Question

A student wants to determine the coefficients of static friction 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 and the plank?

Answer 1

Step-by-step explanation:

Given

at
`\theta =30^(\circ)`

Box slides down
`2.5 m\ in\ t=4 s`

as box just starts to slide at
`\theta =30^(\circ)`

friction force will just balance the sin component of weight

thus

`mg\sin \theta =f_r`

and
`f_r=\mu N`

where
`\mu`is coefficient of static friction

`N=mg\cos \theta`

thus
`\mu =\tan \theta`

`\mu =0.577`

(b)block travels 2.5 m in 4 s

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

`2=0+(a* 16)/(2)`

`a=0.25 m/s^2`

i.e.
`a=\mu _kg`

`\mu_k=0.025`