Answer to Question #92416 in Classical Mechanics for adhil

Question

an object of mass 90 kg is being moved over an inclined plane of two angles 30 and 60. Calculate the force required in each case to achieve the acceleration of 1 m/s^2

Answer 1

Newton’s second law:

$$\vec{N}+m\vec{g}+\vec{F} = m\vec{a}$$

Projection on OX:

$$mg\sin(\alpha)+F = ma\\ F = m(a-g\sin(\alpha))\\ a) \alpha= 30^\circ\\ F=90\cdot(1-9.81\cdot 0.5) = -351.45 N\\ b) \alpha = 60^\circ\\ F=90\cdot(1-9.81\cdot \frac{\sqrt{3}}{2}) = -674.61 N$$