Question

A crate is given a big push, and after it is released, it slides up an inclined plane which makes an angle 0.46 radians with the horizontal. The frictional coefficients between the crate and plane are ($\mu$μ_s = 0.82, $\mu$μ_k = 0.46 ). What is the magnitude of the acceleration (in meters/second²) of this crate as it slides up the incline?

Answer 1

Concept: use Newton’s law of motion on inclined plane with friction to find the acceleration as required ***************************************************************************************************
Check the answer and let me know immediately if you find something wrong or missing... I will rectify the mistakes asap if any

N_0 = mg cos theta f = mu_k N_0 = mu_k mg cos theta mg sin theta + f = ma or, a = mg sin theta + f/m = g sin theta + mu_k g cos theta = g(sin theta + mu_k cos theta), theta = 0.46 rad mu_k = 0.46 = 8.39 m/s^2