Question

A box slides downwards at a constant velocity on an inclined surface that has a coefficient of friction uK = 0.58, find the angle of the incline, in degrees?

Answer 1

30.11°

Step-by-step explanation:

`\mu` = Coefficient of friction = 0.58

g = Acceleration due to gravity = 9.81 m/s²

`\theta` = Angle of incline

As the forces of the system are conserved we have

`mgsin\theta-\mu mgcos\theta=0\\\Rightarrow mgsin\theta=\mu mgcos\theta\\\Rightarrow sin\theta=\mu cos\theta\\\Rightarrow \mu=(sin\theta)/(cos\theta)\\\Rightarrow \mu=tan\theta\\\Rightarrow \theta=tan^(-1)\mu\\\Rightarrow \theta=tan^(-1)0.58\\\Rightarrow \theta=30.11^(\circ)`

The angle of incline is 30.11°