MCAT Physics Question — Object Acceleration | Next Step Test Prep MCAT Physics Question — Object Acceleration | Next Step Test Prep

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An object rests on a plane, with an angle of incline, θ, an acceleration due to gravity, g, and a coefficient of friction μ between the object and the plane. Which of the following gives the acceleration of the object?

 

A) a = g sin θ

B) a = g (sin θ – cos θ)

C) a = g (cos θ – μ sin θ)

D) a = g (sin θ – μ cos θ)

 

 

Explanation

 

The force of gravity down the plane is given by Fg = mg sin θ. The frictional force is given by Ff = μ mg cos θ.

 

Thus, we can set up the overall equation:

 

Fnet = Fg – Ff

 

Applying Newton’s Second Law, we can re-write the equation as:

 

ma = Fg – Ff

 

Substituting the equations given for Ff and Fg we get:

 

ma =  mg sin θ –  μ mg cos θ

 

Canceling out “m” throughout the equation and factoring out the “g” leaves us with:

 

a = g (sin θ – μ cos θ)

 

Thus, choice (D) is the right answer.

 

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