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Chapter 5: Forces in Two Dimensions

Difficulty Level: At Grade Created by: CK-12
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Just as motion in two dimensions introduced vectors, forces in two dimensions also involve more involved issues.  Besides vector foces, there is also the particular case of the forces involved in circular motion. 

Chapter Outline

Chapter Summary

  1. The normal force depends upon many different forces.
  2. Maximum static friction is greater than kinetic friction.
  3. Friction acts to oppose the motion that would be caused by an applied force thus opposing the relative motion between two surfaces. When an object slides along a surface, friction acts opposite to its motion. When you walk or a car tire turns, the force of friction opposes the direction your foot or the tire attempts to move. In the latter cases it is the static friction that is responsible for moving you and the car forward.
  4. Do not confuse the coefficient of friction with the force of friction. The coefficient of friction is not a force!
  5. In solving problems on inclined planes, we usually place the \begin{align*}x-\end{align*}axis along the plane so the acceleration is coincident with the \begin{align*}x-\end{align*}axis.
  6. A sliding object on a frictionless inclined plane has acceleration \begin{align*}a = g \sin \theta\end{align*} and is subject to a normal force \begin{align*}F_N = mg \cos\theta\end{align*}.
  7. The magnitude of the centripetal acceleration is \begin{align*}a_c = \frac{v^2}{r}\end{align*} and its direction is toward the center of the circle.
  8. In solving static problems, it is useful to set up a coordinate system such that the object in equilibrium is at the origin and then resolve all forces into components. Use \begin{align*}\sum F_x = 0\end{align*} and \begin{align*}\sum F_y = 0\end{align*} to generate two equations with two unknowns.

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Difficulty Level:
At Grade
Date Created:
Nov 05, 2015
Last Modified:
Oct 20, 2016
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