Forces in Two Dimensions - Mission F2D6 Detailed Help

A 2.68-kg object is placed upon an inclined plane. The incline angle is 12.7 degrees. The coefficient of friction is 0.097. Use g = 9.8 m/s/sand the free-body diagram to fill in the blanks and to determine the acceleration of the object.

(Note: Numbers are randomized numbers and likely different from the numbers listed here.)

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A successful strategy for answering this question involves the following steps:
  1. Use the formulae in the Math Magic section to determine the parallel and perpendicular components of the force of gravity.
  2. Analyze the two forces perpendicular to the inclined plane. Knowing that there is no acceleration perpendicular to the plane allows you to assume a balance between these two forces.
  3. Use the normal force and the coefficient of friction to determine the force of friction which opposes the motion (see Formula Fix section).
  4. Analyze the forces parallel to the plane to determine the net force and the acceleration. The net force would be the vector sum of the two forces; this would be the same as subtracting the force which opposes the acceleration (friction) from the force which causes the acceleration (parallel component of gravity).
  5. Use the Newton's second law equation (see Formula Fix section) to determine the acceleration from the net force and the mass.

The force of friction experienced by an object is often calculated using the equation:
Ffrict= mu • Fnorm

where mu is the coefficient of friction (dependent predominantly upon the nature of the two surfaces which are in contact) and Fnorm is the normal force.

The acceleration (a) of the object can be calculated from knowledge of the net force (Fnet) and the mass (m) of the object using the equation:
a = Fnet/ m

The force of gravity is neither in the direction of the acceleration nor perpendicular to it. The goal is always to have all forces directed perpendicular or parallel to each other and to the acceleration. So it is the habit on inclined plane problems such as this one to resolve the force of gravity into two components - one being parallel to the inclined plane and the other perpendicular to it. The formulas for resolving the force of gravity into its components are:
Fparallel= m • g • sine(Θ)

Fperpendicular= m • g • cosine(Θ)