Physics: Calculate the Acceleration of a Sled Heading Down a Hill

**Problem: Calculate the acceleration of a sled that is heading down a 40° slope (one that makes an angle of 40° with the horizontal). The coefficient of kinetic friction on ice is **μ_k = 0.100.

First start by drawing a force diagram with positive X down the hill, parallel to the incline, and Y perpendicular to the surface.

Use the formulas Fk = force of kinetic friction =  μ_k  * n  and Fnet = ma

Positive X: MGsin(40), Negative X: μ_k * n

Positive Y: N, Negative Y: MGcos(40)

Now set Fnet = positive X – negative X

Fnet = MGsin(40) – μ_k * n

Substituting MA for Fnet, we get:

Gsin(40) – μ_k * Gcos(40) = A = 5.55 m/s^2

Answer: A = 5.55 m/s^2