Question

A student solving a physics problem to find the unknown has applied physics principles and obtained the expression: μkmgcosθ=mgsinθ−ma, where g=9.80meter/second2, a=3.60meter/second2, θ=27.0∘, and m is not given. Which of the following represents a simplified expression for μk?A student solving a physics problem to find the unknown has applied physics principles and obtained the expression: , where , , , and is not given. Which of the following represents a simplified expression for ?tanθ− agTo avoid making mistakes, the expression should not be simplified until the numerical values are substituted.gsinθ−agcosθThe single equation has two unknowns and cannot be solved with the information given.

Answer 1

Solution :

Given expression :

$\mu_k$mgcosθ = mgsinθ − ma

Here, g = 9.8 $m/s^2$ , a = 3.60 $m/s^2$ , θ = 27°

Therefore,

$\mu_k mg \cos \theta = mg \sin \theta - ma$

$\mu_k mg \cos \theta = m(g \sin \theta - a)$

$\mu_k g \cos \theta = (g \sin \theta - a)$

$\mu_k =\frac{(g \sin \theta-a)}{g \cos \theta}$

Mow calculating the coefficient of kinetic friction as follows :

$\mu_k=\frac{g \sin \theta-a}{g \cos \theta}$

$\mu_k=\frac{9.8 \times \sin 27^\circ-3.60}{9.8 \times \cos 27^\circ}$

$\mu_k=0.097$