1. Newton’s Laws of Motion - 2

2. Multiple Objects – Example with m 2 > m 1 Draw free body diagrams for each object. In magnitude, a 1 = a 2

3. Multiple Objects – Example with m 2 > m 1 Apply Newton’s 2 nd Law to each object.

4. Multiple Objects – Example with m 2 > m 1 Solve the equations.

5. Forces of Friction When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion. This is due to the interactions between the object and its environment. This is resistance is called friction.

6. Friction is proportional to the normal force. The force of static friction is generally greater than the force of kinetic friction. The coefficient of friction (µ) depends on the surfaces in contact. The direction of the frictional force is opposite the direction of motion. The coefficients of friction are nearly independent of the area of contact. Conclusions from Experiments

7. Static Friction, ƒ s Static friction acts to keep the object from moving. If F increases, so does ƒ s. If F decreases, so does ƒ s. ƒ s  µ s. n (Use = sign for impending motion only.)

8. Kinetic Friction, ƒ k The force of kinetic friction acts when the object is in motion. ƒ k = µ k. n (Variations of the coefficient with speed can be ignored.)

9. Setting up a Friction Problem Locate the applied force F on the graph. In the static region, if F < f s,max, then F = f s. Motion begins when F = f s, max. then as F increases, the friction force drops quickly to a (nearly) constant value, f k.