Physics 203 College Physics I Fall 2012

1. Physics 203College Physics IFall 2012 S. A. Yost Chapters 3 – 4 Motion in 2 Dimensions – Part 3 Newton’s Laws – Part 1

2. Today’s Topics • Review and Problems in Projectile Motion • Newton’s Laws – Begin Chapter 4. • I assigned the first 5 sections as reading for today. We will go over the concepts now, and look at detailed situations after the exam.

3. Thursday’s Exam • The exam will be on paper, but bring your clickers for a survey which will precede the exam and be used to help interpret its results. • The exam will be a mixture of conceptual questions and problems, spanning chapters 1 through 3. • Chapter 1 will appear minimally, since few concepts had been introduced yet.

4. Quiz: Battleship • A battleship simultaneously fires shells at ships A and B. The shells follow the trajectories shown. Which ship is hit first? A or B? • Answer C if they are hit simultaneously, D if it can’t be determined based on this information. • A • B

5. Quiz: Dropping a Package • A package is dropped (not thrown) from a helicopter flying over a field. Which trajectory does the package take? Select A, B, C, D, or E.

6. Quiz: Water Balloon • If a boy aims a water balloon directly at someone in a tree, and the person in the tree lets go at the instant the balloon is launched, does it (A) hit him, (B) pass above him, or (C) pass below him?

7. Google’s Trebuchet The trebuchet was an ancient weapon that used gravity and a sling to throw a projectile. In February, 2011, Google built a demonstration trebuchet that launched watermelons, bags of flour, etc. at a “map pin” 76 mdown the parade ground. If the projectile was launched upward at 45ofrom a height of 4.0 m, at what speed should the watermelon leave the sling to hit the target?

8. What is a Force? • The forces we experience come in two categories: contact forces, and forces at a distance. • Gravity is an example of a force acting at a distance. Gravity acts between objects with mass. • Electrostatic force also acts at a distance, between charged objects. • Contact forces between objects are really the result of the electrostatic repulsion between electrons in atoms as they come close together.

9. Reference Frames • Areference frame refers to a coordinate system tied to an observer, in which the positions and velocities of particles can be measured. • Often, we think of reference frames as being at rest, but they don’t have to be: they could be tied to some moving object. • This is usually the case: after all, the earth moves! So does the sun… and the galaxy, etc. The whole universe is expanding.

10. Newton’s First Law • If an object does not interact with any other object, there exist reference frames in which the object has zero acceleration. • Such a reference frame is called an inertial frame. • In an inertial frame, an isolated object moves with a constant velocity. • Any frame moving at a constant velocity with respect to an inertial frame is also inertial.

11. Mass and Inertia • A non-interacting object experiences no acceleration and feels no forces. • If an object interacts, it feels forces, which influence its motion. • How much the motion is influenced by the forces depends on the object’s mass, which is a measure of its inertia, or resistance to acceleration. • The physical use of mass as a measure of inertia distinguishes it from its common usage, as a measure of weight. An object still has inertia even if it is weightless.

12. Newton’s Second Law • Forces act as vectors. If the vector sum of forces on an object is zero, the object experiences no acceleration. • If the total force vector acting on an object is F, then the acceleration of the object is determined by the net force and the object’s mass: • F = ma • Conversely, if the forces on an object balance, so that the net force is zero, it has no acceleration, and moves in a straight line at constant speed. → → →

13. Newton’s Third Law • All interactions occur in pairs. Forces always exist between a pair of objects. • If object 1 acts on object 2 with a force F21, then object 2 acts on object 1 with a force F12that is equal in magnitude and opposite in direction: • F21 = – F12. • Unlike the second law, this holds in any reference frame, intertial or not, regardless of any motion. → → → →

14. Car on the Highway • A car is accelerating onto the highway. • What force is responsible for this? • Friction between the tires and road. F F

15. Car on the Highway • As you accelerate, coffee cup slides backwards off the dashboard. • What force is responsible for this? • None: without friction, the cup would maintain a constant velocity while the car accelerates around it. • The coffee cup does accelerate backward relative to the car, but the car is a non-inertial reference frame, so no force is responsible for this acceleration.

16. Push and Fall Newton’s Third Law Mike pushes Johnny with a force of strength F and Johnny falls. The force Johnny exerts on Mike in the process must be A) less than F B) greater than F C) equal to F FMJ Mike pushes → F FJM Johnny falls → FMJ → → = –FJM

17. Units, Weight • Forces are measured in Newtons. • Weights are forces, and can be given in units of Newtons. It is incorrect to measure weights in kg, because this is a mass, not a force. • The weight of a mass m is W = mg. • 1 kg weighs 9.8 Non Earth. • The units follow from Newton’s 2nd Law: • 1 N = 1 kg m/s2

18. Units, Weight • Technically,poundsare a unit of weight, but are commonly used to measure mass on Earth. • The correct English unit of mass is called the slug, which weighs about 32 lb on Earth. The English pound is1 lb = 1 slug ∙ ft/s2. • 1 kg weighs2.20 lbon Earth, but this would be different elsewhere. The weight of 1kg on Earth is 9.8 N, so 1 lb = 9.8 N / 2.20 = 4.45 N(anywhere). • Roughly, a Newton’s about a quarter pound.

19. Weight and Normal Force If you are standing on a floor, the floor pushes up on you with a force opposite your weight to prevent you from falling through the floor. The perpendicular component of the contact force between two objects is called the normal force. (Here, “normal” means “perpendicular”, not “ordinary”.) N W N+ W = 0

20. Weight and Normal Force Are the weight and normal force an interaction pair, which must be equal and opposite by the third law? No: The normal force is between the person and the floor, while gravity is between the person and the Earth. N W N+ W = 0

21. Weight and Normal Force If you stand on a scale, what force does a scale measure? (N or W) It measures the normal force between you and the scale. This equals the weight by Newton’s second law – provided you are in an inertial reference frame. N W N+ W = 0

22. Weight in an Elevator a = 2.2 m/s2 An elevator accelerates upward at 2.2 m/s2. What does the passenger apparently weigh, as measured by the scale in the elevator, if his mass is 100 kg?

23. Weight in an Elevator a = 2.2 m/s2 A net force on the passenger causes the upward acceleration: F = N – W = ma. W = mg. N = ma + W = m(a+g) = (100 kg)(12.0 m/s2) = 1200 N. N W

24. Rocket at Rest A rocket on earth is at rest. Gravity is pulling down on the rocket with the weight of the rocket. • With what gravitational force does the rocket pull on the Earth? The rocket pulls up on the earth with a force equal to its weight. These are an interaction pair. FRE= W FER=-W

25. Rocket at Rest A rocket on earth is at rest. • What is the net force on the rocket? The net force is zero. • What force balances the rocket’s weight? The normal forceof the earth pushing on the rocket balances its weight. FRE= W N

26. Accelerating Rocket a After the rocket takes off, the engines continue to produce thrust as it accelerates upward into space. What is the force of the earth on the rocket now? • It is the weight of the rocket (which will become gradually less as it rises.) Fthrust FRE=W

27. Accelerating Rocket a What is the force of the rocket on the earth now that it is in space? • It is still the gravitational force of the rocket pulling upward on the earth, which equals the weight of the rocket in magnitude. Fthrust FRE=W FER=-W

28. Accelerating Rocket What is the rocket pushing against to create its thrust ? It has to be interacting with something. The rocket engines expel exhaust gases backwards with a force – Fthrust. The reaction force to expelling the exhaust gases accelerates the rocket forward. Fthrust

29. Tension • Pulling on a rope applies tension. The force always acts along the rope if it is free to bend.

30. Measuring Tension • The magnitude of the tension in the rope shown is the magnitude of the force F pulling on it, which is also what would be reading on the balance.. -F F

31. Example: Gymnast on Rings What is the tension in each rope supporting a 150 lb gymnast if they make the angle of q relative to horizontal? Evaluate the tension at q = 30o. T1 T2 Fg