Question

A student wants to determine the coefficients of static fric- tion and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches 30????, the box starts to slip, and it then slides 2.5 m down the plank in 4.0 s at constant acceleration. What are (a) the coefficient of static friction and (b) the coefficient of kinetic friction between the box andtheplank?

Answer 1

Step-by-step explanation:

Given

Angle at which block started to move

`tan\theta =\mu _s`

`\tan 30=\mu _s`

`\mu _s=0.577`

coefficient of static friction is 0.577

Also When it starts moving coefficient of kinetic friction comes into friction
`\mu _k`

`s=ut+(at^2)/(2)`

here
`a=gsin\theta -\mu _kgcos\theta`

here u=0

s=2.5 m

`2.5=0+((gsin\theta -\mu _kgcos\theta )* 4^2)/(2)`

`2.5=(9.8(sin30-\mu _kcos30)* 16)/(2)`

`\mu _k=0.54`