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?
tanθ− ag
To avoid making mistakes, the expression should not be simplified until the numerical values are substituted.
gsinθ−agcosθ
The single equation has two unknowns and cannot be solved with the information given.

Answer 1

Answer:

$\mu_k=\dfrac{gsin\theta -a}{gcos\theta}$

Explanation:

g = Acceleration due to gravity = 9.80 m/s²

a = Acceleration= 3.6 m/s²

$\theta$ = Angle = 27°

The equation is

$\mu_kmgcos\theta=mgsin\theta -ma$

Mass gets cancelled

$\\\Rightarrow \mu_kgcos\theta=gsin\theta -a$

Rearranging for $\mu_k$

$\\\Rightarrow \mu_k=\dfrac{gsin\theta -a}{gcos\theta}$

The simplified expression is

$\mathbf{\mu_k=\dfrac{gsin\theta -a}{gcos\theta}}$

*the options are incomplete. The above answer is the required solution