleration from multiple forces acting on a mass, first determine the x and y components of each force using trigonometric functions. After obtaining the components, sum the x-components and y-components separately, ensuring to account for any negative values. The resultant force can then be calculated using the Pythagorean theorem, R = (Rx^2 + Ry^2)^(1/2). Finally, apply Newton's second law, F=ma, to find the acceleration by dividing the resultant force by the mass. Proper vector addition is crucial, as squaring the components before summing them is incorrect.
ganondorf29
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Homework Statement


Three forces in the x-y plane act on a 3.40 kg mass: 9.10 N directed at 25o, 12.40 N directed at 156o, and 4.70 N directed at 259o. All angles are measured from the positive x-axis, with positive angles in the Counter-Clockwise direction. Calculate the magnitude of the acceleration.



Homework Equations



F=ma
Rx = F1cos(theta) - Quadrant 1
Ry = F1sin(theta) - Quadrant 1
R = (Rx^2 + Ry^2)^1/2


The Attempt at a Solution



I tried to find the x and y components of each force. Then I added the square of the x-components and took the square root of that answer and I did the same with the y-components. Finally I took the answers from the last step and took the square of them and then the square root of them added. Finally I plugged in that force into F=ma and tried to solve for a, but it doesn't work. I think I am doing something wrong, in that I am not sure what to do about the x,y components that are negative.
 
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Hi ganondorf29! :smile:
ganondorf29 said:
Then I added the square of the x-components and took the square root of that answer …

ah … that's where you're going wrong …

these are vectors, so you use ordinary vector addition …

just add the x-components without squaring first. :smile:
 

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