I have a problem that involves pushing an object with a:
- Mass of 80 kg
- Up a sloped plane (angle of incline is the unknown)
- With an applied force of 700N
- At an acceleration of 4.88 m/s^2
- With a coefficient of friction 0.07 acting against it
My goal is to find the angle that allows for that acceleration, using the 700N of force. I first flipped the axis to make the x-axis go up the inclined plane. So I can find the angle using the sum of the x-forces.
The sum of the x-forces (or m*a) = Applied force - (Weight force y component * coefficient of friction) - (Weight force of the x component).
I rewrote this as m*a = Applied - (coefficient of friction * w * cos theta) - (w * sin theta).
After trying for solve for the angle, I got stuck at (Applied - m*a) / w = (coefficient of friction * cos theta) + sin theta.
Is there a better way to solve this, without ending up with two different trig functions?