Section 1 Work and Energy Chapter 4 and 5
Motion Read Chapter 4 pages 100 121 and Chapter 5 pages: 126-153 Objectives: - Distinguish between kinetic and potential energy; calculate kinetic energy, describe different forms of potential energy; calculate gravitational potential energy; describe how energy can be transformed from one form to another; explain how the mechanical energy system is the sum of the kinetic and potential energy; discuss the law of conservation of energy; Explain the meaning of work; describe how work and energy are related, calculate work and power; explain how machines make doing work easier; calculate the mechanical advantage and efficiency of a machine; describe the six types of simple machines; explain how different types of simple machines make doing work easier; calculate the idea mechanical advantage of different types of simple machines; PSc.3.1.1 Explain thermal energy and its transfer. PSc.3.1.2 Explain the law of conservation of energy in a mechanical system in terms of kinetic energy, potential energy and heat. PSc.3.1.3 Explain work in terms of the relationship among the applied force to an object, the resulting displacement of the object and the energy transferred to an object. PSc.3.1.4 Explain the relationship among work, power and simple machines both qualitatively and quantitatively. Vocabulary: joule Work power mechanical advantage Machine input force output force elastic potential energy Simple machines compound machines energy chemical energy Potential energy kinetic energy mechanical energy screw gravitational potential energy wedge Efficiency law of conservation of energy lever First law of thermodynamics pulley wheel and axle inclined plane Isolated system closed system open system Block and tackle fulcrum nonmechanical energy internal combustion engine Second law of thermodynamics thermodynamics
Key Ideas How is work calculated? What is the relationship between work and power? How do machines make work easier?
What Is Work? How is work calculated? Work is calculated by multiplying the force by the distance over which the force is applied. work = force x distance, or W = Fd The force must be applied in the direction of the object s motion.
What Is Work?, continued work: the transfer of energy to an object by the application of a force that causes the object to move in the direction of the force Work is zero when an object is not moving. Work is measured in joules (J): One joule is equal to kilogram times meter squared per second squared 1 N m = 1 J = 1 kg m 2 /s 2
Visual Concept: Work
Math Skills Work Imagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift if he lifts her 2.0 m and exerts an average force of 190 N? 1. List the given and unknown values. Given: force, F = 190 N distance, d = 2.0 m Unknown: W = Fd W = 380 J
Power Running up a flight of stairs does not require more work than walking up slowly does, but running is more exhausting than walking. The amount of time that a given amount of work takes is an important factor when you consider work and machines. The quantity that measures work in relation to time is POWER.
Power What is the relationship between work and power? Power is the rate at which work is done, or how much work is done in a given amount of time. work power, time or P W t
Power, continued The SI unit used to express power is the watt (W). One watt is the amount of power needed to do one joule of work in one second. It is about equal to the power needed to lift an apple over your head in 1 second. Do not confuse the symbol for work, W, which is italic, with the symbol for the watt, W.
Power, continued Power is a quantity that measures the rate at which work is done or energy is transformed Power is measured in watts (W): 1 W = 1 J/s (One watt is equal to one joule per second)
Visual Concept: Power
Math Skills Power Lifting an elevator 18 m takes 100 kj. If doing so takes 20 s, what is the average power of the elevator during the process? 1. List the given and unknown values. Given: work, W = 100 kj = 1 10 5 J time, t = 20 s Distance is not needed. Unknown: power, P =? W
Math Skills, continued 2. Write the equation for power. Lifting an elevator 18 m takes 100 kj. If doing so takes 20 s, what is the average power of the elevator during the process? 3. Insert the known values into the equation, and solve. P 5 1 10 J 3 5 10 J/s 20 s P 3 5 10 W 5 kw
Machines and Mechanical Advantage Which would be easier, lifting a car by hand or lifting a car with a jack? A jack of course, because it would require less effort. But you may be surprised to learn both methods require the same amount of work. The jack makes the work easier by allowing you to apply less force at any given moment.
Machines and Mechanical Advantage How do machines make work easier? Machines help do work by changing the size of an input force, the direction of the force, or both. Machines redistribute the work that we put into them and can change the direction of an input force. Machines can also make the force greater by decreasing the distance over which the force is applied. This process is called multiplying the force.
Machines and Mechanical Advantage, continued Scientist and engineers use a number that describes how much force or distance is multiplied by a machine; this number is called the mechanical advantage. mechanical advantage: is defined as the ratio between the output force and the input force; it is also equal to the ratio between the input distance and the output distance IF friction is ignored.
Machines and Mechanical Advantage, continued mechanical advantage: a quantity that expresses how much a machine multiplies force or distance; mechanical advantage output force input force input distance output distance Notice, it is output force divided by input force Or, input distance divided by output distance.
Math Skills mechanical advantage output force input force input distance output distance Mechanical Advantage Calculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high. 1. List the given and unknown values. Given: input distance = 5.0 m output distance = 1.5 m Unknown: mechanical advantage =?
Calculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high. 2. Write the equation for mechanical advantage. We need only the distance part of the full equation: input distance mechanical advantage = output distance 3. Insert the known values into the equation, and solve. mechanical advantage = 5.0 m 3.3 1.5 m
Math Skills mechanical advantage output force input force input distance output distance 4. Find the mechanical advantage (MA) of a ramp that is 6.0 m long and 1.5 m tall. = 4.0 5. Alex pulls on the handle of a claw hammer with a force of 15 N. If the hammer has a mechanical advantage (MA) of 5.2, how much force is exerted on the nail in the claw (output force)? Out force = (MA)(input force) (5.2)(15N) = 78 N
Section 2: Simple Machines Key Ideas What are the six types of simple machines? What are the two principal parts of all levers? How does using an inclined plane change the force required to do work? What simple machines make up a pair of scissors?
What Are Simple Machines? What are the six types of simple machines? The six types of simple machines are: simple lever, inclined plane, wedge, pulley, wheel and axle, and the screw.
What Are Simple Machines?, continued Simple machines are divided into two families: the lever family and the inclined plane family. Lever family: simple lever pulley wheel and axle Inclined plane family: simple inclined plane wedge screw
The Lever Family What are the two principal parts of all levers? All levers have a rigid arm that turns around a point called the fulcrum. Levers are divided into three classes: First Class Second Class Third Class
The Lever Family, continued
Visual Concept: Lever
The Lever Family, continued Pulleys are modified levers. The point in the middle of a pulley is like the fulcrum of a lever. The rest of the pulley behaves like the rigid arm of a first-class lever. A wheel and axle is a lever or pulley connected to a shaft. Screwdrivers and cranks are common wheel-and-axel machines.
The Mechanical Advantage of Pulleys
Visual Concept: Pulley
The Inclined Plane Family How does using an inclined plane change the force required to do work? Pushing an object up an inclined plane requires less input force than lifting the same object does.
Visual Concept: Inclined Plane
The Inclined Plane Family A wedge is a modified inclined plane. A screw is an inclined plane wrapped around a cylinder.
Visual Concept: Screws
Compound Machines What simple machines make up a pair of scissors? A pair of scissors uses two first-class levers joined at a common fulcrum; each lever arm has a wedge that cuts into the paper. compound machine: a machine made of more than one simple machine
Compound machines
Section 3: What is Energy? Key Ideas What is the relationship between energy and work? Why is potential energy called energy of position? What factors does kinetic energy depend on? What is non-mechanical energy?
Energy and Work What is the relationship between energy and work? Whenever work is done, energy is transformed or is transferred from one system to another system. energy: the capacity to do work Energy is measured in joules (J).
Potential Energy Why is potential energy called energy of position? Potential energy (PE) is sometimes called energy of position because it results from the relative positions of objects in a system. potential energy: the energy that an object has because of the position, shape, or condition of the object
Potential Energy, continued Any object that is stretched or compressed to increase or decrease the distance between its parts has elastic potential energy. Examples: stretched bungee cords, compressed springs Any system of two or more objects separated by a vertical distance has gravitational potential energy. Example: a roller coaster at the top of a hill
Visual Concept: Potential Energy
Visual Concept: Potential Energy
ELASTIC POTENTIAL ENERGY ELASTIC POTENTIAL ENERGY = is energy stored by something that can stretch or compress. (spring, rubber band etc.) A Stretched rubber band has elastic potential energy. The elastic potential energy in the stretched rubber band was converted to kinetic energy when you released the band.
GRAVITATIONAL POTENTIAL ENERGY Anything that can fall has stored energy called GRAVITATIONAL POTENTIAL ENERGY GPE is energy stored by objects due to their position above the Earth s surface.
GRAVITATIONAL POTATIONAL ENERGY = is stored energy due to position. The hanging apple has energy because of it position above the Earth s surface.
The GPE of an object depends on the object s mass and height above the ground. It can be calculated by the following equation: Gravitational potential energy (Joules) = mass x gravity x height GPE ( J ) = mgh
Potential Energy, continued Gravitational potential energy depends on both mass and height. grav. PE = mass free-fall acceleration height, or PE = mgh The height can be relative.
Math Skills PE = mgh Gravitational Potential Energy A 65 kg rock climber ascends a cliff. What is the climber s gravitational potential energy at a point 35 m above the base of the cliff? 1. List the given and unknown values. Given: mass, m = 65 kg height, h = 35 m free-fall acceleration, g = 9.8 m/s 2 Unknown: gravitational potential energy, PE =? J
Math Skills, continued 2. Write the equation for gravitational potential energy. PE = mgh 3. Insert the known values into the equation, and solve. PE = (65 kg)(9.8 m/s 2 )(35 m) PE = 2.2 10 4 kg m 2 /s 2 PE = 2.2 10 4 J
Kinetic Energy What factors does kinetic energy depend on? Kinetic energy depends on both the mass and the speed of an object. kinetic energy: the energy of an object due to the object s motion KE = ½ mass speed squared, or KE= ½mv 2
Visual Concept: Kinetic Energy
Kinetic Energy, continued Kinetic energy depends on speed more than mass. Atoms and molecules have kinetic energy.
Math Skills Kinetic Energy KE= ½mv 2 or KE = mv 2 What is the kinetic energy of a 44 kg cheetah running at 31 m/s? 2 1. List the given and unknown values. Given: mass, m = 44 kg speed, v = 31 m/s Unknown: kinetic energy, KE =? J
Math Skills, continued 2. Write the equation for kinetic energy. kinetic energy 1 2 mass speed squared KE 1 2 mv 2 3. Insert the known values into the equation, and solve. KE = ½ (44 kg)(31 m/s) 2 = 2.1 10 4 kg m 2 /s 2 KE = 2.1 10 4 J
Other Forms of Energy What is nonmechanical energy? Energy that lies at the level of the atom is sometimes called nonmechanical energy. mechanical energy: the amount of work an object can do because of the object s kinetic and potential energies In most cases, nonmechanical forms of energy are just special forms of either kinetic or potential energy.
Energy has several different forms 1. Electrical 2. Chemical 3. Radiant 4. Thermal 5. Mechanical 6. Nuclear
Other Forms of Energy, continued Chemical reactions involve potential energy. The amount of chemical energy associated with a substance depends in part on the relative positions of the atoms it contains. Living things get energy from the sun. Plants use photosynthesis to turn the energy in sunlight into chemical energy. The sun gets energy from nuclear reactions. The sun is fueled by nuclear fusion reactions in its core.
Other Forms of Energy, continued Energy can be stored in fields. Electrical energy results from the location of charged particles in an electric field. When electrons move from an area of higher electric potential to an area of lower electric potential, they gain energy.
Other Forms of Energy, continued Light can carry energy across empty space. Light energy travels from the sun to Earth across empty space in the form of electromagnetic waves. Electromagnetic waves are made of electric and magnetic fields, so light energy is another example of energy stored in a field.
Conservation of Energy Key Ideas How does energy change? What is the law of conservation of energy? How much of the work done by a machine is actually useful work?
Energy Transformations How does energy change? Energy readily changes from one form to another.
Converting Mass into Energy How does the Sun unleash enough energy to light and warm Earth from so far away? A special kind of energy conversion Nuclear Fusion - A small amount of mass is transformed into a tremendous amount of energy.
Food Energy The food Calorie is a unit used by nutritionists to measure how much energy you get from various foods. 1 C = about 4,184 J Every gram of fat a person consumes can supply 9 C of energy.
Energy Transformations, continued Potential energy can become kinetic energy. Example: As a roller coaster car goes down a hill, PE changes to KE. Kinetic energy can become potential energy. Example: The KE of a roller coaster car at the bottom of a hill can do work to carry it up another hill. Mechanical energy can change to other forms of energy.
Mechanical Energy is the total amount of potential and kinetic energy in a system and can be expressed by this equation. Mechanical energy = potential energy +kinetic energy ME = KE+PE
Energy transformation occurs during projectile motion when an object moves in a curved path. When the ball leaves the bat it has mostly Kinetic Energy. As the ball rises its velocity decreases so its KE must decrease also. However, as the ball rises, the Gravitational Potential Energy increases and the KE decreases. The Mechanical Energy of the ball remains constant as it rises and falls.
ME = PE + KE PE = 100 J KE = 0 J PE = 100 J KE= 0 J PE = 50 J KE = 50 J PE = 0 J KE = 100 J
A large part of the thrill of the rollercoaster is the greater the GPE at the top of the hill the greater the kinetic energy increase as you ride down the hill.
Visual Concept: Energy Conversion in Automobile Engines
The Law of Conservation of Energy = is a universal principle that describes what happens to energy as it is transferred from one object to another or as it is transformed.
The Law of Conservation of Energy What is the law of conservation of energy? Energy cannot be created or destroyed. In other words, the total amount of energy in the universe never changes, although energy may change from one form to another.
Visual Concept: Conservation of Mechanical Energy
The Law of Conservation of Energy, continued Energy does not appear or disappear. Whenever the total energy in a system increases, it must be due to energy that enters the system from an external source. Thermodynamics describes energy conservation. For any system, the net change in energy equals the energy transferred as work and as heat. This form of the law of energy conservation is called the first law of thermodynamics.
The Law of Conservation of Energy, continued Systems may be open, closed, or isolated. open system: energy and matter are exchanged with the surroundings closed system: energy but not matter is exchanged isolated system: neither energy nor matter is exchanged Most real-world systems are open.
Efficiency of Machines How much of the work done by a machine is actually useful work? Only a portion of the work done by any machine is useful work that is, work that the machine is designed or intended to do.
Efficiency of Machines, continued Not all of the work done by a machine is useful work. because of friction, work output < work input Efficiency is the ratio of useful work out to work in. efficiency: a quantity, usually expressed as a percentage, that measures the ratio of useful work output to work input efficiency useful work output work input
Math Skills Efficiency A sailor uses a rope and an old, squeaky pulley to raise a sail that weighs 140 N. He finds that he must do 180 J of work on the rope to raise the sail by 1 m. (He does 140 J of work on the sail.) What is the efficiency of the pulley? Express your answer as a percentage. 1. List the given and unknown values. Given: work input = 180 J useful work output = 140 J Unknown: efficiency =? %
Math Skills, continued 2. Write the equation for efficiency. efficiency useful work output work input 3. Insert the known values into the equation, and solve. 140 J efficiency 0.78 180 J To express this as a percentage, multiply by 100 and add the percent sign, %. efficiency 0.78 100% 78%
Visual Concept: Mechanical Efficiency
Let s Review
A Yeti whose mass is 60 kg is moving at a speed of 3 m/s. What is the Yeti s kinetic energy? A. 270 J B. 310 J C. 450 Answer : A
What is the kinetic energy of a baseball moving at a speed of 40 m/s if the baseball has a mass of 0.15 kg? 120 J 250 J 900 J Answe r : A
An ATV moving at a speed of 20 m/s has a kinetic energy of 300,000 J. What is the ATV s mass? A. 2000 kg B. 1500 kg c. 2400 kg Answer : B
What is the velocity of a dragon and a knight if their combined mass is 300kg and they have a KE of 93750 J.
Answer 40 J What is the kinetic energy of a soccer ball which has a mass of 0.8 kg and is kicked at a velocity of 10 m/s?
An Army Sergeant has a mass of 80 kg and a kinetic energy of 4,000 J. What is his speed? 5 m/s 20 m/s 10 m/s Answer
Answer: 1000 Calculate the mass of a car that has a KE of 200,000J and a velocity of 20 m/s.
A man is running from the ghost with a velocity of 6 m/s. The man has a mass of 24 kg. What is the man s kinetic energy?
is the ability to cause change. A) Momentum B) Work C) Power D) Energy
Answer : A Which of the following objects has kinetic energy? A) a ball rolling across the floor B) a bicycle parked at the top of a hill C) leaves lying on the ground beneath a tree D) a sunny windowsill
A golf pro swings his driver which weighs.75 kg at a velocity of 60 m/s. Calculate the kinetic energy of the club.
What is the gravitational potential energy of a ceiling fan that has a mass of 7 kg and is 4 m above the ground? 350 J 274 J 456 J Answer : B =274J
Find the height of a baseball with a mass of 0.15 kg that has a GPE of 73.5 J 50 m 45 m 35 m Answer : A
What is the mass of a hiker 200 m above the ground if his GPE is 117,600 J? 50 kg 45 kg 60 kg Answer : C
Find the GPE of a coffee mug with a mass of 0.3 kg on a 1 m high desk. A. 3.67 J Answer : B B. 2.94 J C. 5.67 J
Find the kinetic energy of a bird with a mass of 0.06 kg moving at 50 m/s. Answer: A A. 75 J B. 65 J C. 45 J
Answer : A Which of the following objects has potential energy? A) a glass sitting on a table B) a ball rolling across the floor C) a bicycle coasting down a hill D) a bowling ball knocking over a pin
An 80 kg diver jumps from a 10 m high platform. What is the GPE of the diver halfway down.
A baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby has a mass of 1.22 kg. The carriage has how much potential energy?
The Law of Conservation of Energy Energy can change from one form to another, but the total amount of energy never changes. ENERGY IS NEVER DESTROYED!! (Energy is conserved)
Answer : B An 80 kg skater falls from a 10 m high railing. What is the GPE of the skater halfway down. A. 7840 J B. 3920 J C. 1960 J
What is the Mechanical energy of a 500 kg rollercoaster car moving with a speed of 3 m/s at the top of a hill that is 30 m high. A. 2250 J B. 147,000 J C. 149,250 J Answer : C
is energy stored by things that stretch or compress. A) Gravitational potential b) Elastic potential energy c) Chemical kinetic energy
Energy stored in chemical bonds is. A) chemical potential energy B) chemical kinetic energy C) energy of activation D) thermal potential energy
How much gravitational potential energy does a 75- kg diver have stepping off the edge of a 5-m platform? A) 375 J B) 15 J C) 147 J D) 3,675 J
How much kinetic energy does a moving buffalo have if its mass is 100 kg and it is moving at a speed of 5 meters per second? A) 2,500 J B) 250 J C) 1,250 J D) 125,000 J
A baseball is hit into the air with a bat. When does the baseball have the greatest gravitational potential energy? A) when it reaches its highest point B) when it leaves the bat C) when it hits the ground D) when the mechanical and kinetic energies of the baseball are equal
Answer : C As the pendulum bob swings from position A to position B, its total mechanical energy (neglecting friction) A. decreases. B. increases. C. remains the same.
Answer : B What is the SI unit of energy? A. Newtons B. Joules C. watts D. kg
What two factors determine how much potential energy an object has? A) speed and position B) speed and mass C) speed and surface area D) mass and position
During energy transformations, energy is never. A) released as heat B) used to increase an object's potential energy C) created or destroyed D) completely transformed
Kinetic energy is energy of A. Matter B. Height C. Light D. Motion
Answer: C Where does your body get energy from: A. Sun B. Air C. Food D. Water
Answer: 750 J What is the kinetic energy of a dragon going 5 m/s and has a mass of 60 kg?
Answer: 10 kg If a sled rider has a kinetic energy of 1125 joules, and is going at a velocity of 15m/s what is the riders mass?
What is the mass of a panda 200 m above the ground if his GPE is 117,600 J? 50 kg 45 kg 60 kg Answer : C
An T-Rex moving at a speed of 20 m/s has a kinetic energy of 300,000 J. What is the T-Rex s mass? A. 2000 kg B. 1500 kg c. 2400 kg Answer
A 1.8 kg reindeer climbs upwards 12 meters to look for Santa in the chimney. How much potential energy does it possess while it is on the roof?