Physics forces problem?
Three forces in the x-y plane act on a 5.20 kg mass: 10.10 N directed at 25o, 14.20 N directed at 170o, and 11.30 N directed at 248o. All angles are measured from the positive x-axis, with positive angles in the Counter-Clockwise direction. Calculate the magnitude of the acceleration. and what is the direction of the resulting vector?
Comments
In the direction of x the net force is
10.1 cos 25˚ + 14.2 cos 170˚ + 11.3 cos 248˚ = -9.04 N
In the direction of y , the net force is
10.1 sin 25˚ + 14.2 sin 170˚ + 11.3 sin 248˚ = - 3.743 N
Resultant of these two forces is √ { (-9.04)²+( - 3.743)² } = 9.78426 N
Acceleration is 9.78426/ 5.2 = 1.88 m/s²
The resultant is in the 3rd quadrant
tan ( 180 +α) = tan α = 9.04/3.743
( 180 +α) = 180 +67.5 = 247.5˚
This is the direction of the acceleration.
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