1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 11-12

2. Dynamics Connection between force and motion The concept of force gives us a quantitative description of the interaction between two bodies or between a body and its environment

3. Gravitational force Force exerted by a spring: Hooke’s law: If spring is stretched or compressed by some small amount it exerted a force which is linearly proportional to the amount of stretching or compressing. The constant of proportionality is called the spring constant - is deviation from the natural length Normal force

4. The force resisting the pull of the spring – friction There is some maximum value the friction force can achieve, and once we apply a force greater than this maximum there is a net force on the object, so it accelerates. The maximum of the force of friction varied linearly with the amount that the block pushes on the table.  - coefficient of friction, is the vertical force exerted by the block on the table The friction force only exists when there is another force trying to move an object

5. 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!

6. 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?

7. 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

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

9. 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.

10. 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

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

12. 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

13. Quiz

14. 2 nd Law From experiments we know: 1.Force is a vector 2.The direction of acceleration vector is the same as the direction of the force vector 3.The magnitude of the force and acceleration are related by a constant which depends on number of blocks involved.

15. 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.

16. 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

17.  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?

18. 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

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

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

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

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

25. 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

26. 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!

27. 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?

29. 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

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