Work, Power, and Machines: Understanding Energy and Mechanical Advantage

1. Chapter 12Work and Energy Table of contents Section 1 : Work, power, and machines Section 2 : simple machines Section 3 : What is energy? Section 4 : conservation of energy

2. Objectives Define work and power Calculate the work done on an object and the rate at which work is done Use the concept of mechanical advantage to explain how machines make doing work easier Calculate the mechanical advantage of various machines Section 1 : Work, Power, and Machines

3. What is Work? Work is the transfer of energy to a body by the application of a force that causes the body to move in the direction of the force Work is done only when a force causes an object to move in the direction of the force. This is different from the everyday meaning of work. Work Equation work = force x distance w = F x d Section 1 : Work, Power, and Machines

4. What is Work?, continued Work is measured in joules, J. Definition of joules 1 J = 1 N x m = 1 kg x Because work is calculated as force x distance, it is measure in unites of Newtons x meters, N x m. These units are also called joules, J. In terms of SI base units, a joule is equivalent to 1 kg x . Section 1 : Work, Power, and Machines

5. Calculating Work : Math Skills • Imagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift, assuming he lifts her 2.0 m and exerts an average force of 190 N? • Step 1 : List the known and unknown values Force = 190 N distance = 2.0 m Work = ? J • Step 2 : Write the equation for work Work = Force x distance • Step 3 : Insert your information into the equation, and solve. Work = 190 N x 2.0 m = 380 J Section 1 : Work, Power, and Machines

6. Power • Power is a quantity that measures the rate at which work is done or energy is transformed. • Power equation Power = • Power is measured in watts. • A watt (W) is equal to a joule per second (1 J/s) Section 1 : Work, Power, and Machines

7. Calculating Power : Math Skills • It takes 100,000 J of work to lift an elevator 18m. If this is done in 20s, what is the average power of the elevator during the process? • Step 1 : List the known and unknown values Work= 100,000 J time = 20 sPower = ? W • Step 2 : Write the equation for power Power = • Step 3 : Insert your information into the equation, and solve. Power = = 5,000 W Section 1 : Work, Power, and Machines

8. Machines and Mechanical Advantage • Machines multiply and redirect forces • Machines help people by redistributing the work put into them • They can change either the size or direction of the input force • Different forces can do the same amount of work • A machine allows the same amount of work to be done by either • decreasing the distance while increasing the force or by • decreasing the force while increasing the distance Section 1 : Work, Power, and Machines

9. Force and Work Diagram Section 1 : Work, Power, and Machines

10. Machines and Mechanical Advantage, continued • Mechanical Advantage tells how much a machine multiplies force or increases distance • Mechanical Advantage Equation Mechanical Advantage = • Mechanical Advantage (MA) has NO units! • The equation is dividing force by force (N/N) or distance by distance (m/m) so they cancel- there is no unit for mechanical advantage Section 1 : Work, Power, and Machines

11. Calculating Mechanical Advantage : Math Skills • Calculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high • Step 1 : List the known and unknown values Input distance= 5.0 moutput distance = 1.5 m MA= ? • Step 2 : Write the equation for mechanical advantage MA = • Step 3 : Insert your information into the equation, and solve. MA = = = 3.3 Section 1 : Work, Power, and Machines

12. Objectives Explain the relationship between energy and work Define potential energy and kinetic energy Calculate kinetic energy and gravitational potential energy Distinguish between mechanical and nonmechanical energy Section 3 : What is Energy?

13. Energy and Work • Energy is the ability to do work • When you do work on an object, you transfer energy to that object • Whenever work is done, energy is transformed or transferred to another system • Energy is measured in joules, J. • Because energy is a measure of the ability to do work, energy and work are expressed in the same units. Section 3 : What is Energy?

14. Potential Energy • The energy that an object has because of the position, shape, or condition of the object is called potential energy • Potential energy is stored energy • Elastic potential energy is the energy stored in any type of stretched or compressed elastic material, such as a spring or a rubber band • Gravitational potential energy is the energy stored in the gravitational field which exists between any two or more objects ******* Section 3 : What is Energy?

15. Potential Energy, continued • Gravitational potential energy depends on both mass and height • Gravitational potential energy equation GPE = mass x free-fall acceleration x height GPE = mgh • The height can be relative • The height used in the above equation is usually measured from the ground • However, it can be a relative height between two points, such as between two branches in a tree Section 3 : What is Energy?

16. Calculating GPE : Math Skills • 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? • Step 1 : List the known and unknown values mass= 65 kggravity= 9.8 m/s2height= 35 m GPE= ? J • Step 2 : Write the equation for gravitational potential energy GPE = mgh • Step 3 : Insert your information into the equation, and solve. GPE = 65 kg x 9.8 m/s2 x 35 m = 22,000 J Section 3 : What is Energy?

17. Kinetic Energy The energy of a moving object due to the object’s motion is called kinetic energy Kinetic energy depends on mass and speed Kinetic Energy equation Kinetic Energy = KE = Kinetic energy depends more on speed than mass Section 3 : What is Energy?

18. Kinetic Energy Graph Section 3 : What is Energy?

19. Calculating Kinetic Energy : Math Skills • What is the kinetic energy of a 44 kg cheetah running at 31 m/s? • Step 1 : List the known and unknown values mass = 44 kg speed = 31 m/s Kinetic energy = ? W • Step 2 : Write the equation for kinetic energy KE = • Step 3 : Insert your information into the equation, and solve. KE = Section 3 : What is Energy?

20. Other Forms of Energy • The amount of work an object can do because of the object’s kinetic and potential energies is called mechanical energy • Mechanical energy is the sum of the potential energy and the kinetic energy in a system • In addition to mechanical energy, most systems contain nonmechanical energy • Nonmechanical energy does not usually affect systems on a large scale Section 3 : What is Energy?

21. Other Forms of Energy, continued • Atoms and molecules have kinetic energy • The kinetic energy of particles is related to heat and temperature • 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 Section 3 : What is Energy?

22. Other Forms of Energy, continued • The sun gets energy from nuclear reactions • The sun is fueled by nuclear fusion reactions in its core • Electricity is a form of energy • Electrical energy is derived from the flow of charged particles, as in a bolt of lightning or in a wire • Light can carry energy across empty space • Light energy travels from the sun to Earth across empty space in the form of electromagnetic waves Section 3 : What is Energy?

23. Objectives Identify and describe transformations of energy Explain the law of conservation of energy Discuss where energy goes when it seems to disappear Analyze the efficiency of machines Section 4 : Conservation of Energy

24. Energy Transformations • Energy readily changes from one form to another • Potential energy can become kinetic energy • As a car goes down a hill on a roller coaster, potential energy changes to kinetic energy • Kinetic energy can become potential energy • The kinetic energy a car has at the bottom of a hill can do work to carry the car up another hill Section 4 : Conservation of Energy

25. Energy Graphs Section 4 : Conservation of Energy

26. Energy Transformations, continued • Energy transformations explain the flight of a ball • Mechanical energy can change to other forms of energy • Mechanical energy can change to nonmechanical energy as a result of friction, air resistance, or other means. Section 4 : Conservation of Energy

27. Kinetic and Potential Energy Graph Section 4 : Conservation of Energy

28. The Law of Conservation of Energy • The law of conservation of energy states that energy cannot be created or destroyed • Energy doesn’t appear out of nowhere • Whenever the total energy in a system increases, it must be due to energy that enters the system from an external source • Energy doesn’t disappear, but it can be changed to another form Section 4 : Conservation of Energy

29. The law of conservation of energy, continued • Scientists study energy systems • Boundaries define a system • Systems can be open or closed • When the flow of energy into and out of a system is small enough that it can be ignored, the system is called a closed system • Most systems are open systems, which exchange energy with the space that surrounds them Section 4 : Conservation of Energy

30. Efficiency of Machines • Not all of the work done by a machine is useful work • A machine cannot do more work that the work required to operate the machine • Because of friction, the work output of a machine is ALWAYS somewhat less that the work input • Efficiency is the ratio of useful work out to work in. • Efficiency is usually expressed as a percentage (%) • The efficiency of a machine is a measure of how much useful work it can do Section 4 : Conservation of Energy

31. Efficiency of Machines, continued • Efficiency Equation efficiency = • Perpetual motion machines are impossible • Energy is always lost to friction or air resistance • Machines need energy input • Because energy always leaks out of a system, every machine needs at least a small amount of energy input to keep going Section 4 : Conservation of Energy

32. Calculating Efficiency : Math Skills • A sailor uses a rope and an old, squeaky pulley to raise a sail that weight 140 N. He finds that he must do 180 J of work on the rope in order to raise the sail by 1 m (by doing 140 J or work on the sail). What is the efficiency of the pulley? Express your answer as a percentage. • Step 1 : List the known and unknown values Work input= 180 J useful work output = 140 Jefficiency = ? • Step 2 : Write the equation for kinetic energy efficiency = • Step 3 : Insert your information into the equation, and solve. efficiency = Section 4 : Conservation of Energy

33. Concept Map