Can someone me find the magnitude of acceleration using forces?

[shaunamariexx]

Homework Statement

A mass of 8 kg lies on a frictionless, horizontal floor. A force of 145 Newtons is applied to the mass at an angle above the positive x-axis and a force of 16 Newtons is applied to the mass at an angle of 24.5 degrees below the negative x direction. If the angle for 145 Newtons is increased until the object just starts to leave the surface, what is the magnitude of the acceleration on the mass in m/s2 at this point?

The Attempt at a Solution

F1=145 N with unknown angle
F2=16 N with angle of 24.5 degrees
F=ma
145N=8kg(a)
a=18.125

Is this correct?

 

[cheahchungyin]

The solution is incorrect. wouldn't you suspect anything when the question gives so many variables and yet you only used half of them?

First, what makes the object leave the floor?

Its the vertical force! So resolve everything in vertical form...
Force upward is equal force downward at point of leaving surface.

145sinθ=16sin(24.5)+8(9.8) <---assume gravity is 9.8

then you will get θ=35.9° (3 s.f)

Using the angle, you can find the acceleration, by resolving horizontal forces.