Newton's Laws of Motion: Exam-Pattern Drill (8)

Question

A block of mass $m = 5\text{ kg}$ rests on a frictionless inclined plane of angle $\theta = 37°$. A horizontal force $F$ is applied to keep it stationary. Find $F$. Take $g = 10\text{ m/s}^2$, $\sin 37° = 0.6$, $\cos 37° = 0.8$.

Solution — Step by Step

Final answer: $F = 37.5\text{ N}$

Why This Works

When we resolve along the incline, the normal force drops out of the equilibrium equation entirely. This is the whole reason we tilt the axes — fewer unknowns, faster answer.

The horizontal force is “tilted” relative to the incline surface, so only its component $F\cos\theta$ acts along the slope direction. Same for gravity: only $mg\sin\theta$ matters along the slope.

Alternative Method

We could resolve along horizontal and vertical axes instead. Then $N\sin\theta = F$ and $N\cos\theta = mg$, which gives $F/mg = \tan\theta$. Same answer, but you carry $N$ through the algebra. The tilted-axis approach skips that work.

Common Mistake