Conservation of Energy

Work To do work on an object you need an application of a force AND movement due to the force. Example: Lifting a barbell. A force is applied to the barbell and the barbell moves in the direction of the force If there is no movement, there is NO work being done on an object.

Work: force times displacement; when a force is applied at a constant velocity in the same direction. The movement must be along the same plane as the force applied. Units: Joule (J) Equation: W = Fd W = Work (J) F = Force (N) d = Distance (m)

Check Your Understanding A man holds a 50 lbs box in the air. Is he doing any work? No. Even though his muscles are getting tired, according to physics he is not doing any work because there is no displacement of the box. No movement means no work.

Work, Force and Displacement Work is directly proportional to force (displacement stays the same). 2F = 2W ½F = ½W Work is directly proportional to displacement (force stays the same). 2d = 2W ½d = ½W

Check Your Understanding Work is done lifting a barbell. How much more work is done lifting a twice as heavy barbell the same distance? Twice as much work. Force and work are directly proportional, so if you double force then you double the work. W = F d 2W = 2F d

Check Your Understanding How much work is done lifting a twice as heavy barbell twice as far? Four times as much work W = F d 4W = 2F 2d In this case, both the force and the distance were doubled thereby causing four times as much work to be done.

Check Your Understanding An object is accelerating for 5 meters. If a force of 30 N is being applied to the object, what is the work done on the object? W= ? F = 30 N d = 5 m W = Fd W = (30 N)(5m) = 150 J

Power The quantity work has to do with a force causing a displacement. Work has nothing to do with the amount of time that this force acts to cause the displacement. Power describes how quickly work gets done.

Power: the rate at which work is done. The less time it takes for work to be done, the greater the power. Unit: Watt (W) Equation: P = W / t P = Power (Watts) W = Work (Joules) t = time (seconds)

Power, Work, and Time Power is directly proportional to work 2W = 2P Power is inversely proportional to time 2t = ½P ½t = 2P

Check Your Understanding Two physics students, Will N. Andable and Ben Pumpiniron, are in the weightlifting room. Will lifts the 100-pound barbell over his head 10 times in one minute; Ben lifts the 100-pound barbell over his head 10 times in 10 seconds. Which did the most work? Which student delivers the most power? Explain. Both did the same amount of work (Fd). Ben did his work more quickly, so he used more power.

Check Your Understanding Identical twins are late to class. One twin runs up the stairs while the other twin walks up the stairs. Which twin did more work? Both twins applied the same force over the same distance. The twins did the same amount of work. Which twin used more power? Both twins did the same amount of work; however, the twin that ran did the work more quickly and therefore used more power.

Check Your Understanding If an object has a work of 20 J exerted on it for a time of 4 seconds, what is the power? P = ? W = 20 J t = 4 s P = W/t P = 20 J/4s = 5 Watts

Mechanical Energy Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position). Mechanical energy: the energy which is possessed by an object due to its motion or its stored energy of position Mechanical energy is the ability to do work SI Unit: Joule (J) Ex: KE and PE

Potential Energy Potential energy: stored energy due to position. PE has the potential to do work SI Unit: Joule (J) Ex: Elastic and Gravitational Potential Energy

Gravitational Potential Energy Gravitational potential energy: energy that is stored in an object due to its height An object has the potential to fall SI Unit: Joule (J) Equation: PEG = mgh PEG = Gravitational PE (J) M = mass (kg) G = acceleration due to gravity (10m/s2) H = height (m)

Check Your Understanding If a ball with a mass of 2 kg is raised to a height of 10 m, what is the gravitational PE of the ball? PEG = ? m = 2 kg g = 10 m/s2 h = 10 m PEG = mgh PEG = (2 kg)(10 m/s2)(10 m) = 200 J

Elastic Potential Energy Elastic Potential Energy: the potential energy stored in an elastic object due to change in shape. Elastic PE exists in objects that can be stretched and will return to their original shape SI Unit: Joule (J) Ex: rubber bands, springs

Check Your Understanding Does a car hoisted for lubrication in a service station have elastic or gravitational PE? Gravitational How much more work will raise the car twice as high? Twice as much work How much more potential energy will it have then? Twice as much potential energy

Check Your Understanding Which type of potential energy does a bow stretched to shoot an arrow have? Both elastic and gravitational PE. It has elastic because it is stretched and has the potential to move back to its original position, and it has gravitational because it is at a height and has the potential to fall.

Work and PE The amount of PE an object has is equal to the work done to raise the object a vertical distance. The object has the potential to do work. The same amount of work was done in the picture below because all the balls are at the same vertical height. All the balls have the same PE

Kinetic Energy Kinetic energy: energy of an object in motion An object MUST be moving to have KE An object with KE also has momentum SI Unit: Joule (J) Equation: KE = ½mv2 KE = Kinetic energy (J) m = mass (kg) v = velocity (m/s)

Check Your Understanding How much kinetic energy does a 1 kg cart have moving at 1 m/s? KE = ? m = 1 kg v = 1 m/s KE = ½mv2 KE = ½(1)(12) = ½ Joule

KE, Mass & Velocity 2v = 22KE = 4KE 3v = 32KE = 9KE 4v = 42KE = 16KE KE is directly proportional to mass 2m = 2KE ½m = ½KE KE is directly proportional to velocity squared 2v = 22KE = 4KE 3v = 32KE = 9KE 4v = 42KE = 16KE

Work and KE An object that is changing its KE is changing: Its mass Its velocity Both mass and velocity If an object is changing its velocity, it is accelerating, so a force is applied to it So there is work done on it A change in KE means work is done by the object

KE and Stopping Distance KE is equal to the amount of work required to increase the speed of a moving object or the work the object can do while being brought to rest. Consider a car that doubles its speed. 2v = 22KE = 4KE. If 4KE, then 4W. So an object moving TWICE as fast takes FOUR times as much work to stop. If this car were to skid, it would travel FOUR times as far.

Check Your Understanding You are traveling behind a truck on the highway. Knowing that you need to leave 100 ft when traveling at 30 mph to stop, you figure that you can leave 200 ft between you and the next car if you are going 60 mph…in case you need to suddenly stop. The truck in front of you suddenly stops to avoid an accident. You slam on the breaks to avoid hitting the truck, but you still plow into it anyway. Why?

Because your speed had doubled, you had not just double the KE, but 4 times as much KE. Because of this, you actually needed not just double the stopping distance, but 4 times the stopping distance.

Work-Energy Theorem Work-energy theorem: whenever work is done, the energy of a system changes. If you change the PE, you are doing work If you change the KE, you are doing work Ex: An object that changes it KE is moving, thus doing work. An object being lifted or stretched to gain PE is having work done on it. Equations: W = ΔKE; W= -ΔPE

Remember, both work and energy are measured in Joules Movement must have taken place for a change in energy, and therefore work, to have taken place.

Check Your Understanding Does a car slowing down on a rough surface have work being done on it? Yes! The car is slowing down, so it is changing its KE. A change in KE results in work being done on the car by the road Does a student sitting at the top of the stairs have work being done on them? No! They are not moving so they are not changing their KE or PE, so no work is being done.

The Law of Conservation of Energy Law of Conservation of Energy: energy cannot be created or destroyed but can change forms Energy changes from one form to another Ex: PE changes to KE at the bottom of a hill Equation: ME = PE + KE ME before = ME after (PE + KE)before = (PE + KE)after

The total ME (mechanical energy) remains the same throughout a system. It’s just a matter of how much is KE and how much is PE Ex: At the top of a pendulum swing, there are 50 J of PE; there is no KE b/c it is not moving. At the bottom of the swing, all the PE has converted to all KE. So the KE is 50 J and the PE is 0 J. In the middle of the swing, it would be 25 J of PE and 25 J of KE.

Check Your Understanding At the very top of a roller coaster, a girl has a potential energy of 100 J. What would be her kinetic energy at the very bottom of the hill (assuming there is no energy lost to air resistance)? 100 J. Since energy is neither created nor destroyed, all the potential energy at the top of the roller coaster will be converted into all kinetic energy.

Check Your Understanding What would the KE be if there was air resistance? Then there would be less than 100 J because some energy would be lost to heat of friction (like when you rub your hands together).