Physics 110 - Lecture 4 - Momentum, Energy PDF

-Physics 110 - Lecture 4 - Sonia Katdare 1 MOMENTUM AND ENERGY Chapter 6, 7  Physics 110 - Lecture 4 - - Sonia Katdare 2 MOMENTUM Chapter 6  Physics 110 - Lecture 4 - - Sonia Katdare 3 Student Learning Objectives Momentum Impulse Impulse Changes Momen...

-Physics 110 - Lecture 4 - Sonia Katdare 1 MOMENTUM AND ENERGY Chapter 6, 7  Physics 110 - Lecture 4 - - Sonia Katdare 2 MOMENTUM Chapter 6  Physics 110 - Lecture 4 - - Sonia Katdare 3 Student Learning Objectives Momentum Impulse Impulse Changes Momentum Bouncing Conservation of Momentum Collisions More Complicated Collisions  Physics 110 - Lecture 4 - - Sonia Katdare 4 Momentum While mass is a great measure of inertia, there is something extra that’s important for moving objects… A fast moving ball is harder to stop than a slowly moving ball, so speed must be important. Let’s define the momentum of an object as its mass times its velocity: ⃗ = 𝑚𝑚 𝑣𝑣 𝑝𝑝 ⃗ We use the letter 𝑝𝑝 because we’ve run out of m’s!  Physics 110 - Lecture 4 - - Sonia Katdare 5 Momentum A truck rolling down a hill has more momentum than a roller skate with the same speed. But if the truck is at rest and the roller skate moves, then the skate has more momentum.  Physics 110 - Lecture 4 - - Sonia Katdare 6 Quick Question When the speed of an object is doubled, its momentum A. remains unchanged in accord with the conservation of momentum. B. doubles. C. quadruples. D. decreases.  Physics 110 - Lecture 4 - - Sonia Katdare 7 Quick Question When the speed of an object is doubled, its momentum A. remains unchanged in accord with the conservation of momentum. B. doubles. C. quadruples. D. decreases.  Physics 110 - Lecture 4 - - Sonia Katdare 8 Impulse If the momentum of an object changes, either the mass, the velocity, or both must change. We call the change in momentum the impulse delivered to the object: ⃗𝐽𝐽 = Δ𝑝𝑝 ⃗ 𝑝𝑝 To change the momentum of an object, a force must act on it for some time, so we also have ⃗𝐽𝐽 = ⃗𝐹𝐹Δ𝑡𝑡  Physics 110 - Lecture 4 - - Sonia Katdare 9 Impulse When you push with the same force for twice the time, you impart twice the impulse and produce twice the change in momentum.  Physics 110 - Lecture 4 - - Sonia Katdare 10 Impulse To increase the momentum of an object, apply the greatest force possible for as long as possible. A golfer teeing off and a baseball player trying for a home run do both of these things when they swing as hard as possible and follow through with their swing. ⃗𝐹𝐹Δ𝑡𝑡 = Δ𝑝𝑝 Σ𝐹𝐹 ⃗ = Δ(𝑚𝑚𝑣𝑣 𝑝𝑝 ⃗) 𝑣𝑣  Physics 110 - Lecture 4 - - Sonia Katdare 11 Impulse The force of impact on a golf ball varies throughout the duration of impact. A golf club that strikes a golf ball exerts zero force on the ball until it comes in contact with it. The force increases rapidly as the ball becomes distorted. The force diminishes as the ball comes up to speed and returns to its original shape. We can use the average force to solve for the impulse on an object.  Physics 110 - Lecture 4 - - Sonia Katdare 12 Impulse If the change in momentum occurs over a long time, the force of impact is small. If the change in momentum occurs over a short time, the force of impact is large.  Physics 110 - Lecture 4 - - Sonia Katdare 13 Impulse When you extend the time, you reduce the force. A padded dashboard in a car is safer than a rigid metal one. Airbags save lives. To catch a fast-moving ball, extend your hand forward and move it backward after making contact with the ball. When you jump down to the ground, bend your knees when your feet make contact with the ground to extend the time during which your momentum decreases. A wrestler thrown to the floor extends his time of hitting the mat, spreading the impulse into a series of smaller ones as his foot, knee, hip, ribs, and shoulder successively hit the mat.  Physics 110 - Lecture 4 - - Sonia Katdare 14 Quick Question When a dish falls, will the impulse be less if it lands on a carpet than if it lands on a hard floor?  Physics 110 - Lecture 4 - - Sonia Katdare 15 Quick Question When a dish falls, will the impulse be less if it lands on a carpet than if it lands on a hard floor? No, but the force will different The same initial momentum is reduced to zero in both cases. Thus, the change in momentum, and therefore the impulse, is the same in both cases. The average force is less with the carpet than with the floor because soft carpet allows a longer time for the dish to come to rest.  Physics 110 - Lecture 4 - - Sonia Katdare 16 Quick Question When a car is out of control, would it be better to hit a haystack or concrete wall?  Physics 110 - Lecture 4 - - Sonia Katdare 17 Quick Question When a car is out of control, it is better to hit a haystack than a concrete wall. Same impulse either way, but extension of hitting time reduces the force.  Physics 110 - Lecture 4 - - Sonia Katdare 18 Quick Question If a boxer is able to make the contact time five times longer by “riding” with the punch, how much will the force of the punch impact be reduced?  Physics 110 - Lecture 4 - - Sonia Katdare 19 Quick Question If a boxer is able to make the contact time five times longer by “riding” with the punch, how much will the force of the punch impact be reduced? By a factor of 5 In figure a, t is written larger than the f so punch is weak. In figure b, F is larger than the t so punch is hard.  Physics 110 - Lecture 4 - - Sonia Katdare 20 Bouncing For an object to bounce, its momentum must first come to zero, and then be accelerated back in the opposite direction This means the impulse delivered to a bouncing object is more (up to twice) than an object simply brought to rest  Physics 110 - Lecture 4 - - Sonia Katdare 21 Bouncing  Physics 110 - Lecture 4 - - Sonia Katdare 22 Bouncing The waterwheels used in gold mining operations during the California Gold Rush were not very effective. Lester A. Pelton designed a curve-shaped paddle that caused the incoming water to make a U-turn upon impact. The water “bounced,” increasing the impulse exerted on the waterwheel.  Physics 110 - Lecture 4 - - Sonia Katdare 23 Conservation of Momentum The force (impulse) that changes a system’s momentum must be an external one. If no external force is exerted on a system, the momentum doesn’t change: we say the momentum is conserved.  Physics 110 - Lecture 4 - - Sonia Katdare 24 Conservation of Momentum The force on the cannonball inside the cannon barrel is equal and opposite to the force causing the cannon to recoil. The action and reaction forces are internal to the system so they don’t change the momentum of the cannon-cannonball system. Before the firing, the momentum is zero. After the firing, the net momentum is still zero. Net momentum is neither gained nor lost.  Physics 110 - Lecture 4 - - Sonia Katdare 25 Conservation of Momentum Remember that momentum is a vector quantity, so conservation just means that the total (net) momentum is a constant: Σ𝑝𝑝 ⃗ = Σ𝑝𝑝 𝑝𝑝 ⃗′ 𝑝𝑝 To avoid too many subscripts later, I’ll use the notation “prime is after collision, no prime is before”  Physics 110 - Lecture 4 - - Sonia Katdare 26 Quick Question Newton’s second law states that if no net force is exerted on a system, no acceleration occurs. Does it follow that no change in momentum occurs?  Physics 110 - Lecture 4 - - Sonia Katdare 27 Quick Question Newton’s second law states that if no net force is exerted on a system, no acceleration occurs. Does it follow that no change in momentum occurs? Yes net momentum before collision equals net momentum after collision. in equation form: (net mv )before = (net mv )after  Physics 110 - Lecture 4 - - Sonia Katdare 28 Collisions When two (or more) objects collide in the absence of external forces (which is usually a good approximation), the total momentum before the collision is the same as the total momentum after the collision.  Physics 110 - Lecture 4 - - Sonia Katdare 29 Elastic/Inelastic Collisions If kinetic energy is conserved in addition to momentum, the collision is called elastic. These collisions are usually between hard objects like pool balls; there is no “sticking” or “squishing” If a collision does not conserve kinetic energy, the collision is inelastic, meaning some energy goes to heat or deforming the objects. (Momentum, however, is still conserved). When two objects collide together into one object, the collision is completely inelastic.  Physics 110 - Lecture 4 - - Sonia Katdare 30 Inelastic Collision In an inelastic collision between two freight cars, the momentum of the freight car on the left is shared with the freight car on the right.  Physics 110 - Lecture 4 - - Sonia Katdare 31 Quick Question Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is A. the same. B. half. C. twice. D. None of the above.  Physics 110 - Lecture 4 - - Sonia Katdare 32 Quick Question Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is A. the same. B. half. C. twice. D. None of the above. After the collision, the mass of the moving freight cars has doubled. Since the momentum is the product of mass and speed, the speed must be halved to conserve the value of that product.  Physics 110 - Lecture 4 - - Sonia Katdare 33 Quick Question One glider is loaded so it has three times the mass of another glider. The loaded glider is initially at rest. The unloaded glider collides with the loaded glider and the two gliders stick together. Describe the motion (speed) of the gliders after the collision.  Physics 110 - Lecture 4 - - Sonia Katdare 34 Quick Question One glider is loaded so it has three times the mass of another glider. The loaded glider is initially at rest. The unloaded glider collides with the loaded glider and the two gliders stick together. Describe the motion (speed) of the gliders after the collision. m’ = m + 3m so the gliders move at 1/4th the initial speed  Physics 110 - Lecture 4 - - Sonia Katdare 35 Quick Question Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. a) If the larger fish swims at 1 m/s, what is its velocity immediately after lunch? b) What if the small fish were swimming to the left at 3 m/s?  Physics 110 - Lecture 4 - - Sonia Katdare 36 Quick Question Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. a)If the larger fish swims at 1 m/s, what is its velocity immediately after lunch? ¾ m/s b)What if the small fish were swimming to the left at 3 m/s? 0 m/s  Physics 110 - Lecture 4 - - Sonia Katdare 37 Quick Question On roller blades you horizontally toss a ball away from you. The mass of the ball is one tenth your mass. Compared with the speed you give to the ball, your recoil speed will ideally be A. one tenth as much. B. the same. C. ten times as much. D. 100 times as much.  Physics 110 - Lecture 4 - - Sonia Katdare 38 Quick Question On roller blades you horizontally toss a ball away from you. The mass of the ball is one tenth your mass. Compared with the speed you give to the ball, your recoil speed will ideally be A. one tenth as much. B. the same. C. ten times as much. D. 100 times as much.  Physics 110 - Lecture 4 - - Sonia Katdare 39 Momentum Vectors Remember that momentum is a vector, so if we have a two-dimensional collision, momentum is conserved in each component separately Σ𝑝𝑝𝑝𝑝𝑥𝑥𝑥𝑥 = Σ𝑝𝑝𝑝𝑝𝑥𝑥𝑥𝑥′ Σ𝑝𝑝𝑝𝑝𝑦𝑦𝑦𝑦 = Σ𝑝𝑝𝑝𝑝𝑦𝑦′𝑦𝑦  Physics 110 - Lecture 4 - - Sonia Katdare 40 Momentum Vectors When the firecracker bursts, the vector sum of the momenta of its fragments add up to the firecracker’s momentum just before bursting.  Physics 110 - Lecture 4 - - Sonia Katdare 41 Quick Question A falling firecracker bursts into two pieces. Compared with the momentum of the firecracker when it bursts, the two pieces A. combined have the same momentum. B. each have half as much momentum. C. have more momentum. D. may or may not have more momentum.  Physics 110 - Lecture 4 - - Sonia Katdare 42 Quick Question A falling firecracker bursts into two pieces. Compared with the momentum of the firecracker when it bursts, the two pieces A. combined have the same momentum. B. each have half as much momentum. C. have more momentum. D. may or may not have more momentum.  Physics 110 - Lecture 4 - - Sonia Katdare 2 ANGULAR MOMENTUM Chapter 8  Physics 110 - Lecture 4 - - Sonia Katdare 43 Student learning Objectives Angular Momentum Conservation of Angular Momentum  Physics 110 - Lecture 4 - - Sonia Katdare 44 Angular Momentum If (linear or translational) momentum is a measure of inertia in motion, there should be a similar quantity for a rotating object. The angular momentum of a rotating object is defined as 𝐿𝐿 = 𝐼𝐼𝜔𝜔 It depends on the moment of inertia and the angular velocity  Physics 110 - Lecture 4 - - Sonia Katdare 45 Angular Momentum An object of concentrated mass m, whirling in a circular path of radius r with a speed ω has angular momentum L=Iωr This applies to a tin can swinging from a long string or a planet orbiting in a circle around the sun.  Physics 110 - Lecture 4 - - Sonia Katdare 46 Rotational version of Newton's first law: An object or system of objects will maintain its angular momentum unless acted upon by an external net torque. An external net torque is required to change the angular momentum of an object.  Physics 110 - Lecture 4 - - Sonia Katdare 47 Quick Question Suppose you are swirling a can around and suddenly decide to pull the rope in halfway; by what factor would the speed of the can change? A. Double B. Four times C. Half D. One-quarter  Physics 110 - Lecture 4 - - Sonia Katdare 48 Quick Question Suppose you are swirling a can around and suddenly decide to pull the rope in halfway; by what factor would the speed of the can change? A. Double B. Four times C. Half D. One-quarter Angular Momentum is proportional to radius of the turn. No external torque acts with inward pull, so angular momentum is conserved. Half radius means speed doubles.  Physics 110 - Lecture 4 - - Sonia Katdare 49 Angular Impulse To change the angular momentum of an object, an angular impulse must be applied. This means an external torque must act on the object for some time: ∑ 𝜏𝜏𝑡𝑡 ⃗ = Δ𝐿𝐿 = Δ 𝐼𝐼𝜔𝜔 In the absence of external torque, angular momentum is conserved!  Physics 110 - Lecture 4 - - Sonia Katdare 50 Angular Momentum It is easier to balance on a moving bicycle than on one at rest. The spinning wheels have angular momentum. When our center of gravity is not above a point of support, a slight torque is produced. When the wheels are at rest, we fall over. When the bicycle is moving, the wheels have angular momentum, and a greater torque is required to change the direction of the angular momentum.  Physics 110 - Lecture 4 - - Sonia Katdare 51 Law of conservation of angular momentum The law of conservation of angular momentum states: If no external net torque acts on a rotating system, the angular momentum of that system remains constant. Analogous to the law of conservation of linear momentum: If no external force acts on a system, the total linear momentum of that system remains constant.  Physics 110 - Lecture 4 - - Sonia Katdare 52 Conservation of Angular Momentum When the man pulls his arms and the whirling weights inward, he decreases his rotational inertia, and his rotational speed correspondingly increases.  Physics 110 - Lecture 4 - - Sonia Katdare 53 Conservation of Angular Momentum Rotational speed is controlled by variations in the body’s rotational inertia as angular momentum is conserved during a forward somersault. This is done by moving some part of the body toward or away from the axis of rotation.  Physics 110 - Lecture 4 - - Sonia Katdare 55 ENERGY Chapter 7  Physics 110 - Lecture 4 - - Sonia Katdare 56 Student Learning Objectives Energy Work Mechanical Energy: Potential and Kinetic Work-Energy Theorem Conservation of Energy Power Machines Efficiency Recycled Energy Energy for Life Sources of Energy Energy Quantifies a system’s ability to do work Occurs in a variety of forms Observed when it is being transferred or being transformed Is a conserved quantity  Physics 110 - Lecture 4 - - Sonia Katdare 57 Work Work is the product of a force exerted through some distance (in the same direction) 𝑊𝑊 = F.d The unit of measurement for work combines a unit of force, N, with a unit of distance, m. The unit of work is the newton-meter (N m), also called the joule. One joule (J) of work is done when a force of 1 N is exerted over a distance of 1 m (lifting an apple over your head).  Physics 110 - Lecture 4 - - Sonia Katdare 58 Quick Question Suppose that you apply a 60-N horizontal force to a 32-kg package, which pushes it 4 meters across a mailroom floor. How much work do you do on the package?  Physics 110 - Lecture 4 - - Sonia Katdare 59 Quick Question Suppose that you apply a 60-N horizontal force to a 32-kg package, which pushes it 4 meters across a mailroom floor. How much work do you do on the package? 𝑾𝑾= 𝑭𝑭. d = (mg).d 𝑾𝑾= (60)(32)(10) = 240 J Quick Question You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is A. less than twice as much. B. twice as much. C. more than twice as much. D. zero. Quick Question You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is A. less than twice as much. B. twice as much. C. more than twice as much. D. zero. 𝑾𝑾= 𝑭𝑭. d = 𝑭𝑭.2d = 2W  Physics 110 - Lecture 4 - - Sonia Katdare 60 Work Twice as much work is done in lifting 2 loads 1 story high versus lifting 1 load the same vertical distance. Reason: force needed to lift twice the load is twice as much. Twice as much work is done in lifting a load 2 stories instead of 1 story. Reason: distance is twice as great.  Physics 110 - Lecture 4 - - Sonia Katdare 61 Work Note that if a force is exerted but there is no displacement, no work is done. Also, the force must have some component parallel to the displacement; only force in the direction of motion will do work! A weightlifter raising a barbell from the floor does work on the barbell. Work done against gravity.  Physics 110 - Lecture 4 - - Sonia Katdare 62 Power Power is the rate at which work is done The unit of power is the joule per second, also known as the Watt. One watt (W) of power is expended when one joule of work is done in one second. Power A worker uses more power running up the stairs than climbing the same stairs slowly. Doubling the power of an engine doubles the work done in a particular time interval. In the United States, we customarily rate engines in units of horsepower and electricity in kilowatts, either may be used. Units for Power Horsepower is a unit of measurement for the rate at which work is done. The term was adopted in the late 18th century by Scottish engineer James Watt to compare the output of steam engines with the power of draft horses. One horsepower is the amount of power used by a horse to lift a 550 pounds heavy object from a depth of 1 foot in one second. I Hp = 746 Watts  Physics 110 - Lecture 4 - - Sonia Katdare 64 Quick Question A job can be done slowly or quickly. These methods require the same amount of work, but different amounts of A. energy. B. momentum. C. power. D. impulse.  Physics 110 - Lecture 4 - - Sonia Katdare 65 Quick Question A job can be done slowly or quickly. These methods require the same amount of work, but different amounts of A. energy. B. momentum. C. power. D. impulse. Power is the rate at which work is done, so doing the job faster requires more power.  Physics 110 - Lecture 4 - - Sonia Katdare 66 Mechanical Energy Mechanical energy is due to position or to motion, or both. When work is done by an archer in drawing back a bowstring, the bent bow acquires the ability to do work on the arrow. When work is done to raise the heavy ram of a pile driver, the ram acquires the ability to do work on the object it hits when it falls. When work is done to wind a spring mechanism, the spring acquires the ability to do work on various gears to run a clock, ring a bell, or sound an alarm.  Physics 110 - Lecture 4 - - Sonia Katdare 67 Mechanical Energy Something has been acquired that enables the object to do work. It may be in the form of a compression of atoms in the material of an object; a physical separation of attracting bodies; or a rearrangement of electric charges in the molecules of a substance. The property of an object or system that enables it to do work is energy. Like work, energy is measured in joules. Mechanical energy is the energy due to the position of something or the movement of something.  Physics 110 - Lecture 4 - - Sonia Katdare 70 Potential Energy An object may store energy by virtue of its position. Energy that is stored and held in readiness is called potential energy (PE) because in the stored state it has the potential for doing work. Note: in your book, they will use the symbol 𝑃𝑃E for potential energy. While this makes logical sense, it’s never a good idea to have a variable that is made of two characters: this could mean 𝑃𝑃 times E (and in fact, this combination does occasionally occur). I will use the symbol 𝑈𝑈 to represent potential energy of a system.  Physics 110 - Lecture 4 - - Sonia Katdare 72 Elastic Potential Energy A stretched or compressed spring has a potential for doing work. When a bow is drawn back, energy is stored in the bow. The bow can do work on the arrow. A stretched rubber band has potential energy because of its position. These types of potential energy are elastic potential energy.  Physics 110 - Lecture 4 - - Sonia Katdare 73 Chemical Energy The chemical energy in fuels is also potential energy. It is energy of position at the submicroscopic level. This energy is available when the positions of electric charges within and between molecules are altered and a chemical change takes place.  Physics 110 - Lecture 4 - - Sonia Katdare 74 Gravitational Potential Energy Work is required to elevate objects against Earth’s gravity. The potential energy due to elevated positions is gravitational potential energy. Water in an elevated reservoir and the raised ram of a pile driver have gravitational potential energy. We may express the gravitational potential energy near the surface of Earth as 𝑈𝑈g = mgh Here, h is the height of the object above some reference point.  Physics 110 - Lecture 4 - - Sonia Katdare 71 Potential Energy Potential energy of 10-N ball is the same in all 3 cases because work done in elevating it is the same. In figure a, a ball rises from the floor to the top of a vertical pole. In figure b, a ball rises 5 meters along an incline. In figure c, a ball rises up 3 steps with a total height of 3 meters.  Physics 110 - Lecture 4 - - Sonia Katdare 75 Gravitational Potential Energy The potential energy of the 100-N boulder with respect to the ground below is 200 J in each case. a) The boulder is lifted with 100 N of force. b) The boulder is pushed up the 4-m incline with 50 N of force. c) The boulder is lifted with 100 N of force up each 0.5-m stair.  Physics 110 - Lecture 4 - - Sonia Katdare 68 Quick Question Does a crate lifted by a pulley have increased potential energy relative to the floor? A. Yes B. No C. Sometimes D. Not enough information  Physics 110 - Lecture 4 - - Sonia Katdare 69 Quick Question Does a crate lifted by a pulley have increased potential energy relative to the floor? A. Yes B. No C. Sometimes D. Not enough information If the crate were twice as heavy, its increase in potential energy would be twice as great.  Physics 110 - Lecture 4 - - Sonia Katdare 76 Quick Question You lift a 100-N boulder 1 m. a) How much work is done on the boulder? b) What power is expended if you lift the boulder in a time of 2 s? c) What is the gravitational potential energy of the boulder in the lifted position?  Physics 110 - Lecture 4 - - Sonia Katdare 77 Quick Question You lift a 100-N boulder 1 m. a) How much work is done on the boulder? 100 J b) What power is expended if you lift the boulder in a time of 2 s? 50 W c) What is the gravitational potential energy of the boulder in the lifted position? 100 J  Physics 110 - Lecture 4 - - Sonia Katdare 78 Kinetic Energy If an object is moving, it is capable of doing work, so it has mechanical energy. The energy of motion is called kinetic energy, and depends on the mass and speed of the object: 1 𝐾𝐾 = 𝑚𝑚𝑣𝑣 2 2 Note that it depends on the square of the speed!  Physics 110 - Lecture 4 - - Sonia Katdare 79 Quick Question Does a car with momentum have kinetic energy? A. Yes, because the car is in motion B. Only if the car is accelerating C. Only if the car is not accelerating D. No  Physics 110 - Lecture 4 - - Sonia Katdare 80 Quick Question Does a car with momentum have kinetic energy? A. Yes, because the car is in motion B. Only if the car is accelerating C. Only if the car is not accelerating D. No If a car has momentum it is necessarily in motion. Anything in motion necessarily has kinetic energy, regardless of whether it is accelerating or not.  Physics 110 - Lecture 4 - - Sonia Katdare 81 Work-Energy Theorem To increase the kinetic energy of an object, work must be done on it. The net work (two words ) must give rise to the change in kinetic energy: 𝑊𝑊 = Δ 𝐾𝐾 If there is no change in an object’s kinetic energy, then no net work was done on it. Push against a box on a floor. If it doesn’t slide, then you are not doing work on the box. On a very slippery floor, if there is no friction at all, the work of your push times the distance of your push appears as kinetic energy of the box.  Physics 110 - Lecture 4 - - Sonia Katdare 82 Work-Energy Theorem If there is some friction, it is the net force of your push minus the frictional force that is multiplied by distance to give the gain in kinetic energy. If the box moves at a constant speed, you are pushing just hard enough to overcome friction. The net force and net work are zero, and, according to the work-energy theorem, Δ 𝐾𝐾 = 0. The kinetic energy doesn’t change.  Physics 110 - Lecture 4 - - Sonia Katdare 83 Work-Energy Theorem Due to friction, energy is transferred both into the floor and into the tire when the bicycle skids to a stop. a) An infrared camera reveals the heated tire track on the floor. b) The warmth of the tire is also revealed.  Physics 110 - Lecture 4 - - Sonia Katdare 84 Work-Energy Theorem Typical stopping distances for cars equipped with antilock brakes traveling at various speeds. The work done to stop the car is friction force × distance of slide.  Physics 110 - Lecture 4 - - Sonia Katdare 85 Quick Question A friend says that if you do 100 J of work on a moving cart, the cart will gain 100 J of KE. Another friend says this depends on whether or not there is friction. What is your opinion of these statements?  Physics 110 - Lecture 4 - - Sonia Katdare 86 Quick Question A friend says that if you do 100 J of work on a moving cart, the cart will gain 100 J of KE. Another friend says this depends on whether or not there is friction. What is your opinion of these statements? It’s net work, so it does depend on whether there is friction.  Physics 110 - Lecture 4 - - Sonia Katdare 87 Quick Question A fast-moving crate slides across a factory floor subject to a known frictional force. The crate slows down and eventually stops. Which of the following equations most directly determines the stopping distance? A. F = ma B. Ft = Δmv C. KE = 1/2mv2 D. Fd = 1/2mv2  Physics 110 - Lecture 4 - - Sonia Katdare 88 Quick Question A fast-moving crate slides across a factory floor subject to a known frictional force. The crate slows down and eventually stops. Which of the following equations most directly determines the stopping distance? A. F = ma B. Ft = Δmv C. KE = 1/2mv2 D. Fd = 1/2mv2 The work-energy theorem is the physicist's favorite starting point for solving many motion-related problems.  Physics 110 - Lecture 4 - - Sonia Katdare 89 Quick Question When the brakes of a car are locked, the car skids to a stop. How much farther will the car skid if it’s moving 3 times as fast?  Physics 110 - Lecture 4 - - Sonia Katdare 90 Quick Question When the brakes of a car are locked, the car skids to a stop. How much farther will the car skid if it’s moving 3 times as fast? 9 times farther  Physics 110 - Lecture 4 - - Sonia Katdare 91 Conservation of Energy In a closed system (one that does not share energy with the rest of the universe), the total energy is conserved. In other words, energy may neither be created nor destroyed, but can change forms. This is probably the most important single fact in physics.  Physics 110 - Lecture 4 - - Sonia Katdare 92 Conservation of Energy As you draw back the arrow in a bow, you do work stretching the bow. The bow then has potential energy. When released, the arrow has kinetic energy equal to this potential energy. It delivers this energy to its target. The small distance the arrow moves multiplied by the average force of impact doesn’t quite match the kinetic energy of the target. However, the arrow and target are a bit warmer by the energy difference. Energy changes from one form to another without a net loss or a net gain.  Physics 110 - Lecture 4 - - Sonia Katdare 93 Conservation of Energy Part of the PE of the wound spring changes into KE. The remaining PE goes into heating the machinery and the surroundings due to friction. No energy is lost.  Physics 110 - Lecture 4 - - Sonia Katdare 94 Conservation of Energy Everywhere along the path of the pendulum bob, the sum of PE and KE is the same. Because of the work done against friction, this energy will eventually be transformed into heat.  Physics 110 - Lecture 4 - - Sonia Katdare 95 Conservation of Energy When the woman leaps from the burning building, the sum of her PE and KE remains constant at each successive position all the way down to the ground.  Physics 110 - Lecture 4 - - Sonia Katdare 96 Conservation of Energy Each atom that makes up matter is a concentrated bundle of energy. When the nuclei of atoms rearrange themselves, enormous amounts of energy can be released. The sun shines because some of its nuclear energy is transformed into radiant energy. In nuclear reactors, nuclear energy is transformed into heat. Enormous compression due to gravity in the deep, hot interior of the sun causes hydrogen nuclei to fuse and become helium nuclei. This high-temperature welding of atomic nuclei is called thermonuclear fusion. This process releases radiant energy, some of which reaches Earth. Part of this energy falls on plants, and some of the plants later become coal.  Physics 110 - Lecture 4 - - Sonia Katdare 97 Conservation of Energy Another part supports life in the food chain that begins with microscopic marine animals and plants, and later gets stored in oil. Part of the sun’s energy is used to evaporate water from the ocean. Some water returns to Earth as rain that is trapped behind a dam. The water behind a dam has potential energy that is used to power a generating plant below the dam. The generating plant transforms the energy of falling water into electrical energy. Electrical energy travels through wires to homes where it is used for lighting, heating, cooking, and operating electric toothbrushes.  Physics 110 - Lecture 4 - - Sonia Katdare 98 Kinetic Energy and Momentum Compared Similarities between momentum and kinetic energy: Both are properties of moving things. Difference between momentum and kinetic energy: Momentum is a vector quantity and therefore is directional and can be canceled. Kinetic energy is a scalar quantity and can never be canceled. Velocity dependence Momentum depends linearly on velocity. Kinetic energy depends on the square of velocity. Example: An object moving with twice the velocity of another with the same mass, has twice the momentum but four times the kinetic energy.  Physics 110 - Lecture 4 - - Sonia Katdare 99 Machines A machine is a device that multiplies or changes the direction of a force. There are six simple machines  Physics 110 - Lecture 4 - - Sonia Katdare 100 Lever Rotates on a point of support called the fulcrum Allows a small force over a large distance to induce a large force over a short distance The point under the horizontal lever is to the far right and not centered. When the lever falls left, force F is small and pulls down while vector d is larger and pulls up. On the right side, force F pulls up and is large while force d pulls down and is smaller. F d = F d, where the first d is large and the second F is large. The point under the horizontal lever is to the far right and not centered. When the lever falls left, force F is small and pulls down while vector d is larger and pulls up. On the right side, force F pulls up and is large while force d pulls down and is smaller. The given equation is F d = F d, where the first d is large and the second F is large.  Physics 110 - Lecture 4 - - Sonia Katdare 101 Levers There are three classes of levers, depending on where the effort, load, and fulcrum are  Physics 110 - Lecture 4 - - Sonia Katdare 102 Pulley Operates like a lever with equal arms— changes the direction of the input force Operates as a system of pulleys (block and tackle) Multiplies force A pulley hangs from the ceiling and holds a weight below it. On a platform that is below the ceiling but above the pulley, a child pulls up on the other side of the rope. The balance point in the pulley is to the far left. The output pulls up vertically from the center of the pulley while the input pulls up from the far right. The output is larger than the input. A pulley hands from the ceiling and holds a weight below it. On a platform that is below the ceiling but above the pulley, a child pulls up on the other side of the rope. The balance point in the pulley is to the far left. The output pulls up vertically from the center of the pulley while the input pulls up from the far right. The output is larger than the input.  Physics 110 - Lecture 4 - - Sonia Katdare 103 Mechanical Advantage All machines operate under the principle: work in = work out. However, since 𝑊𝑊= 𝐹𝐹.d the input force may be made small if the effort distance is large. The ratio of output force to input force is the mechanical advantage of the machine: 𝐹𝐹𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑀𝑀 = = 𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖  Physics 110 - Lecture 4 - - Sonia Katdare 104 Efficiency Pushing the block of ice 5 times farther up the incline than the vertical distance it’s lifted requires a force of only one fifth its weight. If friction is negligible, we need apply only one fifth of the force. The inclined plane shown has a theoretical mechanical advantage of 5. However, due to friction, not all of the applied work will be against gravity. The actual mechanical advantage will be less than the theoretical.  Physics 110 - Lecture 4 - - Sonia Katdare 105 Efficiency The efficiency of a machine is It will always be a number less than 1. Even the best-designed car engines are unlikely to be more than 35% efficient (more on heat engines later) We could also define efficiency as  Physics 110 - Lecture 4 - - Sonia Katdare 106 Quick Question A certain machine is 30% efficient. This means the machine will convert A. 30% of the energy input to useful work— 70% of the energy input will be wasted. B. 70% of the energy input to useful work— 30% of the energy input will be wasted. C. 30% of the energy input into heat. D. None of the above.  Physics 110 - Lecture 4 - - Sonia Katdare 107 Quick Question A certain machine is 30% efficient. This means the machine will convert A. 30% of the energy input to useful work— 70% of the energy input will be wasted. B. 70% of the energy input to useful work— 30% of the energy input will be wasted. C. 30% of the energy input into heat. D. None of the above.  Physics 110 - Lecture 4 - - Sonia Katdare 108 Quick Question Almost all energy available to us here on Earth comes from the sun, directly or indirectly List some sources of energy that come from the sun in some form Can you think of sources that don’t ultimately come from the sun?  Physics 110 - Lecture 4 - - Sonia Katdare 109 Quick Question Almost all energy available to us here on Earth comes from the sun, directly or indirectly List some sources of energy that come from the sun in some form Can you think of sources that don’t ultimately come from the sun? Geothermal and Nuclear