Chapter 6 Applications of Newton s Laws. Copyright 2010 Pearson Education, Inc.

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Deirdre Reeves
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1 Chapter 6 Applications of Newton s Laws

2 Units of Chapter 6 Frictional Forces Strings and Springs Translational Equilibrium Connected Objects Circular Motion

3 6-1 Frictional Forces Friction has its basis in surfaces that are not completely smooth:

4 6-1 Frictional Forces Kinetic friction: the friction experienced by surfaces sliding against one another The kinetic frictional force depends on the normal force: (6-1) The constant is called the coefficient of kinetic friction.

5 6-1 Frictional Forces

6 6-1 Frictional Forces The kinetic frictional force is also independent of the relative speed of the surfaces, and of their area of contact.

7 6-1 Frictional Forces The static frictional force keeps an object from starting to move when a force is applied. The static frictional force has a maximum value, but may take on any value from zero to the maximum, depending on what is needed to keep the sum of forces zero.

8 6-1 Frictional Forces (6-2) where (6-3) The static frictional force is also independent of the area of contact and the relative speed of the surfaces. Note: μ k < μ s

9 6.2 Frictional Force: Motion of a crate with applied forces There is no attempt at sliding. Thus, no friction and no motion. NO FRICTION Force F attempts sliding but is balanced by the frictional force. No motion. STATIC FRICTION Force F is now stronger but is still balanced by the frictional force. No motion. LARGER STATIC FRICTION Force F is now even stronger but is still balanced by the frictional force. No motion. EVEN LARGER STATIC FRICTION f s is the static frictional force f k is the kinetic frictional force Finally, the applied force has overwhelmed the static frictional force. Block slides and accelerates. WEAK KINETIC FRICTION To maintain the speed, weaken force F to match the weak frictional force. SAME WEAK KINETIC FRICTION Static frictional force can only match growing applied force. Kinetic frictional force has only one value (no matching).

10 6.2 Frictional Force: Motion of a crate with applied forces Static frictional force can only match growing applied force. Kinetic frictional force has only one value (no matching). f s is the static frictional force f k is the kinetic frictional force

11 6.3 Properties of Friction Property 1. If the body does not move, then the static frictional force and the component of F that is parallel to the surface balance each other. They are equal in magnitude, and is f s directed opposite that component of F. Property 2. The magnitude of has a maximum value f s,max that is given by where μ s is the coefficient of static friction and F N is the magnitude of the normal force on the body from the surface. If the magnitude of the component of F that is parallel to the surface exceeds f s,max, then the body begins to slide along the surface. F N F mg

12 6.3 Properties of Friction Property 3. If the body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value f k given by where μ k is the coefficient of kinetic friction. Thereafter, during the sliding, a kinetic frictional force f k opposes the motion. F N F mg

13 F N F 1. Static: not sliding mg f = μ F s,max s N 0 < f μ F s s N 2. Kinetic: sliding Note: μ k < μ s f = μ F k k N Note 1: The static and kinetic friction acts parallel to the surfeces in contact The direction opposes the direction of motion (for kinetic friction) or of attempted motion (in the case of static friction) Note 2: The coefficient μ does not depend on the speed of the sliding object k

Actually, no perfectly frictionless surface exists. For two surfaces in contact, tangential forces, called friction forces, will develop if one

Chapter 8 Friction Actually, no perfectly frictionless surface exists. For two surfaces in contact, tangential forces, called friction forces, will develop if one attempts to move one relative to the other.