1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 13-15

2. Newton’s Laws 1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration 2nd Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. 3rd Law: For every action there is an equal, but opposite reaction

4. Newton’s law of gravitation

6.  Pulling Against Friction A box of mass m is on a surface with coefficient of kinetic friction . You pull with constant force F P at angle  The box does not leave the surface and moves to the right. 1.What is the magnitude of the acceleration? 2.What angle maximizes the acceleration?

7. Is it better to push or pull a sled? You can pull or push a sled with the same force magnitude, F P, and angle , as shown in the figures. Assuming the sled doesn’t leave the ground and has a constant coefficient of friction, , which is better? FPFP FPFP

8. Hockey Puck Which of these three best represents a hockey puck in the real world? a) b) c)

9. Newton’s 1 st Law A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration

10. Aristotle: a natural state of an object is at rest; a force is necessary to keep an object in motion. It follows from common sense. Galileo: was able to identify a hidden force of friction behind common- sense experiments 1564-1642 384-322 B.C.

11. Galileo: If no force is applied to a moving object, it will continue to move with constant speed in a straight line Galilean principle of relativity: Laws of physics (and everything in the Universe) look the same for all observers who move with a constant velocity with respect to each other. Inertial reference frames

12. Kinetic Friction For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write F Friction =  Kinetic N Here  is a constant Warning: –THIS IS NOT A VECTOR EQUATION!

13. Static Friction This is more complicated For static friction, the friction force can vary F Friction   Static N Example of the refrigerator: –If I don’t push, what is the static friction force? –What if I push a little?

14. H Coefficient of friction:  What is the normal force? What is the velocity of the block when it reaches the bottom?

15. Newton’s 3 rd Law For every action there is an equal, but opposite, reaction

16. Skater Skater pushes on a wall The wall pushes back –Equal and opposite force The push from the wall is a force –Force provides an acceleration –She flies off with some non-zero speed

17. P m1m1 m2m2 No friction m1m1 Free body diagram m1m1 m1gm1g P N1N1 F 21 m2gm2g F 12 N2N2 m2m2 F 12 =F 21

18. A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is 0.25. If the larger block is on a frictionless table, what is the largest horizontal force that can be applied to it without the small block slipping?

20. Massless, unstretchable string; frictionless pulley Force of tension

21. A Problem With First Year Physics Strings and Pulleys m1m1 m 1, m 2 are given m 2 >m 1 m2m2 String is massless and unstretchable Find accelerations of m 1 and m 2 (assume no friction)

22. V0V0 A block of mass m is given an initial velocity V 0 up an inclined plane with angle of incline θ. Find acceleration of the block if a)  = 0 b) non-zero 

23. A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F is applied to the wedge. What must the magnitude of F be if the block is to remain at a constant height above the tabletop?

24. Block 1, of mass m 1, is placed at rest on an inclined plane. It is attached by a massless, unstretchable string to block 2, of mass m 2. The pulley is massless and frictionless and just changes the direction of the tension in the string. The coefficient of friction between the plane and m 1 is the constant . 2 1 Determine what range of values for mass m 2 will keep the system at rest. Find acceleration if mass 2 goes down.

25. F Find F necessary to drag the box 1 at constant speed. 1 2 Friction everywhere.

26. The advantage of a pulley What minimum force F is needed to lift the piano of mass M?

28. Quiz a) A crate of mass m is on the flat bed of a pick up truck. The coefficient of friction between the crate and the truck is . The truck is traveling at the constant velocity of magnitude V 1. Draw the free body diagram for the crate. b) The truck starts to accelerate with an acceleration a c. Draw the free body diagram for the crate, if the crate does not slip.

29. The Elevator Problem

30. WORK (Chapter 7)

31. 2 or 3 D motion Definition of work: Kinetic energy: Work-energy theorem:

32. Have a great day! Reading: Chapter 7 Hw: Chapter 6 problems and exercises