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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.

Respuesta :

boffeemadrid

Answer:

[tex]\mu_k=\dfrac{gsin\theta -a}{gcos\theta}[/tex]

Explanation:

g = Acceleration due to gravity = 9.80 m/s²

a = Acceleration= 3.6 m/s²

[tex]\theta[/tex] = Angle = 27°

The equation is

[tex]\mu_kmgcos\theta=mgsin\theta -ma[/tex]

Mass gets cancelled

[tex]\\\Rightarrow \mu_kgcos\theta=gsin\theta -a[/tex]

Rearranging for [tex]\mu_k[/tex]

[tex]\\\Rightarrow \mu_k=\dfrac{gsin\theta -a}{gcos\theta}[/tex]

The simplified expression is

[tex]\mathbf{\mu_k=\dfrac{gsin\theta -a}{gcos\theta}}[/tex]

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

onyebuchinnaji

The simplified expression for coefficient of kinetic friction is 0.097.

The given parameters:

  • g = 9.8 m/s²
  • a = 3.6 m/s²
  • θ=27.0∘

The simplified expression for coefficient of kinetic friction is calculated as follows;

μkmgcosθ = mgsinθ − ma

m(μkgcosθ) = m(gsinθ − a)

μkgcosθ = gsinθ − a

[tex]\mu_k = \frac{gsin\theta - a}{gcos\theta} \\\\\mu_k = \frac{(9.8 \times sin27) - 3.6}{9.8 \times cos(27)} \\\\\mu_k = 0.097[/tex]

Thus, the simplified expression for coefficient of kinetic friction is 0.097.

Learn more about coefficient of kinetic friction here: https://brainly.com/question/20241845

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