A 2 kg block slides down a frictionless 30 degree incline. Find its acceleration.

Answer

The acceleration is 4.9 m/s² down the slope.

Explanation

Step 1 — Draw the free-body diagram

Two forces act on the block: its weight mg straight down, and the normal force N perpendicular to the surface. The incline is frictionless, so there is no third force along the slope.

Step 2 — Resolve the weight along the slope

Take the x-axis along the incline, pointing downhill:

component along the slope = mg sin θ component into the surface = mg cos θ

Only the first component accelerates the block; the second is balanced by N.

Step 3 — Apply Newton's second law

ma = mg sin θ → a = g sin θ

The mass cancels — the acceleration on a frictionless incline does not depend on how heavy the block is.

Step 4 — Substitute

a = 9.8 m/s² × sin 30° = 9.8 × 0.5 = 4.9 m/s²

Check

sin 30° = 0.5, so the answer must be exactly half of g. If a mass appears anywhere in your final expression, the weight was not resolved correctly.