1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 11

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

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

5. 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.

6. 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

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

8. Quiz

9. 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

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

11. Newton’s second law The vector acceleration of an object is in the same direction as the vector force applied to the object and the magnitudes are related by a constant called the mass of the object.

12. A Recipe for Solving Problems 1.Sketch Isolate the body (only external forces but not forces that one part of the object exert on another part) 2. Write down 2 nd Newton’s law Choose a coordinate system Write 2 nd Newton’s law in component form: 3. Solve for acceleration

13. Units of Force British system: units of mass: units of force: One pound is 0.4536 kg One pound is the weight of 0.4536 kg on the Earth

14. Units are important! The Mars Climate Orbiter was part of missions conducted by NASA. US$327.6 million mission The craft ended up with a trajectory 170 km closer to Mars than planned Reason of the failure: CONFUSION IN UNITS! Thrust information was sent in pounds instead of Newtons!

15.  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?

16. What is the normal force? What is the velocity of the block when it reaches the bottom? H No friction:  =0

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

18. 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!

19. 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?

20. 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

21. 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?

23. A block of mass 20 kg is pushed against a vertical surface as shown. The coefficient of friction between the surface and the block is 0.2. If θ=30 0, what is the minimum magnitude of P to hold the block still? θ P

24. Have a great day! Reading: Chapters 5,6 Hw: Problems 1, 2, 3, 4, 6 and exercises 1, 4, 5, 6, 9