Be on time Switch off mobile phones. Put away laptops. Being present = Participating actively

A couple of house rules Be on time Switch off mobile phones Put away laptops Being present = Participating actively http://www.phys.tue.nl/nfcmr/natuur/collegenatuur.html

LEARNING GOALS What the concept of force means in physics, and why forces are vectors. The significance of the net force on an object, and what happens when the net force is zero. The relationship among the net force on an object, the object s mass, and its acceleration. How the forces that two bodies exert on each other are related. 3

Problem Time to fall 1 m? 1/2 gt 2 =1 t=0.45 sec 560 gr 1 meter 1) < 0.45 sec 2) 0.45 sec 3) > 0.45 sec 4) do not know 550 gr

Newton Dynamics Origin of motion (Newton s laws) 5

Force In everyday language, a force is a push or a pull. Better definition: A force is an interaction between two bodies or between a body and its environment 6

Normal force Normal Force A solid object resists the action of another force which compresses it with what we call the normal force. The normal force always acts outward and perpendicular to the surface of the compressed object. The symbol for the normal force is n. 8

Normal force The normal force is always perpendicular to the surface that produces it. 9

Contact/long distance force Contact force normal force friction Long distance force gravity weight: mg electro-magnetic 10

Force Force is measured with a spring balance: vector property 12

Force = vector A force has a magnitude and a direction and can be decomposed in components F F ˆi F ˆj F kˆ x y z 13

Combining Forces Forces add vectorially. F F F F net n 1 2 i 1 i 14

Clicker Question 1 Two forces are exerted on an object. Which third force would make the net force point to the left? (1) (2) (3) (4) 15/29

BE SMART! Wiggle else force twice Choose x and Y axis along the slope 16

Newton s First law A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration v For "moving forward" is no cause needed. But rather to hold law of inertia Measure of inertia: mass 17

Mass Mass is the measure of how hard it is to change an object s velocity. Mass can also be thought of as a measure of the quantity of matter in an object or the quantity of inertia possessed by the object. One liter of water has a mass of 1 kg. 18

ESA 19

ALSO IN ROTATION 22

HOWEVER : THINK OF OBSERVER POSITION observer on table (accelerating frame) observer on ground 23

HOWEVER : THINK OF OBSERVER POSITION observer on table (accelerating frame) observer on ground FORCE NO FORCE Newton only valid: NO acceleration INERTIAL FRAME OF REFEENCE 24

First law of Newton always valid? Blue coordinate system: When the car is accelerating, the speed of the skaters seem to change (= also acceleration) Is there a net force? Red coordinate system Skater has constant speed (=zero) No Force! 25

Inertia If no force acts on an object, an inertial reference frame is any frame in which there is no acceleration on an the object. In (a) the plane is flying horizontally at constant speed, and the tennis ball does not move horizontally. In (b) the pilot suddenly opens the throttle and the plane rapidly gains speed, so that the tennis ball accelerates toward the back of the plane. Inertia is the tendency of mass to resist acceleration, so that a force must be supplied to overcome inertia and produce acceleration. 26

Inertial frame Any frame which moves with constant velocity relative to an inertial frame, is also an inertial frame First law of Newton valid in any inertial frame The earth is an inertial frame? (rotation earth + earth around sun) 27

Rotation earth around axis (R = 6.38 10 6 m) Rotation earth around sun (R = 1.5 10 11 m) Compare this acceleration with gravity g 1. Radius earth R = 6.38 10 6 m, T = 24 uur, so speed at equator v = 2 R/T, a = v 2 /R, a = 0.034 m/s 2 = 3.4 10-3 g 2. Beam orbit sun-earth R = 1.5 10 11 m, T=1 year, a = 5.91 10-3 m/s 2 = 5.9 10-4 g Conclusie: The earth is an inertial frame 28

Inertial frame/newtons s first law You are standing in an elevator that moves downward with constant speed. How large is the normal force (the force that the floor of the elevator exerts on you)? 1. Larger than the gravity working on you 2. Equal than the gravity working on you 3. Smaller than the gravity working on you 4. Depends on the speed Answer: 2. Sum of the forces (net force) must be zero, because moves at constant speed. So W = N

Newton s Second law If a net external force acts on a body, the body accelerates. The direction of accelaration is the same as the direction of the net force The net force vector is equal to the mass of the object times its acceleration 30

Car stopping What is the net force needed for a car of 1500 kg driving at a speed of 100 km / h driving to stop within a distance of 55 m? Answer.: 2 2 v v a x x 0 0 2 ( ) hence a = -7.1 m/s 2. So net force: F ma 1.1 10 4 N. 31

Gravitation: weight w=mg Same : spring balance 1 kg 1 kg

Weight is equal to the force of gravity Gravity ( w) works always! On earth: by the attraction of the earth The weight (w) depends on the acceleration due to gravity earth: g a = 9.81 m/s 2 ; moon: g m = 1.63 m/s 2 The mass is constant for an object = equal everywhere 33

Newton s laws A woman pulls a crate of 6.0 kg, which via a rope is connected to another crate of 4.0 kg. The massless rope remains tight. Compared with the 6.0 kg crate, the 4.0 kg crate: 1. experiences the same net force, and has the same acceleration 2. experiences a smaller net force and has the same acceleration 3. experiencies the same net force and has smaller acceleration 4. experiences a smaller net force and has smaller acceleration Answer: 2. The acceleration is the same, but the mass is smaller, so the net force is smaller (2e Law).

Newton s laws Consider a person in an elevator that accelerates upward. The upward normal force that the floor of the elevator on the person is exercising, 1. is greather than 2. equal to 3. Smaller than... the weight (= gravity) of the person. Answer: 1. To accelerate upwards a net force must act on the person, which is directed upwards: N W > 0 => N>W

Newton s Third law If body A exerts a force on body B (an action), then body B exerts a force on body A (a reaction). These two forces have the same magnitude but are opposite in direction F F action reaction These forces act on different bodies. 36

Saturn V Apollo rockets Height : 110 m Diameter: 10 m Mass: 2,800,000 kg 41

Question An apollo 2,800,000kg rocket accelerates upward at a rate of 3.0m/s 2. Find the force exerted by the engines. Hint: Don't forget gravity. From the diagram we see that in order for the rocket to accelerate upward it must at least counteract the force of gravity. F net = F Engine -F gravity F Engine = F net + F gravity F Engine = ma + mg This means that the force of the engine is F = m(a+g) = 28,000,000(3.0+9.8) = 35,840,000N. 42

Example: Comparing Tensions Blocks A and B are connected by String 2 and pulled across a frictionless surface by String 1. The mass of B is larger than the mass of A. Is the tension in String 2 smaller, equal, or larger than the tension in String 1? The blocks must be accelerating to the right, because there is a net force in that direction. We relate the string tensions on A and B due to String 2: T A on B =T B on A (F A net ) x =T 1 -T B on A = T 1 -T 2 = m A a Ax so T 1 = T 2 +m A a Ax Therefore, T 1 >T 2. 43

Free body diagram Free body diagrams show which forces act on an object Control question: What (other!) object causing the force (Which reaction force is part of it). Method of free body diagrams: very important! 44

Free body diagram Free-body diagrams method: A free-body diagram shows every force acting on an object. To draw a free-body diagram: Sketch the forces Isolate the object of interest Choose a convenient coordinate system Resolve the forces into components Apply Newton s second law to each coordinate direction 45

Example of a free-body diagram: 46

Normal force The normal force is the force exerted by a surface on an object. 47

EXAMPLE: Free body diagram 48

Free body diagram y x 49

Free body diagram F N Floor on block y F z Gravity on block x 50

Free body diagram F N Floor on block y Rope on block F w Friction of floor on block F z a Gravity on block F t x 51

Free body diagram F N Floor on block y Rope on block F w Friction of floor on block F z a Gravity on block F t x Fx m ax m a x = F t -F w F m a F m a y y 0 = F z -F N 52

Free body diagram (equilibrium) The engine of a car is suspended by chains, as can be seen in the figure. What forces must at least occur in a drawing of the free body diagram of the engine. 1. Tension T 1 2. Tension T 2 3. Tension T 3 4. All three Answer: 1. Only T 1 works directly on the block (besides of course the gravity)

Free body diagram (equilibrium) Equilibrium F = 0, Two dimensions F x = 0 en F y = 0 54

A crate on an inclined plane: tension in rope rope α 55

A crate on an inclined plane α w 56

A crate on an inclined plane n w cos α α w 57

A crate on an inclined plane n T w sin α w cos α α w Check: α = 0 T=0 α = 90 T=w 58

Pulleys and Ropes An ideal pulley is one that simply changes the direction of the tension: 59

Pulleys Massless String Approximation Strings and ropes often pass over pulleys that change the direction of the tension. In principle, the friction and inertia in the pulley could modify the transmitted tension. Therefore, it is conventional to assume that such pulleys are massless and frictionless. Massless and Frictionless Pulley Approximation 60

Free body diagram (acceleration) EA trolley with weight w 1 accelerates upwards along an inclined plane, after the bucket with weight w 2 is released. The inclined plane is frictionless. Which figure shows the correct free body diagram for the cart? n n n T T T m 1 a m 1 a w 1 w 1 w 1 1. 2. 3. Answer 3.

problem A bucket of water 4.8kg is accelerated upward by a rope with a breaking strength of 75N. Find the maximum acceleration that the rope does not break identify what should we calculate? what laws can we use? 1st, 2nd, 3rd law? Are there are other relationships a constant, a = dv /dt set up Make free body diagram Indentify action-reaction F execute Translate in to set of equations (calculus) a evaluate Does it make any sense? 62

problem A bucket of water 4.8kg is accelerated upward by a rope with a breaking strength of 75N. Find the maximum acceleration that the rope does not break set up F rope on bucket a mg execute ma = F te -mg a = F/m g < 75/4.8-9.8 = 5.8 m/s 2 63

problem You raise a chain with a force of 12N. The chain consists of three rings of 300g each. Determine A) acceleration of the upper ring? B) force of the upper ring on the middle identify what should we calculate? set up execute evaluate what laws can we use? 1st, 2nd, 3rd law? Are there are other relationships a constant, a = dv /dt Make free body diagram Indentify action-reaction Translate in to set of equations (calculus) F Does it make any sense? 64

F F 21 F 32 F F a a a a m 1 F 21 m 1 g F 32 m 2 g ma 1 F mg 1 F21 m2a F21 m2 g F32 ma F mg 3 32 3 1 2 3 1 2 3 m 3 g ( m m m ) a F ( m m m ) g a (m 1 +m 2 +m 3 )g F g m m 2 m 3 3.5m/s 65 2

F 21 F 32 F 21 F a a a m 1 F 32 m 2 g m 3 g (m 2 +m 3 )g m 2 m2a F21 m2 g F32 ma F mg 3 32 3 m 3 ( m m ) a F ( m m ) g 2 3 21 2 3 F ( m m )( a g) 8.0N 21 2 3 66

Problem Time to fall 1 m? 1/2 gt 2 =1 t=0.45 sec 560 gr 1 meter 1) < 0.45 sec 2) 0.45 sec 3) > 0.45 sec 4) do not know 550 gr

Special effects: ATWOOD Machine T T T a a a a m 2 g m 1 g F T m g ma 1, x 1 1 m 2 g F mg T ma 2, x 2 2, T m g m a T T m ( g a) m ( g a) 1 2 m 1 g m m a g m m 2 1 2 1 a=0.009 g 1/2 0.009 gt 2 =1 t=10 x0.45 sec 69

Circular motion and net force 70

Circular motion and net force Which direction will the ball move after the rope is cut? 1. To the right 2. Right front 3. Straight on 4. Left front Answer: 3. In the horizontal plane no force is acting on the ball

Circular motion and net force Free body diagram shows only one force The ball accelerates, so apply the second law of Newton After breaking rope, T =0, so net force is zero First law of Newton: ball moves with constant speed 72

Examining a misnomer People have adopted the popculture use of centrifugal force but it really results from reference frames. It is fictional and results from a car turning while a person continues in straight-line motion (for example). 73

Summary 1 th law: inertia F 0 v constant 2nd law: acceleration F m a 3th law: action = -reaction F A B F B A Free body diagram 74

Drawing a Free Body Diagram Identify all forces acting on the object. Draw a coordinate system. Use the axes defined in your pictorial representation. If those axes are tilted, for motion along an incline, then the axes of the free-body diagram should be similarly tilted. Represent the object as a dot at the origin of the coordinate axes. This is the particle model. Draw vectors representing each of the identified forces. Be sure to label each force vector. Draw and label the net force vector F net. Draw this vector beside the diagram, not on the particle. Or, if appropriate, write F. net 0 Then check that F points in the same direction as the net acceleration vector a on your motion diagram. 75

Examination question

Summary 79

Summary 80

READY 81