Question

A 4 kg object starts from rest from the top of an rough 30o incline and slides 3.0 m down the incline in 2.0 s. Find the coefficient of friction between the block and the incline. A. 0.43 B. 0.25 C. 0.33 D. 0.90

Answer 1

from the given phenomena ,

m*g*sin $\theta$ - F_r = m*a

m*g*sin $\theta$ - $\mu$ k*N = m*a

m*g*sin $\theta$ - $\mu$ k *m*g*cos $\theta$ = m*a

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

first we find the a.

s = 1/2*a*t²

3 = 0.5*a*4

a = 1.5 m/s²

so,

$\mu$ k = g*sin $\theta$ - a/g*cos $\theta$ = (9.81*sin30 - 1.50) /9.81*cos30

$\mu$ k $\approx$ 0.43

option A is right.