1. The first exam will be held on Tuesday, September 23, in room 109 Heldenfels from 7 to 9:30 p.m. Section 807 and half of section 808 (students with last names beginning from letters A through K) should come at 6:55 p.m. for an exam that starts at 7:00 and ends at 8:00 p.m. The rest of section 808 and section 809 should come at 8:10 for an exam that starts at 8:15 and ends at 9:15 p.m. Those who take the first exam cannot leave before 8 p.m. No textbook, calculators, or notes are permitted on the exam. The exam will include Chapters I through VI.

2. A Recipe for Solving Problems 1.Sketch Identify all forces acting on each body, or “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 convenient coordinate system Write 2 nd Newton’s law in component form: 4. Solve for acceleration or whatever is asked 3. Apply 3 rd Law

3. 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

4. Weight, the force of gravity, and the normal force

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

6. P

7. Friction Two types of friction: 1.Kinetic: The friction force that slows things down 2.Static: The force that makes it hard to even get things moving

8. Refrigerator If you push a refrigerator when there is no friction what happens? In the real world what happens? Especially when it’s fully loaded and on a sticky kitchen floor? –When does static friction kick in? –When does kinetic friction kick in?

9. 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.  < 1- coefficient of friction, is the normal force The friction force only exists when there is another force trying to move an object

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

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

12. 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

13.  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?

14. Box on an inclined plane A box with mass m is placed on a frictionless incline with angle  and is allowed to slide down. a)What is the normal force? b)What is the acceleration of the box?  c) What is the box velocity at the bottom of the plane? H

15. 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?

17. 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