1. Multiple Object Systems 1. Analyze the system as one object. 2. Analyze each object individually. 3. Create multiple equations to solve for multiple unknowns. If the system has acceleration a, then each body in the system has acceleration a.

2. Sample Three blocks on a frictionless horizontal surface are in contact with each other. A force F = 96.0 N is applied to block A (m a = m b = m c = 12.0 kg) a) Determine the acceleration of the system. b) The force of contact (F n ) between each block.

3. Sample Three blocks on a frictionless horizontal surface are in contact with each other. A force F = 96.0 N is applied to block A (m a = m b = m c = 12.0 kg) a) Determine the acceleration of the system. b) The force of contact (F n ) between each block.

4. Atwood Machines The use of two or more objects to produce an acceleration of the system. Usually involves a pulley.

5. Sample Determine the acceleration of this system as well as the tension in the rope?

6. Sample a) Determine the acceleration of the system shown. b) Determine the tension in the rope during the acceleration. c) Determine the speed of the system after the bucket has fallen 1.5 m.

7. Friction Friction is a force that opposes relative motion between objects in contact. If the objects are moving relative to one another, the friction is called kinetic. If the objects are not moving relative to one another, the friction is called static.

8. Kinetic Friction Friction is caused by the roughness of the surfaces. If there is relative motion (i.e. sliding) kinetic friction will oppose that motion.

9. Kinetic Friction

10. Coefficients of Friction

11. Sample A 20. kg block of ice is to be pulled by a force of 200. N at 25° to the horizontal as shown. There is a coefficient of friction of 0.15 between the ice and surface. Determine the acceleration of the ice.

12. Sample – Inclined Plane w/o Friction A skier is sliding down a snowy slope inclined at an angle of 30°. Ignoring friction, determine the rate of the acceleration down the incline.

13. Sample – Inclined Plane w/ Friction A skier is sliding down a snowy slope inclined at an angle of 30°. If the coefficient of friction between the skis and the snow is 0.2, determine the rate of the acceleration down the incline.

14. Sample A block slides down an inclined plane at a constant velocity. What angle is the inclined plane if the coefficient of kinetic friction is µ k ?