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MCAT Physics Question — Object Acceleration

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)

Click for 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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