2.3 Work, Energy and Power

2.3 Work, Energy and Power 2.3.1 Outline what is meant by work. Work…  First a demo: Everybody stand up . Hold a couple of books and walk across the room. . How much work was done to the book? . Any? A lot? A little? None?  Is the product of the magnitude of the displacement and the component of the force acting in the direction of the displacement  Is the force applied over a distance  When a force acts upon an object to cause a displacement of the object  two key ingredients:  ______ ______ Everyday examples: 1. a horse pulling a plow through the field 2. a father pushing a grocery cart down the aisle of a grocery store 3. a weightlifter lifting a barbell above his head 4. Olympian launching the shot-put . Can you identify the two parts in each example?  Are these examples of work? 1. A teacher applies a force to a wall and becomes exhausted. Y or N 2. A book falls off a table and free falls to the ground. Y or N 3. A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed. Y or N 4. A rocket accelerates through space. Y or N  Or… W = F s cosΘ  s is displacement or Δs  F is force applied  Θ is the angle between the force and the displacement vector  Notice that the ______of a force alone does not constitute work.  Work can only be done when looking at the force applied ______to the displacement.  Most of the time F is in the direction of d so θ = 0° and cos 0° = 1 so… it all works out.  Consider theta: (draw the chart)  Three basic situations

 Pay attention to the direction of the displacement and the applied force. . Ex. A car being pushed up a ramp  Consider “the sign”:  If force and displacement are in the… . Same directions, + W . ______directions, - W . Perpendicular directions, W = 0

 From all that we can say that the total work done is dependent on the total force applied. So…. . Wnet = Fnet d cosΘ  So, what are the units?  If we break it down W = F * d => ? = N * m => J = N * m  Basic question:  What work is done to lift your Physics book (m=12kg) up 1 m?

 What work is done to carry the book 1 m across the room?

2.3.3 Solve problems involving the work done by a force.  Try this: What is the work done on a vacuum cleaner pulled 3m by a force of 50N at an angle of 30° above the horizontal?

. The angle of the force means we have to find the force acting in the direction that the bag moves. It moves in the x-position, so we will use the Fx component. The upward component doesn’t do any work as the y-position doesn’t change. A few more Practice Problems: 1) A 20kg suitcase is raised vertically 3m above a platform by a conveyor belt. How much work is done on the suitcase? 2) A 100 N force is applied to move a 15kg object a horizontal distance of 5m at constant speed. 3) A 100N force is applied at an angle of 30° to the horizontal to move a 15kg object at a constant speed for a horizontal distance of 5m. 4) An upward force is applied to lift a 15kg object to a height of 5m at constant speed. Work Space

2.3.2 Determine the work done by a non - constant force by interpreting a force–displacement graph.  This work equation is only applicable if the force is constant.  In real life there are lots of non-constant forces.  We can use a graph to determine work done.  On a Force/Displacement graph the area under the graph is the work done. 2.3.7 List different forms of energy and describe examples of the transformation of energy from one form to another. Energy – Flow Chart

2.3.4 Outline what is meant by kinetic energy. Kinetic Energy  Associated with objects in ______ Depends on both an object’s ______and ______ It is a ______quantity  Formula  Kinetic energy = 1/2 *mass*speed2  KE= ______ The unit of KE is joule(J)  Notice: If the speed is doubled the energy is ______Example: A bowling ball and a volleyball roll at the same speed.  Which has more kinetic energy? ______2.3.11 Solve problems involving momentum, work, energy and power. Example: A 7kg bowling ball moves at 3 m/s. How fast must a 2.45 g ping pong ball move to have the same kinetic energy as the bowling ball?  KE=1/2 mv2

 Practice: 1) Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s. 2) If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy? 3) Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 12000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed? 4) A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic energy if it is moving at 30 mi/hr. (HINT: use the kinetic energy equation as a "guide to thinking.") 2.3.5 Outline what is meant by change in gravitational potential energy. Potential Energy  Associated with an object that has the potential to move because of its ______ Depends on the interaction with its ______ store energy as the result of its position  Gravitational potential energy - Potential energy due to ______ the energy stored in an object as the result of its vertical position or height.  PEg = mass*free-fall acceleration*height  PEg = ______ Notice that PEg is dependant on free-fall acceleration being ______. Meaning this usually only applies to things ______.  Also notice that g and h ______properties of the actual object.  The higher that an object is elevated, the ______the gravitational potential energy . a doubling of the height will result in a ______of the gravitational potential energy

Is it possible to have a negative potential energy? ______ Can an object have both a positive potential energy and a negative potential energy?  How is h defined? - Relative to a “zero”  What can be a “zero”? - Anything can be defined as “zero”  Discussion: A ball that falls from one building rooftop to another buildings rooftop. Where is zero? (Draw the picture)

Springs!!! – Elastic Potential Energy  a device which can store elastic potential energy due to either ______or ______ ______is required to compress a spring  the amount of force is ______to the amount of stretch or compression  ______– when a spring isn’t being stretched or compressed  Fspring = k * x . ______is the spring constant  Small for flexible springs  Large for stiff springs  Units of (N/m) . ______is the amount stretched or compressed  ______length  Length of spring when no external forces are acting on it.  Nothing is pulling or pushing it.

2.3.11 Solve problems involving momentum, work, energy and power. PEtotal = PEg + PEspring 2  PEelastic = ½*spring constant*(distance compressed or stretched) 2  PEelastic = ½kx Practice Problems  A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?  If a force of 14.7 N is used to drag the loaded cart (from previous question) along the incline for a distance of 0.90 meters, then how much work is done on the loaded cart?  A 70kg stuntman is attached to a bungee cord with an un-stretched length of 15m. He jumps off a bridge spanning a river from a height of 50m. When he finally stops, the cord has a stretched length of 44m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8N/m, what is the total potential energy relative to the water when the man stops falling?

2.3.6 State the principle of conservation of energy. Energy  The ability to do ______. Potential energy is the energy of position . Kinetic energy is the energy of motion (depends on speed and mass)  ______energy= Potential + Kinetic energy The Law of Conservation of Energy  States that energy can be neither ______nor ______, it is conserved  Energy can transform from one form to another, but it always adds up to the ______amount. Ex.Mechanical energy is converted into thermal energy whenever you bounce a ball. Each time the ball hits the ground, some of the energy of the ball's motion is converted into heating up the ball, causing it to slow down at each bounce  Energy Transformation - Energy can neither be created nor destroyed, but it can be changed into different forms of energy…  The forms include: thermal (heat), chemical, electrical, sound, light, nuclear

Conservation of Energy  Mechanical Energy is:  the energy which is possessed by an object due to its ______or due to its ______.  the total kinetic energy and potential energy associated with an object  ME = KE + PEtotal . Mechanical energy is just a classification, not another type of energy.  Nonmechanical energy:  Other forms of energy  Ex. light, sound, heat  Mechanical energy is conserved (in the absence of friction)  So => initial mechanical energy = final mechanical energy  So => MEi = MEf  So => KEi + Ptotal,i = KEf + Petotal,f

Ex.The question is if a 75g egg falls off a 1m counter top what is it’s total ME half way down?  To better understand lets remember a few things.  First Vf = Vi + aΔt  Second Δx = ½ (Vi + Vf)Δt

Time Vf KE Δx Height PE ME 0s .1s .2s .3s .4s .5s

Conservation of Energy  Mechanical energy is not conserved in the presence of Kinetic ______.  So what happens to the energy?  Ex rubbing your hands together  Total energy is always conserved, but mechanical energy is ______.  Mechanical energy is converted in to…

 Now can you answer this basic question: If an object (m=10kg) falls from a height of 10 m, what is it’s:  Potential and kinetic energy at the top ______ Potential and kinetic energy just before hitting the ground. ______ Practice: 1. Starting from rest, a child zooms down a frictionless slide from an initial height of 3m. What is her speed at the bottom of the slide? Assume she has a mass of 25kg 2. A frog is sitting on a rock. It sees a cat that is trying to eat it. The frog jumps directly up with an initial velocity of .85m/s. What is the total height the frog jumps? 3. The cat then jumps directly upward 1.2m. What was the initial velocity of the cat’s jump? 2.3.9 Define power POWER!!!  What is power? Let’s look at: . a rock climber takes 30min. to elevate his body up a few meters along the side of a cliff. . a trail hiker, who selects the easier path up the mountain, might elevate his body a few meters in 10min. . They both do the same amount of work. . Which one had more power? ______

 is the rate at which ______is done  or the rate at which ______is consumed  P = ______ The more power you have the ______work you can do in the ______time.  The more power you have you can do the ______amount of work in a ______time.  There is an ______relationship between work and time  This equation shows us that a powerful machine is both strong (big force) and fast (big velocity).  Ex. A powerful car engine is strong and fast.  Equations for power are:  P = W/t  P = F (d/t)  P = F v  P = ΔE/t  What units? The SI unit of power is the ______ 1 watt is = 1______/ second  W = J / s  Horsepower is also a unit.  1 horsepower = ______watts  Hp = 746W  Examples of power  A dim light bulb 40 W  A really bright bulb 500 W  Indoor Christmas light .7 W  Outdoor Christmas light 7 W

2.3.11 Solve problems involving momentum, work, energy and power.  Examples situation  A 193kg curtain needs to be raised 7.5m, in 5s. You have 3 motors with power ratings 1.0kW, 3.5kW and 5.5kW. Which motor is best for the job? How much time would it take for each motor to do the same amount of work?  Examples situation  Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min.  1) What is the power delivered by the horses?  2) How much work is done by the two horses?

 Practice:  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 student does the most work? Which student delivers the most power?  During a physics lab, Jack and Jill ran up a hill. Jack is twice as massive as Jill; yet Jill ascends the same distance in half the time. Who did the most work? Who delivered the most power? (plug in fake numbers)  When doing a chin-up, a physics student lifts her 42.0-kg body a distance of 0.25 meters in 2 seconds. What is the power delivered by the student's biceps?  Mr. B gets bored after school one day and decides to play in the hall. He sits in his rolling chair and pushes off the wall with 12N of force producing 30W of power. What was his resulting speed he traveled down the hallway?