A block slides down a smooth, frictionless incline at an angle of 29°

Question

1) Determine the acceleration of the block

2) If the block starts from rest, determine its speed after it has travelled a distance of 2.13m down the incline

Answer 1

F = m*a

To solve, find the force component in line with the slope, and use that to find the acceleration.

The basic force on the block is gravity. F = ma, where a is the acceleration of gravity: 9.8m/sec^2

F(g) = 9.8 * m

This force resolves into 2 components: The "normal force" at right angles to the plane, and the "inline force" parallel to the plane. We want the latter, which is F(i) = F(g) * cos29

We can now write a formula for the inline acceleration: F(g) cos29 = a*m

But F(g) = 9.8m, so 9.8m * cos 29 = a*m

a = 9.8cos 29