Only two forces act on an object (mass = 3.80 kg), as in the drawing. (F = 51.0 N.) Find the magnitude and direction (relative to the x axis) of the acceleration of the object.

Question

anonymous · Answer

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agreene · Answer

|F|=m|a| 
51=3.8|a|
13.42=|a|
In a perfect world, the angle will be 40 deg. because the object will move in the direction of the force (in real life, there are more than just this one force.

anonymous · Answer

First resolve the F into its x & y components...
Fx=F*cos45
Fy=F*sin45

Total forces acting on the mass becomes
Ry=Fy in the y direction &
Rx=40+Fx in the x direction
that is the magnitude of the total force acting is
$$R=\sqrt{Rx^2+Ry^2}$$
at an angle
$$X=\tan^{-1} (Ry/Rx)$$
relative to x-axis...

The direction of acceleration will be in the direction of the force (that is X itself)
The magnitude of accl is R/m