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Newton’s Laws of Motion • The Laws of Motion are governed by three principles developed by one man…Sir Isaac Newton (16431727) Law of Inertia • Every object in motion stays in motion and any object at rest stays at rest until acted upon by an outside force. • Inertia: is the term for the property of matter that resists change in its state of motion. – Why aren’t you falling out of your seats? – Why is it so hard to push a car out of the mud? – Why is it even harder to push a cruise ship off the dock? • Objects at rest want to stay that way! Motion • Motion is a change in position relative to a frame of reference • Speed is the distance traveled in a given amount of time • Speed=distance time Objects in motion want to stay that way! Why is it harder to stop an 18-wheeler moving at 60 mph than a compact car moving at the same speed? A: 18 wheeler has more mass!!! • If no breaks were applied, would the two vehicles move forever? NO!!!!!!!!! • But I thought objects in motion wanted to stay that way??? • Friction is a force opposing motion, caused by the contact of two surfaces. Drawing Net forces 1 • The law of inertia is most commonly experienced when riding in cars and trucks. • Consider the unfortunate collision of a car with a wall. – Upon contact with the wall, an unbalanced force acts upon the car to abruptly decelerate it to rest. – Any passengers in the car will also be decelerated to rest if they are strapped to the car by seat belts. • Being strapped tightly to the car, the passengers share the same state of motion as the car. – As the car accelerates, the passengers accelerate – As the car decelerates, the passengers decelerate As the car maintains a constant speed, the passengers maintain a constant speed. But what would happen if the passengers were not wearing the seat belt? What motion would the passengers undergo if they failed to use their seat belts and the car were brought to a sudden and abrupt halt by a collision with a wall? 1 1 • If the car were to abruptly stop and the seat belts were not being worn, then the passengers in motion would continue in motion. • Assuming a negligible amount of friction between the passengers and the seats, the passengers would likely be propelled from the car and be hurled into the air. • Once they leave the car, the passengers become projectiles and continue in projectilelike motion. 1) From: The Car and The Wall http://www.geocities.com/Athens/Academy/9208/cci.html Velocity • Speed in a given direction • Velocities in the same direction combine by adding • Velocities in different directions combine by subtracting Acceleration • • • • The change in velocity Acceleration is measured in m/sec/sec or m/sec2 Formula is: (final velocity - original velocity)/time Deceleration vs. Acceleration • A decrease in velocity is deceleration or negative acceleration • A distance-time graph for acceleration is always a curve Centripetal Acceleration • Acceleration directed toward the center of circular path Law of Inertia An object’s orientation can change it’s inertia by altering its center of gravity! Center of Gravity: the average location of the weight of an object. While all objects exhibit the property of inertia, all objects do not have the same inertia! Think about it… is it easier to kick an empty can or a full can? Inertia is affected by mass. Mass: is the quantity of matter in an object. **Mass is not weight!** Weight: is a measure of an object’s gravitational attraction to earth. Weight can change. Mass does not! Why is it easier to kick an empty can than a full can? The full can had more mass and therefore, more inertia. In other words, the more mass an object has, the more it will resist change in its state of motion. Newton’s 2nd Law (a.k.a.) F=mxa • The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object. • So what does this mean??? The amount of force applied to an object is equal to the mass of the object multiplied by its acceleration due to that force: F=mxa • What is acceleration? How fast something speeds up. Gravity • Gravity is a force of attraction between two bodies with mass. • Since all object have mass, all objects exert gravity on all other objects. Even you have your own gravity. • So why don’t we observe our own gravity? Because compared to the earth, our mass is very, very small…so small that our own gravity is too small to observe. • More mass = More Gravity Gravity • Gravity is a force applied to all objects by the earth. No matter what the object, the acceleration due to gravity is 9.8 m/s2. Example: A textbook has a mass of 1 kg and a piece of paper has a mass of 0.0001kg. What is the force of gravity on each of these falling objects? F = ma F= ma Ftextbook = 1kg x 9.8 m/s2 Fpaper = 0.0001kg x 9.8m/s2 Ftextbook = 9.8 N Fpaper = 0.00098 N A Newton, N, is equal to a kg m/s2 Was the force of gravity on the textbook and the paper the same? Does this mean that they should fall at the same time or not? What was the real reason that they did not fall at the same time? Air resistance works against the force of gravity. Air Resistance: Friction due to air. Because the piece of paper has more air resistance, its acceleration due to gravity is slowed. Other forces are resisted by friction. • Free Fall: falling free of air resistance or other constraints. • On earth, we do not have the luxury of experiencing free fall, but we can experience something similar… • Terminal Velocity: The point in movement where the force propelling the object forward is equal to the forces resisting the forward motion (i.e. air resistance/friction = gravity) causing the speed of the object to be constant. • Suppose that air resistance could be eliminated so neither the elephant nor the feather would experience any air drag during the course of their fall. • Which object - the elephant or the feather - will hit the ground first? • Many people are surprised by the fact that in the absence of air resistance, the elephant and the feather strike the ground at the same time. 3) From: Elephant and Feather-Air Resistance http://www.geocities.com/Athens/Academy/9208/efff.html • In the absence of air resistance, both the elephant and the feather are in a state of free-fall. That is to say, the only force acting upon the two objects is gravity. • This force of gravity is what causes both the elephant and the feather to accelerate downwards. The force of gravity experienced by an object is dependent upon the mass of that object. Why then does it hit the ground at the same time as the feather? 3 • When figuring the acceleration of object, there are two factors to consider - force and mass. • The elephant experiences a much greater force (which tends to produce large accelerations. Yet, the mass of an object resists acceleration. • The greater mass of the elephant (which tends to produce small accelerations) offsets the influence of the greater force It is the force/mass ratio which determines the acceleration.. • The greater mass of the elephant requires the greater force just to maintain the same acceleration as the feather. • We say that mass and acceleration are inversely proportional. A large mass will accelerate slowly, while a small mass will accelerate quickly with the same force. • Other forces are affected by the area the force is applied to. How does a snow shoe work? • Because your mass and the acceleration due to gravity do not change, the force you apply to the ground is the same with each step. • So why then can you walk across deep snow without sinking in a snow shoe and not in a regular boot? • The snow shoe allows the force of your step to be applied over a large surface area. • The force per unit area is a called pressure. Inertia, Gravity and Satellites 4 • Satellites require great speeds to avoid crashing! – Altitude determines it speed – a satellite in low orbit (about 800km/497mi) from the Earth is exposed to an immense amount of gravity – has to move at considerable speed to keep from crashing • Gravity is important to keep the satellite from moving off into space. 4) From: Satellite Orbits http://www.eduspace.esa.int/subtopic/default.asp?document=297 • As the satellites are in orbit outside the atmosphere there is no air resistance, and therefore, the speed of the satellite is constant. • If orbiting inside the atmosphere, the satellite must overcome air resistance (must be able to speed up when it slows down because of air resistance)4. • Satellites are both natural (the moon) and man made. Newton’s 3rd Law • Whenever one object exerts a force on a second object, the second object exerts an equal but opposite force on the first object. • Newton’s Third Law says that for every action there is an equal but opposite reaction. • There is a pair of forces acting on the two interacting objects. • The size of the forces on the first object equals the size of the force on the second object. • The direction of the force on the first object is opposite to the direction of the force on the second object. • Forces always come in pairs - equal and opposite action-reaction force pairs. Rifle has Ma Bullet is Shot Out by force from gun powder Bullet has mA • Have you ever shot a rifle and felt the kickback? Where does that come from and how does this help us explain how a rifle works? • The rifle shoots the bullet with a force and the bullet pushes the rifle back with the same force. Because the rifle has a much larger mass than the bullet, it will accelerate much less than the bullet. What about two forces in opposite directions? Me You • I hit a football and you hit a football in the opposite direction. • The two opposite forces “cancel” each other out and the ball goes nowhere. • The football will give us both a reaction force though. Work & Energy WORK WORK: It is used by physicists to measure something that is accomplished. So it results in the equation: Work = Force x displacement The symbol for work is the variable = W W=(F)(d) You must move something (d) with a force (F) to accomplish work. Is work being done? Pushing a car. Attempting to lift 2,000,000 N. Swimming in a rip current. WORK SO WHAT IF I PUSH ON A WALL THAT DOES NOT MOVE? HAVE I DONE WORK?… NO! HAVE I USED ENERGY?... YES! WHAT IS ENERGY? UH OH… another definition coming… Energy… • …is the ability to make things move The seven types of energy… • Chemical - gasoline, • Light – flash light, • Heat – burner on a stove, • Nuclear - sun, • Mechanical - car, • Sound – music on the radio, • Electrical - lightning POTENTIAL ENERGY How do you “store up energy?... There are two kinds we study… GPE - GRAVITY POTENTIAL ENERGY: If you put an object up in the air… gravity will pull it down and make it move some distance… WORK will be done… an object is moved some displacement… GPE = mgh… mg=force gravity, h=height… the heavier the object is, the more force on it, the higher it is, the further down it moves… GPE = mgh EPE - ELASTIC POTENTIAL ENERGY: This is stored in a spring or rubber band. The stronger the spring, or the further you stretch it, the more work it can do. So, the EPE=(1/2)(k)(x2) … k = how strong the spring is, and x= how far you stretch it… EPE=(1/2)(k)(x2) KINETIC ENERGY KINETIC ENERGY = KE: This is moving energy. Something that is moving will collide and crash into another object, and move it a distance,… SO, the energy that it has, will be equal to how BIG it is, m (mass), and how FAST, v (velocity), it is moving…. KE = (1/2)(m)(v2) Definitions • Kinetic Energy: the energy of motion • KE = ½ mv2 • Potential Energy: stored energy • PE = mgh A Roller Coaster A roller coaster speeds along its track. It has kinetic energy because it is moving. A Roller Coaster As it slows to a stop at the top of a hill, it has potential energy because of where it is. It has the potential to move because it is above the ground and has somewhere to go. • Substances like wood, coal, oil, and gasoline have stored energy because of their chemistry – they can burn • Stored energy is potential energy NEW FORMULAS W=(F)(d) EPE=(1/2)(k)(x2) GPE=(m)(g)(h) KE=(1/2)(m)(v2) ENERGY is what you “can do”……… WORK is what you “do do”……… and isn’t work doo-doo? Calculating Work F d m A mass is being pulled to the right by a force, F , it is moving to the right so that the displacement is d… BUT is ALL of the force, F , doing work?.... NO…. because some of the force is lifting up in the positive +y direction This means that the part of F that is pulling to the right in the +x direction is doing work, because that is the way the box is moving… Calculating Work F d m What about the other forces on the box like weight, mg, pulling down, or the F-normal, of the ground pushing up…. NO… they do NO WORK, because the box is not moving up or down…. Calculating Work F d m • What about F-friction, is it doing work?... YES… BUT WAIT… THE FRICTION FORCE IS NOT IN THE SAME DIRECTION THE BOX IS MOVING!! IT IS TO THE LEFT!! • This force is fighting the work being done by F. It is doing what we call negative work because it is being done in the OPPOSITE DIRECTION THAT THE OBJECT IS MOVING… Calculating Work F d m • FINALLY, we can find the TOTAL WORK, Wt, done on the box…. It is the positive work done by F plus the negative work done by friction Ff… Wt = W - Wf QUICK OVERVIEW ON WORK…. 1)Work equals Force x displacement… W = (F)(d) 2)Work is measured in Nm called Joules, or J 3)Work is positive if the force, F, is in the same direction as the displacement 4)Any force that pushes on the object, but does not move the object in the direction it is pushing… does NO work 5)Any force that pushes in the opposite direction that the object is moving, (especially friction), does negative work • Potential Energy can be changed into Kinetic Energy • Also Kinetic Energy can be changed into Potential Energy KE and PE are conserved! KEfinal + PEfinal = KEinitial + PEinitial Momentum and Impulse Momentum and Impulse • Momentum describes the motion of an object before and after a collision • Common sense tells us that when you collide with another object or person… HOW MUCH you feel that collision, or how much it hurts!... Depends on two things: – 1) How big the object was that hit you – 2) How fast it was going when it hit you • But this is PHYSICS: 1) MASS (in kilograms) is a measure of the object’s size, and 2) VELOCITY (in m/s) is a measure of the object’s speed • Formula for momentum is P = mv (YES… the variable P is momentum) Momentum and Impulse • Impulse is what happens during a collision… It is measured by the force during the collision… and the time, (how long), that collision occurs… • Formula for Impulse is: I = (F)(t) (I is the variable for Impulse) • There is ANOTHER way to measure Impulse … • Impulse = the change in momentum… in terms of common sense, this means that if an object’s momentum changes… you put an impulse on it • Formula for Impulse is: I = Δmv = (mvf – mvi) How does this work? • Formula I = (F)(t) = (mvf – mvi) Momentum and Impulse • CONSERVATION OF MOMENTUM: • CONSERVATION means that the momentum of ALL the objects BEFORE the collision, will EQUAL the momentum of ALL the objects AFTER the collision…so… the total momentum is NOT lost, only transferred • All right… There are TWO kinds of collisions: ELASTIC collisions, where the two objects hit and bounce apart…. Or…. INELASTIC collisions, where the two objects hit and stick together…. • Formula: for an ELASTIC COLLISION is: m1v1 m2 v2 m1v1' m2 v2' • Formula: for an INELASTIC COLLISION is: m1v1 m2 v2 (m1 m2 )v ' Work Done by a Spring • Work done by a spring is different… WHY?... Because the more you displace it, the MORE force it takes to do it… SO… you can not just multiply F x d, because F gets bigger as you stretch it…. F IS CHANGING!... OK… so how do you handle this? Work Done by a Spring • Let’s take a spring that is not stretched or compressed, we will call its length, Lo. • So Lo is how long the spring is when it is not stretched or compressed. • Look at the diagram…. x is called the deformation, it is how far you stretch or compress the spring from its original length, measured in meters, m. Work Done by a Spring • If we are going to write a formula for the work done by a spring, or the potential energy stored in a spring, we have to know HOW STRONG IS THE SPPRING? • How do you measure this? In words it is “how much force does it take to stretch or compress the spring”…. The scientist Hooke gave us a formula: F = kx • Simply, if we rearrange this formula: k = F/x…. What does this mean in words?.... • The strength of a spring, k, is measured by HOW MANY NEWTONS OF FORCE, F, it takes to stretch (or compress) a spring, divided by the AMOUNT YOU STRETCH OR COMPRESS IT, x (the deformation)… Work Done by a Spring • SO…. How much WORK is done on a spring?... Or How much ENERGY is stored in a spring?... They are the same!... • WORK on a spring, OR ENERGY stored in a spring…. Wspring = EPE (Elastic Potential Energy) = (1/2)(k)(x2) CONSERVATION OF ENERGY FORMULA 1) Is there any GPE, gravity potential energy, mgh? 2) Is there any EPE, elastic potential energy,½kx2 ? 3) Is there any KE, kinetic energy, ½mv2? KEfinal + PEfinal + EPEfinal = KEinitial + PEinitial + EPEinitial POWER • POWER… What is it? There seems to be political power, military power, personal power, and automobile engine power to mention a few…. • Physics will concern itself with mechanical power… So what is that?.... In words it means “how fast you do work”….. So the formula for power is P = W/t • Let’s see if this makes sense…. W, work is in the numerator, so if you do more work in the same amount of time, it takes more power… t, time is in the denominator, so if you do the same amount of work in less time, it takes more power… finally, if you do more work in less time, you need a lot more power! Work and Simple Machines History of Work Before engines and motors were invented, people had to do things like lifting or pushing heavy loads by hand. Using an animal could help, but what they really needed were some clever ways to either make work easier or faster. Simple Machines Ancient people invented simple machines that would help them overcome resistive forces and allow them to do the desired work against those forces. Simple Machines • A machine is a device that helps make work easier to perform by accomplishing one or more of the following functions: – transferring a force from one place to another, – changing the direction of a force, – increasing the magnitude of a force, or – increasing the distance or speed of a force. Simple Machines • The six simple machines are: – – – – – – Lever Wheel and Axle Pulley Inclined Plane Wedge Screw Mechanical Advantage • It is useful to think about a machine in terms of the input force (the force you apply) and the output force (force which is applied to the task). • When a machine takes a small input force and increases the magnitude of the output force, a mechanical advantage has been produced. Mechanical Advantage • Mechanical advantage is the ratio of output force divided by input force. If the output force is bigger than the input force, a machine has a mechanical advantage greater than one. • If a machine increases an input force of 10 pounds to an output force of 100 pounds, the machine has a mechanical advantage (MA) of 10. • In machines that increase distance instead of force, the MA is the ratio of the output distance and input distance. • MA = output/input No machine can increase both the magnitude and the distance of a force at the same time. The 3 Classes of Levers • The class of a lever is determined by the location of the effort force and the load relative to the fulcrum. First Class Lever • In a first-class lever the fulcrum is located at some point between the effort and resistance forces. – Common examples of first-class levers include crowbars, scissors, pliers, tin snips and seesaws. – A first-class lever always changes the direction of force (I.e. a downward effort force on the lever results in an upward movement of the resistance force). Fulcrum is between EF (effort) and RF (load) Effort moves farther than Resistance. Multiplies EF and changes its direction Second Class Lever • With a second-class lever, the load is located between the fulcrum and the effort force. – Common examples of second-class levers include nut crackers, wheel barrows, doors, and bottle openers. • A second-class lever does not change the direction of force. When the fulcrum is located closer to the load than to the effort force, an increase in force (mechanical advantage) results. RF (load) is between fulcrum and EF Effort moves farther than Resistance. Multiplies EF, but does not change its direction Third Class Lever • With a third-class lever, the effort force is applied between the fulcrum and the resistance force. • Examples of third-class levers include tweezers, hammers, and shovels. – A third-class lever does not change the direction of force; third-class levers always produce a gain in speed and distance and a corresponding decrease in force. EF is between fulcrum and RF (load) Does not multiply force Resistance moves farther than Effort. Multiplies the distance the effort force travels To find the MA of a lever, divide the output force by the input force, or divide the length of the resistance arm by the length of the effort arm. Wheel and Axle • The wheel and axle is a simple machine consisting of a large wheel rigidly secured to a smaller wheel or shaft, called an axle. • When either the wheel or axle turns, the other part also turns. One full revolution of either part causes one full revolution of the other part. Pulley • A pulley is said to be a fixed pulley if it does not rise or fall with the load being moved. A fixed pulley changes the direction of a force; however, it does not create a mechanical advantage. • A moveable pulley rises and falls with the load that is being moved. A single moveable pulley creates a mechanical advantage; however, it does not change the direction of a force. • The mechanical advantage of a moveable pulley is equal to the number of ropes that support the moveable pulley. • For example, below are four puly systems. If we divide the input force (the amount of force needed to • pull on the rope) into the weight we are trying to lift, we will have the mechanical advantage for the • system. The systems below have a mechanical advantage of 1, 2, 3, and 4 respectively. 100 N / 1 = 100 N 100 N / 2 = 50 N 100 N / 3 = 33.3 N 100 N / 4 = 25 N Inclined Plane • An inclined plane is an even sloping surface. The inclined plane makes it easier to move a weight from a lower to higher elevation. Inclined Plane • The mechanical advantage of an inclined plane is equal to the length of the slope divided by the height of the inclined plane. • While the inclined plane produces a mechanical advantage, it does so by increasing the distance through which the force must move. Although it takes less force for car A to get to the top of the ramp, all the cars do the same amount of work. A B C Wedge • The wedge is a modification of the inclined plane. Wedges are used as either separating or holding devices. • A wedge can either be composed of one or two inclined planes. A double wedge can be thought of as two inclined planes joined together with their sloping surfaces outward. Screw • The screw is also a modified version of the inclined plane. • While this may be somewhat difficult to visualize, it may help to think of the threads of the screw as a type of circular ramp (or inclined plane). Efficiency • We said that the input force times the distance equals the output force times distance, or: Input Force x Distance = Output Force x Distance However, some output force is lost due to friction. • The comparison of work input to work output is called efficiency. • No machine has 100 percent efficiency due to friction. Complex Machines • Complex machines are made from combining many simple machines to perform • complex tasks. A car contains many varieties of simples machines combined together to make a complex machine. A Complex Machine Electricity & Magnetism Static, Currents, Circuits Magnetic Fields & Electro Magnets Motors & Generators Electrons… • Are located on the outer edges of atoms…they can be moved. • A concentration of electrons in an atom creates a net negative charge. • If electrons are stripped away, the atom becomes positively charged. What is this electrical potential called? • Static Electricity - - - - + ++ ++ Static Electricity • The build up of an electric charge on the surface of an object. • The charge builds up but does not flow. • Static electricity is potential energy. It does not move. It is stored. Static Discharge… • Occurs when there is a loss of static electricity due to three possible things: • Friction - rubbing • Conduction – direct contact • Induction – through an electrical field (not direct contact) Electricity that moves… • Current: The flow of electrons from one place to another (symbol = I). • Measured in amperes (amps) • Kinetic energy How can we control currents? • With circuits. • Circuit: is a path for the flow of electrons. We use wires. There are 2 types of currents: • Direct Current (DC) – Where electrons flow in the same direction in a wire. • Alternating Current (AC) – electrons flow in different directions in a wire There are 2 types of circuits: • Series Circuit: the components are lined up along one path. If the circuit is broken, all components turn off. Series Circuit There are 2 types of circuits: • Parallel Circuit – there are several branching paths to the components. If the circuit is broken at any one branch, only the components on that branch will turn off. Parallel Circuit Conductors vs. Insulators • Conductors – material through which electric current flows easily. • Insulators – materials through which electric current cannot move. Examples • Conductors: –Metal –Water • Insulators: –Styrofoam –Rubber –Plastic –Paper What is Resistance (R)? • The opposition to the flow of an electric current, producing heat. • The greater the resistance, the less current gets through. • Good conductors have low resistance. • Measured in ohms (Ω). What Influences Resistance? • Material of wire – aluminum and copper have low resistance • Thickness – the thicker the wire the lower the resistance • Length – shorter wire has lower resistance • Temperature – lower temperature has lower resistance What is Voltage (V)? • The measure of energy given to the charge flowing in a circuit. • The greater the voltage, the greater the force or “pressure” that drives the charge through the circuit. Difference b/t Volts and Amps • Example – you could say that… –Amps measure how much water comes out of a hose. –Volts measure how hard the water comes out of a hose. Ohm’s Law • Voltage = Resistance x Current • V = IR Magnetism What is Magnetism? • Magnetism is the attraction of a magnet to another object. What are Magnetic Poles? • Magnets have two ends, called magnetic poles. • Magnetism is strongest at the poles of a magnet. S S N Magnetic Poles • Magnetic poles that are alike repel each other. • North repels North • South repels South • Poles that are not alike attract each other • North attracts South • South attracts North What is a Magnetic Field? • The magnetic force exerted in the region around the magnet is the magnetic field. • This allows magnets to interact without touching. What are Magnetic Field Lines? • Magnetic Field Lines spread out from one pole, curve around the magnet, and return to the other pole. S N What do atoms have to do with it? • All atoms have magnetic fields because of the charged particles inside. • Most atoms’ magnetic fields point in random directions, so they all cancel each other out. What do atoms have to do with it? • In magnetized material, all or most of the magnetic fields are arranged in the same direction. • A material that keeps its magnetism is called a permanent magnet. What do Electric Currents have to do with Magnets? • An electric current produces a magnetic field. • The direction of the current determines the direction of the magnetic field. What is an Electromagnet • An Electromagnet is a strong magnet that can be turned on and off. • It consists of a current-carrying wire wrapped around an iron core. Characteristics of Electromagnets • Strength depends on the number of coils and the size of the iron core. • The greater the number of turns the coil has the stronger the magnet will be. • The closer the coils are the stronger the magnet will be.