Question

A block is moving up an inclined plane of inclination 60 degree with velocity 20 ms-1 and stops after 2 sec. If g=10, find coefficient of friction

Answer 1

Given,

v = 20 m/s

angle = 60°

t = 2s

g = 10 m/$s^{2}$

now we have to find  acceleration due to gravity

v = u +at

$\frac{v}{t} = a$           [ u = 0 ]

$\frac{20}{2} = a$

a = $10m/s^{2}$

now lets find the coefficient of friction "z" - let's use this symbol to denote friction as we don't have the appropriate symbol here

mg sinβ + z(mg cosβ) = ma

mg [ sinβ + zcosβ ]  = ma

sinβ + z cosβ = $\frac{ma}{mg}$

sinβ + z cosβ = 10/10

sinβ + z cosβ = 1

z = $\frac{1-sin\beta }{cos\beta }$

z = $\frac{1 - sin60}{cos60}$

z = 2-$\sqrt{3}$ =  co efficient of friction