Question

A crate is sliding down a ramp that is inclined at an angle 30.6 ° above the horizontal. The coefficient of kinetic friction between the crate and the ramp is 0.360. Find the acceleration of the moving crate.

Answer 1

Answer:$1.95 m/s^2$

Explanation:

Given

inclination $\theta =30.6^{\circ}$

coefficient of kinetic friction $\mu =0.36$

As crate is moving Down therefore friction will oppose the motion

using FBD

$mg\sin \theta -f_r=ma$

$f_r=\mu N$

$f_r=\mu mg\cos \theta$

$mg\sin \theta -\mu mg\cos \theta =ma$

$a=g\sin \theta -\mu g\cos \theta$

$a=g(\sin (30.6)-0.36\cdot \cos (30.6))$

$a=9.8\times 0.199$

$a=1.95 m/s^2$