Magnitude of acceleration is 3.35 m/[tex]s^{2}[/tex]
Explanation:
- Here, the box is sliding down in a frictional force. When we draw the free body diagram, the forces acting on it are normal force and gravitational force.
- We know that normal force would act in a perpendicular direction.
- The gravitational force has x and y components since it is sliding down. These two components are mg cosθ and mg sinθ, where θ is the angle of the ramp. Since the motion is along the x-direction, the force act on it is mg sinθ.
- According to Newton's second law, F = ma, to find acceleration a = [tex]\frac{F}{m}[/tex]
- When you substitute the x-axis force, the equation will simplify into
a = g sinθ, so the answer is 3.35 m/[tex]s^{2}[/tex]
