1. Herriman High Honors Physics Chapter 5 Work, Power and Energy What You Need to Know

2. Herriman High Honors Physics Energy Facts There are different types of energy Energy of all types is measured in Joules Law of Conservation of Energy – Energy can be neither created nor destroyed, merely changed from one form to another

3. Herriman High Honors Physics Types of Energy (Unit Overview) Mechanical Potential Energy Energy of Position Gravitational Elastic Kinetic Energy Energy of Motion If it moves it has kinetic energy Heat Energy Heat is a form of Energy Transfer Other Forms of Stored Energy Chemical Fuels - usually release energy by combusion Food – energy released by digestion Electrical Generated from other forms of energy

4. Herriman High Honors Physics Work The Physics definition of work requires a displacement, i.e. an object must be moved in order for work to be done! The Applied force which causes the displacement contributes to the work, i.e. in order to contribute to the work, the applied force must be parallel to the displacement.

5. Herriman High Honors Physics Work: A Mathematical Definition Work = (Force)(Displacement) Units of Work = (Newton)(Meter) 1 NewtonMeter = 1 Joule A Joule is a unit of Energy and it takes energy to do work and work done on an object either causes it to move (kinetic energy) or is stored (potential energy)

6. Herriman High Honors Physics Work done Parallel to the Applied Force Sample Problem What work is done sliding a 200 Newton box across the room if the frictional force is 160 Newtons and the room is 5 meters wide? W = F f ΔX = (160 N)(5 m) 800 Joules

7. Herriman High Honors Physics Work (Not Parallel to the Applied Force) Sample Problem How much work is done on a vaccum cleaner pulled 3.0 meters by a force of 50 N at an angle of 30° above the horizontal? Solve Given: F = 50 N θ = 30° Δx = 3 m Find W W = F cos θ (Δx) = (50 N)(cos 30°)(3 m) = 130 Joules Try: p. 162 Practice A Problems 1 & 3

8. Herriman High Honors Physics Kinetic Energy Kinetic Energy is energy of Motion Any moving object has kinetic energy Dependent on the mass of the object and its velocity. Mathematically expressed as: E k = ½ mv 2

9. Herriman High Honors Physics Sample Problem What is the kinetic energy of a car with a mass of 2000 kg moving at 30 m/s? E k = ½ mv 2 = (½)(2000 kg)(30 m/s) 2 = 900,000 Joules Try: p. 166 Practice B Problems 1, 3 & 5

10. Herriman High Honors Physics Work – Energy Theorem The net work done on a body equals its change in kinetic energy. Mathematically: W net = ΔKE Net work = change in kinetic energy

11. Herriman High Honors Physics Work-Energy Theorem Sample Problem On a frozen pont, a person kicks a 10 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10? Try: p. 168 Practice C Problems 2 & 4

12. Herriman High Honors Physics Energy of Position: Gravitational Potential Energy Occurs due to the accelerating force of gravity Is determined by the position of the object in the gravitational field Is a form of stored energy Mathematically determined by: PE g = mgh where m is mass, g is the acceleration due to gravity and h is the height above a determined baseline.

13. Herriman High Honors Physics Sample Problem What is the potential energy of a 10 kg rock sitting on a cliff 30 meters high? The acceleration due to gravity is 9.8 m/s 2. E p = mgh = (10 kg)(9.8 m/s 2 )(30 m) 2940 Joules

14. Herriman High Honors Physics Elastic Potential Energy Bungee cords, rubber bands, springs any object that has elasticity can store potential energy. Each of these objects has a rest or “zero potential” position When work is done to stretch or compress the object to a different position elastic potential energy is stored

15. Herriman High Honors Physics Elastic Potential Energy Top picture is “rest position”; x = 0 This is a point where the elastic potential energy = 0 Bottom picture is “stretched position” Here elastic potential energy is stored in the spring PE elastic = ½ kx 2 where k is the “spring constant” in N/m

16. Herriman High Honors Physics Sample Problem What is the Elastic potential energy of a car spring that has been stretched 0.5 meters? The spring constant for the car spring is 90 N/m. PE elastic = ½ kx 2 = (½)(90 N/m)(0.5 m) 2 =11.25 Joules

17. Herriman High Honors Physics Where Does “K” Come From? K is measured in Newtons/meter. It is defined as the force required to displace a spring 1 meter. So: K = F/x Often K is determined by hanging a known weight from the spring and measuring how much it is stretched from its rest postion.

18. Herriman High Honors Physics Sample Problem A spring is hung from a hook and a 10 Newton weight is hung from the spring. The spring stretches 0.25 meters. What is the spring constant? If this spring were compressed 0.5 meters, how much energy would be stored? If this spring were used to power a projectile launcher, which fires a 0.2 kg projectile, with what velocity would the projectile leave the launcher? Assume 0.5 m compression.

19. Herriman High Honors Physics Solution K = F/x K =10 N/0.25 m = 40 N/m E p = ½ Kx 2 E p = ½ (40 N/m)(0.5 m) 2 = 5 Joules E p = E k = ½ mv 2 5 Joules = ½ (0.2 kg)(v 2 ) V = 7.05 m/s Try: p. 172 Practice D Problems 1 & 3

20. Herriman High Honors Physics Conservation of Energy To say something is conserved is to say that it stays the same. In the absence of friction, mechanical energy (kinetic, gravitational, elastic) is always conserved. Mathematically: ME i = ME f Most commonly we talk about a combination of kinetic and gravitational energies so this becomes:

21. Herriman High Honors Physics Conservation of Energy Sample Problem Starting from rest a child zooms down a frictionless slide from an initial height of 3 meters. What is her speed at the bottom of the slide? Assume she has a mass of 25 kg. Answer: 7.67 m/s Try: p. 177 Practice E Problems 1, 3 & 5

22. Herriman High Honors Physics Power Power = Work/time = Joules/Second = watt Mathematically there are two formulas for Power: or since then

23. Herriman High Honors Physics Power Sample Problem A 193 kg curtain needs to be raised 7.5 meters at a constant speed, in as close to 5 seconds as possible. The power ratings for three motors as listed as 1 kW, 3.5 kW, and 5.5 kW. Which motor is best for the job? Given: M = 193 kg T = 5 sec Δx = 7.5 meters So: P = W/t = FΔx/t = mgΔx/t Substituting: P = (193 kg)(9.8 m/s 2 )(7.5 m)/5 sec = 2.8 kW Which means that the 3.5 kW motor is best for the job Try: p. 181 Practice F Problems 2 & 4