Work and Energy

WORK Work measures the effects of a force acting over a distance. Work = F*d force units are in Newtons (N) and distance units are in meters (m) So Work units are N*m which is called a Joule 1 N * m = 1 Joule (J) (F) * (d) = Work (1kg x m/s2 x m)= 1kg x m2/s2 force units x distance unit = Work units

Why isn’t any work done when there is no motion? Work requires motion, no work no motion! Work = force x distance W = F x d Work in Joules Force in Newtons Distance in meters

Why can’t a machine never be 100% efficient or more? All energy transformation requires some energy be changed to heat due to frictional forces of resistance. If a machine were ever 100% efficient that would mean there were no frictional forces. That doesn’t even happen in space! Law of conservation of energy states that……

The Law! Energy

Work Practice Problem = (1200kg)*(9.8m/s2) = How much work is done if an object with a mass of 1200 kg is lifted 0.5 M? What data are we given? What do we need to solve the problem? d = 0.5m m = 1200kg What else do we know? (g = 9.8m/s2) How do we get it? F = m*g = (1200kg)*(9.8m/s2) = 11,760N W = F*d = (11,760N)*(.5m) = 5880J

Work Practice Problems 1.) F = 12N d = 5m W = F*d W = ? J = (12N)*(5m) = 60J 2.) F = 3N d = 3m W = F*d W = ? J = (3N)*(3m) = 9J 3.) F = 400N d = 10m W = F*d W = J = (400 N) * (10m) = 4000 J 4.) F = 7.5 N d = 18.4M W = F*d W = J = 7.5N * 18.4N = 138 J

Work Practice Problems 4.) F = 165N d = .800m W = F*d W = ? J = (165N)*(.800m) = 132J*30 =3960J

WORK Q: If you try to lift a car with 12,000N of force and it doesn’t move…How much work have you done? A: NONE!!! Because… W = 0J b/c the distance was 0m and W = 12,000N* 0m = 0J

Power Does running require more work than walking? No! So what is the difference between running and walking? A: The time it takes!!! So we need to account for the time it takes to do work… the equation that measures that is P = W (Units for Power are Joules = Watts) t sec Power = how much work is done in a given amount of time.

Power While running track, Drew’s legs do 5780J of work in 183s. What is his power output? P = W/t W = 5780 J t = 183 s P = 5780 J / 183 s = 31.6 W 2. The chain that is pulling a rollercoaster up the first hill does 24652J of work over a 79s time interval. What is the power output of the chain? P = W/t W = 24652 J t = 79 s P = 24652 J / 79 s = 312 W

Power practice problem It takes Ms. Webb 20s to apply 23N of force to lift a box 5m. What was her power output? t = 20 s F = 23N d = 5m W= F * d = 23N x 5m = 115 J P = W / t = 115J / 20s = 5.75 W

Power Problems Remember a Watt= Joule/seconds 1. P= W 3960J =66.0 W T 60.0s 2. P= W 900MJ =900 MW T 1s 3. P= W 5350J =107 W T 50.0s 4a. ***Challenge Question*** Hint* W=F x D W= F(60.0N) x D(12.0m)=720J P= W 720J =36 W T 20.0s

ENERGY What do you transfer when you do work? ENERGY!!! Energy is the ability to do work. There are several types of energy: Mechanical, Electrical, Chemical, Thermal (heat), Gravitational, light, sound, wave Potential and Kinetic.

POTENTIAL energy (PE) Potential Energy (PE) is the stored energy of an object resulting from the position of the object in a system. PE is measured by multiplying the mass of the object times the gravity and then times the height. PE = m*g*h (g = 9.8m/s2) Units are Joules!!! (J)

POTENTIAL energy (PE) Examples of objects with high PE: Water being held back by a dam A stretched rubber band Any hanging object Any compressed object (like a spring) Compressed Rock Trapped gasses Any object that is high up

Solving Energy Problems Plug PE = m*g*h into a Power Triangle Write the equations when you solve for m and h. P E m g h

Solving Energy Problems h m = PE h = PE g*h g*m do this 1st do this 1st

Calculating PE Which apple has more PE? Apples have a mass= 1.5kg Apple “A” height= 15m Apple “B” height= 20m Remember PE=mgh So… Apple “A” PE= 220.5J Apple “B” PE= 294 J So the winner is…Apple “B” Apple “B” Apple “A” 20m 15m

KINETIC energy (KE) Kinetic Energy (KE) is the energy of any moving object. KE = ½m * v2 Units are Joules!!! (J) KE depends on the mass and the velocity (speed) of an object. In the equation the value for velocity is squared… so if the velocity of an object changes it has more of an effect on the KE than an equivalent change in mass. (If mass doubles then KE doubles but if velocity doubles then KE quadruples!)

Solving Energy Problems Plug KE = ½ m * v2 into a Power Triangle Write the equations when you solve for m and v. K E 1/2 m v 2

Solving Energy Problems KE = ½ m * v2 ***Remember PEMDAS (order of operations) Calculator help: .5*20*2x2 Page 89: Calculate the energy of the full cart if it has a mass of 20 Kg and the man with the tight shorts is pushing it with a velocity of 2 m/s If the mass doubles, what is the new value of KE? If the velocity doubles, what is the new value for KE?

Answers to KE calculations 400 kgm2/s2 or just 400 J 800 kgm2/s2 or just 800 J (that is twice as much!) 1600 kgm2/s2 or just 1600 J (that is four times as much as the original 400 J !)

PE, KE and P Calculations 1. PE= 6856 J 2. m= 4.7 kg 3. h= 19.2m 4. PE=7763 J 5. m=.348 kg 6. h= 24.7 m Power 13. P= 0.84 watts 14. P= 6.6 watts KE 7. KE=18021 J 8. KE= 1292 J 9. KE=5006 J 10. KE=38423 J 11. KE=1701 J 12. KE=2795 J Power 15. P= 0.003 watts 16. P=143987 watts

Elastic Potential Energy Elastic potential energy is Potential energy stored as a result of deformation of an elastic or stretchy object. What’s deformation? A change in the shape or size of an object due to an applied force, such as the stretching of a spring or rubber band. Can you thin k of any other examples of Elastic PE?

Elastic Potential Energy Elastic Potential energy can be determined from the objects stretch squared and the constant that reflects the elasticity of the material. What’ this mean in English? Elastic PE= 1/2kx2

Elastic Potential Energy What does x represent? What does mg represent? What does F represent? Why is the purple F arrow pointing in the opposite direction as the red mg arrow? Why are these arrows equal but opposite?

Energy Lab 1. Decide lab jobs 2. Calculate height at different angles in meters. (Convert cm to m) 3. Find average time (s). Three trials. 4. Clean up lab. 5. Calculate velocity. 6. Calculate PE at different angles. 7. Calculate KE at different angles. 8. Remember your UNITS!

Warm-Up 1. A 3.4 kg defensive lineman moving at 2.1 m/s2 sacks the quarterback, who is standing still. What is the net force of the collision? 2. Give an example of a specific object that has high PE. 3. Give an example of a specific object that has high KE.

Units Review Force = Newtons (N) 1 Newton = 1 kg x m/s2 1 Joule = 1 kg x m2/s2 Speed or velocity = distance/time (d/t = m/s) Energy (Work, KE, PE, TE, EE ) = Joules (J) Mass = kilograms (kg) Distance or height = meters (m) Time = seconds (s) Power = Watts (W)

Chemical Energy vs. Nuclear Energy is energy stored in the bonds of atoms and molecules. It is the energy that holds and electrons together that move around the nucleus. Ex: any chemical reaction Nuclear Energy is energy stored in the nucleus of an atom––the energy that holds the nucleus together. The energy can be released when the nuclei are combined or split apart.

Salem Nuclear Power Plant Nuclear power plants split the nuclei of uranium atoms in a process called fission. The sun combines the nuclei of hydrogen atoms in a process called fusion. Scientists are working on creating fusion energy on earth, so that someday there might be fusion power plants.

There are three ways that energy can be transferred: ENERGY TRANSFER There are three ways that energy can be transferred: Conduction – The transfer of energy through matter by direct contact of particles. Radiation – The transfer of energy in the form of a wave. Convection – The transfer of energy by the movement of gases or liquids.

EXAMPLES of ENERGY TRANSFER Conduction: a pot on a stove, a metal spoon in a bowl of soup…the handle gets hot too. Radiation: how the Earth gets energy from the sun Convection: Example is when heat leaves the coffee cup as the currents of steam and air rise and the coffee cools off. Hot air rises (less dense) and cool air sinks (more dense)!

LAW OF CONSERVATION of ENERGY Energy cannot be created or destroyed; it can only be transformed from one type to another or transferred. (The TOTAL ENERGY (TE) stays the same!!!) TE = PE + KE + heat TE= the PE at the highest point in a system! So when an object falls… how is energy transformed? It goes from PE to KE…

LAW OF CONSERVATION of ENERGY Let’s look at some systems where energy transformation is taking place…(i.e. changing from one type of energy to another type of energy.) A Bungee jumper A Pendulum A Hydroelectric Power Plant

PE, KE, and TE Calculations ***For A-E calculate: PE, KE, and TE (assume NO friction) A. h=100m m = 2kg g = 9.8 m/s2 B. mid-point C. D. E. h=0m

LAW OF CONSERVATION of ENERGY The TOTAL ENERGY of a system can be measured by adding PE + KE + Heat. Remember…TE= the PE at the highest point in a system! And TE=ALWAYS stays the same in a system! TE = KE + PE + heat Q: Where does the heat come from??? A: Friction!!! (Rub your hands together and see what happens!!!)

HYDROELECTRIC POWER PLANT Electrical Energy Kinetic Energy Potential Energy Mechanical Energy

Efficiency Let’s talk about reasonable efficiencies… Can any system be 100% efficient? NO… b/c some energy is given off from the system in the form of heat as a product of friction. Would it be reasonable to have a system that has a very low efficiency? No… b/c then you are wasting energy.

LAW OF CONSERVATION of ENERGY Why won’t the beginning energy ever equal the end energy??? Hint: Can heat be contained in an open system? NO… please remember that energy is not destroyed, but some of it can escape from the system to the surroundings in the form of heat. This is why no system will ever be 100% efficient… meaning the beginning energy will never equal the end energy…there is no such thing as a frictionless system!!!

Efficiency Let’s talk about reasonable efficiencies… Of the following efficiencies, which is most reasonable? .32% 100% 41% 89%

Solving Energy Problems K E 1/2 m v 2 ½ m = KE v2 = KE v2 ½ m

KINETIC Energy Lab Data Fill in on DATA TABLE 2 1. v = .140 m/s 2. v = 1.27 m/s 3. v = 1.74 m/s 4. v = .597 m/s 5. v = 1.74 m/s