WHAT DO OBJECTS DO WHEN NO FORCE IS

WHAT DO OBJECTS DO WHEN NO FORCE IS ACTING ON THEM ? ? ? Aristotle (384 -322 B. C. ) : of CELESTIAL objects (Moon, planets, stars, Sun) was circular - without beginning or end. of TERRESTRIAL bodies (apple, smoke, you) was for light things to rise up and heavy things to fall objects would seek their natural resting places: apple on the ground and smoke high in the air like the clouds. no need for gravity to explain this motion – it is JUST NATURAL – what a life for physics student!!!! was imposed motion – result of forces that pushed or pulled. Important: violent motion had an external cause, it was not natural to the objects

THOUGHT FOR NEARLY 2000 YEARS: IF AN OBJECT WAS MOVING, IT IS AGAINST ITS NATURE AND THE FORCE OF SOME KIND WAS RESPONSIBLE. NO FORCE – NO MOTION, No wonder that most thinkers before the 16 th century consider it obvious that the Earth must be in its natural resting place and assumed that the force large enough to move it was unthinkable, it was clear that Earth did not move. – THE CENTER OF UNIVERSE And in this intellectual climate of the 15 th century Nicolaus Copernicus (14731543) formulated, in secret to escape persecution, his famous HELIOCENTRIC THEORY – idea that was extremely controversial at the time - the Earth is just a small planet and together with other planets circle around Sun. Only in the final days of his life he sent his ideas to the printer. The first copy of his work, De Revolutionibus, reached him on the day of his death.

One of his most outspoken supporters was Galileo Galilei, the foremost scientist of late -Renaissance Italy. It took the genius of Galileo to claim that NO FORCE is needed to keep an object in the motion (straight-line, constant speed) Galileo argued (brainstorm – just pure thought – no experimental proof) that forces only CHANGE THE MOTION Left alone things would travel in a straight line with constant speed forever. It is the force of friction that slows them down. Aristotle: It is the nature of the ball to come to rest. Galileo: In the absence of friction the ball would keep on moving. No force needed to maintain the motion. The force changes the motion – velocity. Every object resists change to its state of motion/velocity. To change it, the force must act on it. We call this resistance INERTIA. Galileo’s findings about motion and his concept of inertia discredited Aristotle’s theory of motion. So why in the world do we STILL sometimes think the same way? ? ?

On Christmas day in the year Galileo died Isaac Newton (1642 -1727) was born. By the age of 24 he gave the world his famous three laws of motion.

Before we talk about force, let us introduce inertia, mass and weight.

Inertia is resistance an object has to a change of velocity. • sort of laziness (inerzia – laziness in Italian) Mass is numerical measure of the inertia of a body unit: 1 kg • more mass – harder change of velocity is a measure of the amount of matter in the object • depends only on the number and kind of atoms in it. • doesn’t depend on the location of the object • If the object has mass of 1 kg here on earth it would have the mass of 1 kg on the moon, but it would weigh only one-sixth as much. Weight is the gravitational force acting on an object. • acting straight down toward the center of the earth (moon …) • depends on the location of the object. • depends on its mass and acceleration due to gravity: W = mg N unit: 1

All forces result from interactions between objects. To have a force, you have to have 2 objects - one object pushes, the other gets pushed. FORCE is an interaction between two objects involving a push or a pull. “ FORCE is an influence on an object that causes the object to accelerate. Forces are vector quantities, having both direction and magnitude. unit: (F) = Newton (N), 1 N is the force that causes a 1 -kg object to accelerate 1 m/s 2.

The net force – resultant force is the vector sum of all forces acting on ONE object. Fnet or ΣF the object accelerates as if only one force – net force is applied Applied forces Net force

Galileo’s Law of inertia so, if Fnet = 0, a = 0 no change in velocity, then An object continues in motion in a straight line at constant speed or at rest unless acted upon by a net external force. " "How many ways can you state Newton's First Law? "

Translational equilibrium Definition: If the net force acting on an object is zero, the speed and direction of the motion will not change (the object won’t accelerate). If it was at rest it will stay at rest, and if it was in motion it will continue the motion with constant velocity (in the straight line at constant speed). We say the object is in (TRANSLATIONAL) EQUILIBRIUM.

how to apply concept of translational equilibrium: 8 N 1. Two forces are acting on a body. Describe the motion of the body. Since the net force on this body is zero, it is in equilibrium: - which means that the object is not accelerating - the body is either at rest, or is moving with a constant velocity 2. object is moving at 3 m/s in a straight line. 8 N 8 N Two forces are acting on it. Find Since velocity is constant, the body is in translational equilibrium: - which means that the object’s acceleration is zero - therefore net force is zero ● F = 8 N, 00 equilibrium math: if net F = 0 then a = 0, and velocity is constant or zero if velocity is constant or zero, then a = 0, and net

Six force are acting on an object. What can you tell about the motion of that object? Is it at rest? Is it moving? If it is moving, how?

The tendency of moving objects to continue in motion can have very unpleasant consequences. Seat belts: Passenger and the vehicle share the same destiny. Straps provide the force for accelerated and decelerated motion for passengers too. No seat belts: The passengers maintain their state of motion assuming a negligible friction between the passengers and the seats. The passengers can become projectiles and continue in projectile-like motion.

In a car accident, the safest place to be is in the car; yet in a motorcycle accident, the worst place to be is on the motorcycle. Car: Wear your seat belt. Remember it's the law - the law of inertia. Law of inertia would safe you from sharing the fate of the motorcycle itself.

No functioning straps: the ladder in motion would continue in motion. Assuming a negligible friction between the truck and the ladder, the ladder would slide off the top becoming a projectile. You are driving at the same speed as a huge truck behind you. You apply the brakes. A huge truck behind you applies the brakes too, but has more inertia. Lazy thing. And then Bang!!!

A car is turning left not changing the speed. But it is still changing velocity. Imagine a basket full of lazy strawberries in that car sitting on the seat. It tends to stay in the same state of the motion. If you don’t support that basket somehow, it will simply continue in the straight line. For the small speeds friction force is usually strong enough to keep the basket in place. When the car makes a turn, the passengers tend to continue in their straight line path. This straight line motion continues until the presence of a side door or another passenger pushes upon the passenger in order to accelerate him/her towards the center of the turn. The force experienced by the passenger is an inward force; without it, the passenger would slide out of the car.

The acceleration of an object produced by a net force on that object is directly proportional to the net force applied, and inversely proportional to the mass of the object. Direction of the acceleration is in the direction of the net force, greater mass – greater inertia (laziness) – smaller acceleration more force – greater acceleration If net force is zero, acceleration is zero, velocity is constant (or zero). The object is in translational equilibrium.

YOU CAN’T TOUCH WITHOUT BEING TOUCHED Whenever object A exerts a force on object B, object B exerts an equal in magnitude and opposite in direction force on object A. In every interaction, the forces always occur only in pairs, BUT these forces act on two different bodies. Common definition: - to every action there is an equal and opposite reaction is very dangerous, so please do not use it. It is not defined what is action and what is reaction, so it looks as if we were talking about one body, but that’s not true. These forces act on different bodies.

You push the water backward, the water pushes you forward. action: tire pushes road reaction: road pushes tire action: foot pushes the ground reaction: the ground pushes the foot that propels the turtle forward action: cannon pushes the cannonball reaction: cannonball pushes the cannon (recoil) The same force F (opposite direction), BUT cannonball: cannon: = Fm = F a a m action: earth attracts ball a = F/m = 9. 80 m/s 2 reaction: ball attracts earth a. E = F/ME ≈ 0

Koka, the clever horse, taught physics by Mrs. Radja says: You taught me Newton's third law: to every action there is an equal and opposite reaction. It says that if I pull on the wagon, the wagon pulls me back. If these two forces are equal and opposite, they will cancel, so that the net force is zero, right? So the wagon can never move! Since it is at rest, it must always remain at rest! Get over here and unhitch me, since I have just proven that Newton's law says that it is impossible for a horse to pull a wagon! Please help me! Why don’t action and reaction forces cancel? Should I find myself a less educated horse, or should I teach better?

Only the forces that act on the same object cancel. Koka: when the ground pushes forward on the horse harder than the cart pulls backward Koka accelerate forward. (Fnet = F 1’ – F 2’ > 0) Cart : accelerates forward when horse force is greater the frictional force When we want to find acceleration of one body we have to find all forces acting on that body.

Forces between roller-skaters If one skater pushes another, they both feel a force. The forces must be equal and opposite, but the acceleration will be different since they have different masses. The person with a smaller mass will gain the greater velocity.

A roller-skater pushes off from a wall The force on the girl causes her to accelerate backwards. The mass of the wall is so large compared to the girl’s mass that the force on it does not effectively cause any acceleration.

It looks unbelievable but it is true. when they clinch forces are equal – you would expect that when they clinch forces are equal – would you expect that?

again, the same force but different acceleration Sudden acceleration can kill Our organs are not firmly attached to anything. When head is hit it gains acceleration. But the brain was not hit. It continues with the same velocity. Skull and brain crash!!!!!

again, the same force but different acceleration

Tension: the force that the end of the rope exerts on whatever is attached to it. Direction of the force is along the rope. T 2 T 1 physics T 2

That’s why normal force is always perpendicular (normal) to the surfaces in contact. The normal force results from strong repulsive electromagnetic force between electrons of two bodies. The atoms in the surface are compressed microscopically to create the normal force. The surface deforms slightly and produces a reaction force equal to the force pressing the object into the surface.

Existence: by evidence – object is not accelerating in vertical direction, therefore, the vertical net force must be zero Fn Fn Fn F F mg mg mg For an object sitting on a If there is a force F trying to If there is push down lift up the object, it helps the force F horizontal surface, the normal force – the clever – the desk has to exert normal force is equal to the desk doesn’t need to exert so more force weight of the object. much force Fn = mg Fnet = ma = 0 Fn + F = mg Fn = mg - F Fnet = ma = 0 Fn = mg + F If the desk can not exert enough force it will break

Friction force Ffr Friction is a force that is created whenever two surfaces move or try to move across each other. Friction always opposes the motion or attempted motion of one surface across another surface. Friction is dependent on the texture/roughness of both surfaces. Friction acts parallel to surface in direction opposed to intended motion. Friction is also dependent on the force which presses the surfaces together, normal force. Fn pulling force Ffr = m Fn mg coefficient of proportionality μ is called coefficient of friction m has no units it is a measure of surface-to-surface roughness depends on characteristics of both surfaces different values for static and kinetic coefficient of friction (tables). kinetic μ is smaller than static μ. You probably noticed that once you moved something from rest it becomes easier to push around.

surface-on-surface μs μk hook velcro-on-fuzzy velcro >6. 0 >5. 9 avg tire-on-dry pavement 0. 9 0. 8 grooved tire-on-wet pavement 0. 8 0. 7 glass-on-glass 0. 9 0. 4 metal-on-metal (dry) 0. 6 0. 4 smooth tire-on-wet pavement 0. 5 0. 4 metal-on-metal (lubricated) 0. 1 0. 05 steel-on-ice 0. 1 0. 05 steel-on-Teflon 0. 05 You should keep in mind that it isn't possible to give accurate values for the coefficient of frictions due to changing surface smoothness. For example, not all pieces of metal have the same surface smoothness. Some that are highly polished may be more slippery than others that are pitted or scratched. These values are just meant to give you the approximate values.

Origin of friction : 1. Mechanical interlocking of "rough" surfaces – teeth on the surfaces 2. Microscopic level – On an atomic scale, few surfaces are very smooth. Bumps far smaller then we can see loom like mountains to an atom. At the points of direct molecular contact, electrons become confused. They forget which object they belong to, and wind up trying to orbit nuclei in molecules of both! The resulting bond is called molecular adhesion or a “cold-weld. ” Each time they form a bond between uneven surfaces, force is required to break this bond Thoughts of an electron with an identity crisis. . .

Air Drag and Terminal Velocity If a raindrops start in a cloud at a height h = 1200 m above the surface of the earth they would hit us at 340 mi/h; serious damage would result if they did. Luckily: When an object moves through air or any other fluid, the fluid exerts drag force on the moving object. The force is called. Unlike the friction between surfaces, however, this force depends upon the speed of the object, becoming larger as the speed increases. It also depends upon the size and the shape of the object and the density and kind of fluid. A falling object accelerates due to the gravitational force, mg, exerted on it by the earth. As the object accelerates, however, its speed increases and the drag on it becomes greater and greater until it is equal to the weight of the object. At this point, the net force on the falling object is zero, so it no longer accelerates. Its speed now remains constant; it is traveling at its terminal speed. Terminal speed occurs when the weight force (down) is equaled by the drag force (up).

Terminal velocity of table tennis ball is 9 m/s after approximately 10 m. A basketball has a terminal velocity of 20 m/s after approximately 47 m. ; the terminal velocity of a baseball is 42 m/s after approximately 210 m. Skiers increase their terminal velocity by decreasing the drag force. They hold their bodies in egg shape and wear smooth clothing and streamlined helmets. How do skydivers control their velocity? By changing body orientation and shape, sky divers can both increase and decrease their terminal velocity. (60 m/s after approximately 430 m) Parashoot – 5 m/s after approximately 3 m. AND THE RAINDROP? How fast is a raindrop traveling when it hits the ground? It travels at 7 m/s (17 mi/h) after falling approximately only 6 m. This is a much “kinder and gentler” speed and is far less damaging than the 340 mi/h calculated without drag.

Draw all forces that act on a parachutist. Find Fnet and acceleration for a. parachutist that has just stepped out of the airplane. Fnet = mg a=g mg a = Fnet/m = mg/m b. parachutist is falling at increasing speed. Fdrag = Fnet = mg - Fdrag a = (mg - Fdrag) /m a<g Fnet mg a = Fnet/m the speed is still increasing, and therefore air friction too until c. parachutist is traveling downward with constant velocity (terminal velocity) Fdrag Fnet = 0 = mg Fnet = 0 a=0

Forces are usually divided into two types or classes. 1. Contact forces, arising because of physical contact between objects. For example when you push on a door to open it or throw or kick a ball, you exert a contact force on the door or ball. 2. Field forces – they act (push or pull) “on distance through space” - the presence of an object effects the space around it so, and that region is called a field (for example gravitational field of the earth).

Although there are many different contact forces, they are all some form of only four different fundamental field forces existing in the nature. Contact Forces Field Forces Frictional Force Gravitational Force attraction between objects due to their masses Tension Force Normal Force Air Resistance Force – Drag Force Applied Force Spring Force Electromagnetic Force between charges Strong Nuclear Force keeps nucleus together Weak Nuclear Force arise in certain radioactive processes At the atomic level – all contact forces are result of repulsive electromagnetic forces (at very small distances) That means that objects have no actual contact, but their electric fields (outer electrons repel each other)

One of the most significant intellectual achievements in the history of thought. It is universal – it applies to all objects regardless of their location anywhere in the Universe. Every object in the universe attracts every other object. The force between two objects is proportional to their masses and inversely proportional to the square of the distance between their centers. The force acts along the line joining the two objects. r G = 6. 67 x 10 -11 Nm 2/ kg 2 – “Universal gravitational constant” the same value anywhere in the universe - very small value – no significant forces of attraction between ordinary sized objects.

The force between an object of mass m close to the Earth surface and the Earth r. E – Earth’s radius m. E – Earth’s mass. This force is commonly called weight W = mg. Now we can see that the gravitational acceleration g is a consequence of the gravitational force. Its magnitude depends on how far is the object from the center of the earth. Double the distance from the centre, r = 2 r. E , g is 4 times less, g = 2. 45 m/s 2 , and so is weight

STEPS Draw free body diagram/force diagram sketch of an object and all forces acting on that object No velocity on that diagram, no acceleration on that diagram, only object (circle or a box, and you can write mass in it) and all forces acting on that object

Second step is to find net force hird step is to apply second newton’s la

3. Identify forces that act on the system How to draw a force diagram Label them on diagram 1. Choose ONE body to be isolated decision: cart dog or the cart? dog 2. Make a simple sketch of the system – point system fr net 4. Find out the net force by adding the force vectors 5. Apply Newton’s second law

So 1. Add all vectors to get net force 2. Apply newton's second law Don’t worry, there is a way out.

Separate everything into vertical and horizontal motion

Howard, the soda jerk at Bea’s diner, slides a 0. 60 -kg root beer from the end of the counter to a thirsty customer. A force of friction of 1. 2 N brings the drink to a stop right in front of the customer. a) What is the acceleration of root beer? b) What is the coefficient of kinetic friction between the glass and the counter? c) If the glass encounters a sticky patch on the counter, will this spot have a higher or lower coefficient of friction? Vertical direction: Fn 0. 60 kg Ffr mg = 6 N c. higher Vertical acceleration = 0 Vertical net force = 0 Fn = mg = 6. 0 N Horizontal direction: Net force = friction force: Fnet = Ffr =1. 2 N Fnet = ma 1. 2 = 0. 60 a a = 2. 0 m/s 2

A boy exerts a 36 -N horizontal force as he pulls a 52 -N sled across a cement sidewalk at constant speed. What is the coefficient of kinetic friction between the sidewalk and the metal sled runners? Ignore air resistance. W = mg = 52 N m = 5. 2 kg Vertical direction: Vertical acceleration = 0 Vertical Fnet = 0 Fn = mg = 52 N

A force of 40. 0 N accelerates a 5. 0 -kg block at 6. 0 m/s 2 along a horizontal surface. a. How large is the frictional force? b. What is the coefficient of friction? m = 5. 0 kg F = 40. 0 N a = 6. 0 m/s 2 Vertical direction: a = 0, so Fnet = 0 Fn = mg = 50 N → horizontal direction: a = 6. 0 m/s 2 Fnet = ma F – Ffr = ma 40. 0 – Ffr = 30 Ffr = μ Fn Ffr = 10 N Ffr = μ Fn = 50 μ

Luke Skywalker starts to pull a sled with Princess Leia across a large ice pond with the force of 100 N at an angle of 30. 0° with the horizontal (with nails on his shoes). Find normal force and initial acceleration if the weight of sled and Princess Leia is 800 N and the friction force is 40 N. mg = 800 N m = 80 kg F = 100 N free body diagram Ffr = 40 N components vertical direction : F sin θ + Fn = mg 50 + Fn = 800 Fn = 750 N Horizontal direction: F cos θ – Ffr = ma 86. 6 – 40 = 80 a a = 0. 58 m/s 2

INCLINE

An object is on a rough incline θ. Fn Components: Ffr one parallel to the incline one perpendicular to the incline. The only force that we have to resolve into components is weight mg Fn Ffr Why? Simply because we know that acceleration perpendicular to the surface is zero, and acceleration is in the direction of the motion, parallel to incline.

Resolve vector mg into two components. Now instead of three forces, we have four forces Fn Ffr direction perpendicular to the incline: Fnet = ma = 0 Fn = mg cos θ force pressing the object into the surface is not full weight mg, but only part of it, So the normal force acting on the object is only part of full weight mg: Fn = mg cos θ If the surface is horizontal: θ = 00 → Fn = mg If the object is in free fall not pressing the surface: θ = 900 → Fn = 0

A cute bear, m = 60 kg, is sliding down an iced incline 300. The ice can support up to 550 N. Will bear fall through the ice? If the coefficient of the friction is 0. 115, what is the acceleration of the bear? Perpendicular direction: Fnet = ma a=0 Fn - mg cos θ = 0 Fn = 520 N < 550 N ice can support him, but he should not eat too much Parallel direction: Fnet = ma mg sin θ – Ffr = ma 300 – 60 = 60 a a = 4 m/s 2 Ffr = μ Fn = 60 N cute bear is speeding up!!!!

Question: How does the weight of a person in an elevator depend on the motion of that elevator? What will the scale show if the elevator is 1. at rest or moving with constant speed 2. speeding up 3. slowing down Newton’s 3. law: Force with which the person acts on the scale (reading of the scale) is equal to the normal force on the person. So, if we find normal force we know the reading of the scale, so called APPARENT WEIGHT

Let’s assume that elevator is moving upward, and let this be positive direction. 1. draw free body diagram 2. apply Newton’s 2. law : Fnet = ma + Fn + 1. elevator is at rest or moving with constant speed Fn – mg = ma = 0 → Fn = mg apparent weight = weight Fn 2. elevator is speeding up: a is positive Fn – mg = ma → Fn = mg + ma apparent weight > weight the scale would show more, and you would feel heavier Fn 3. elevator is slowing down: a is negative Fn – mg = - ma → Fn = mg - ma apparent weight < weight the scale would show less, and you would feel lighter

WHEN THERE ARE TWO BODIES YOU HAVE TO DRAW TWO BODY DIAGRAMS !!!!!!

Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, find a) the magnitude of the acceleration of each block b) Tension force on the blocks the same string – the same tension the same acceleration, except that 110 g accelerate down, and 90 g accelerate up. Fnet = ma T – mg = ma T – 0. 9 = 0. 09 a Fnet = ma mg – T= ma 1. 1 – T = 0. 11 a two equations with two unknowns T – 0. 9 = 0. 09 a 1. 1 – T = 0. 11 a 0. 09 a + 0. 9 = 1. 1 – 0. 11 a � 0. 2 a = 0. 2 a = 1 m/s 2 T = 1. 1 – 0. 11 a = 1. 1 – 0. 11(1) = 0. 99 N a is up first equation a is up second equation

A 10 -kg block is connected to a 40 -kg block as shown in the figure. The surface on which the blocks slide is frictionless. A force of 50 N pulls the blocks to the right. a) What is the magnitude of the acceleration of the 40 -kg block? b) What is the magnitude of the tension T in the rope that connects the two blocks? As these two objects are connected with the same rope, tension is the same and acceleration is the same for two objects. Fnet = ma T = 10 a 50 – T = 40 a 50 – 10 a = 40 a a = 1 m/s 2 T = 10 a = 10 N