Section: Chemical and Physical Foundations of Biological Systems

38) An object rests on a plane, with an angle of incline, ?, 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?

1. a = g sin ?
2. a = g (sin ? – cos ?)
3. a = g (cos ? – µ sin ?)
4. a = g (sin ? – µ cos ?)

The force of gravity down the plane is given by Fg = mg sin ?. The frictional force is given by Ff = µ mg cos ?. 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 ? – µ mg cos ? Canceling out “m” throughout the equation and factoring out the “g” leaves us with: a = g (sin ? – µ cos ?) Thus, choice (D) is the right answer.