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Energy What is it? It is how nature keeps score. Like a “currency” of the universe. To cause a change requires energy Dr. Joseph W. Howard ©Spring 2008 First Steps How do we “measure” effort? How do you get paid ($$$) in the world? Job! ($$$) Work! Dr. Joseph W. Howard ©Spring 2008 Work & Energy Technical Definition of Work net WORK = FORCE DISTANCE = mad ENERGY IS THE CAPACITY TO DO WORK. It takes some work (energy) to cause a change. Dr. Joseph W. Howard ©Spring 2008 Work Example A donkey pulls a 10 kg box a distance of 5 m by applying a 90 N net force. How much work has the donkey done? Work = Net Force × distance Work = (90 N) × (5 meters) Work = 450 Ngm = 450 Joules 90N 10kg 5m Dr. Joseph W. Howard ©Spring 2008 Conceptual Pitfall Hoyt carries a very heavy boulder 10m across the garden at a constant speed of 3 m/s. What is the overall work done on the boulder? Work = ZERO!! 3m/s 10m Dr. Joseph W. Howard ©Spring 2008 Types of Energy Kinetic & Potential Energies KE is often thought of as energy of motion PE is often thought of as energy of position Dr. Joseph W. Howard ©Spring 2008 Gravitational PE A 10 kg ball rests at the top of a set of stairs. The stairs reach a height of 3 m above the ground. What is the potential energy of the ball? P .E . mgh m P .E . (10kg ) 9.8 2 (3m) s P .E . 294 N gm 294 Joules Dr. Joseph W. Howard ©Spring 2008 Kinetic Energy An oxygen atom has a mass of 2.66 10-23 g. If an oxygen atom were moving at 200 m/s, what would the kinetic energy of that atom be? 1 K .E . mv 2 2 1 m 26 K .E . 2.66 10 kg 200 2 s K .E . 5.32 1022 Joules Dr. Joseph W. Howard ©Spring 2008 2 Kinetic Energy A 3-kg ball is rolling at a constant speed. If you had to transfer 30 J of energy to the ball to cause this motion, what must the velocity of the ball be? 1 K .E . mv 2 m 2 2(30 kg 2 m) 2 s v 1 2 3.0kg 30 J 3.0kg v 2 m2 2 v 20 2 2(30 J ) 2 v s 3.0kg m m2 2 v 4. 5 v 20 2 2(30 N m) 2 s s v 3.0kg Dr. Joseph W. Howard ©Spring 2008 Law of Conservation of Energy Total energy in any process is constant. The energy may be transferred or transformed, but not created nor destroyed. Dr. Joseph W. Howard ©Spring 2008 Law of Conservation of Energy Total Energy at Total Energy at the beginning of = the end of an an event event Form of energies my change Dr. Joseph W. Howard ©Spring 2008 Conservation of Energy Consider a 20-kg ball rolling down a hill that is 5 m high. How fast will the ball be moving when it reaches the bottom of the hill? KE PE KE PE top What energy here? top bottom bottom m PEtop (20kg ) 9.8 2 (5m) 980 Joules s 980 Joules KEbottom 5m The PE energy at the top becomes the KE energy at the bottom 1 980 Joules (20kg )v 2 2 m v 9. 9 s What energy here? Dr. Joseph W. Howard ©Spring 2008 Conceptual Pitfall A young boy skates down each of the frictionless playground ramps illustrated below. Which ramp will give the skateboarding boy the fastest speed at the bottom of the ramp? h A D C B Ramp A Ramp B Ramp C Ramp D Any Ramp, all ramps will produce the same speed at the bottom. Dr. Joseph W. Howard ©Spring 2008 Law of Conservation of Energy Total Energy at Total Energy at the beginning of = the end of an an event event Form of energies my change Dr. Joseph W. Howard ©Spring 2008 Conservation of Energy A 5 kg bowling ball falls from rest a distance of 78.4 m. How fast is the ball falling at that point? What energy here? KEtop PEtop KE bottom KE bottom 1 mgh mv 2 2 m 1 (5kg )(9.8 2 )(178.4m) (5kg ) v 2 s 2 78.4m 3841.6 J (2.5kg ) v 2 What energy here? m2 v 1536.6 2 s 2 v 39.2 Dr. Joseph W. Howard ©Spring 2008 m s Conservation of Energy Consider dropping a ball from a height of 15 m in a vacuum. What is the velocity of the ball the instant it strikes the ground? What energy here? 15m The PE energy at the top becomes the KE energy at the bottom What energy here? KEtop PEtop KE bottom PE bottom 1 mgh mv 2 2 m 1 m (9.8 2 )(15m) m v 2 s 2 1 2 m v (9.8 2 )(15m) 2 s v 2 2 (9.8 v 17.1 Dr. Joseph W. Howard ©Spring 2008 m )(15m) 2 s m s Conservation of Energy A 5kg ball is rolling along a sidewalk with a constant velocity of 3 m/s. Suddenly, the ball encounters a 0.5 m dip in the sidewalk and then continues rolling along a flat section of the sidewalk. What will the velocity be for the ball after it encounters the dip? What energy here? What energy here? Dr. Joseph W. Howard ©Spring 2008 Conceptual Pitfall Tracks A and B are of equal length and have hills of the same curvature except A curves up and B curves down. If two identical balls are rolled simultaneously with the same initial velocity, which will reach the end of its track first? A B a. A b. B c. same Dr. Joseph W. Howard ©Spring 2008 Energy & Motion A 10kg dog runs from a speed of 4 m/s up to a speed of 10 m/s in 3 seconds. What is the dog’s acceleration? How far does he run in those 3 seconds? How much did the dog’s kinetic energy change? How much work did the dog accomplish? Dr. Joseph W. Howard ©Spring 2008 Two pumpkins of equal size and mass are dropped off the roof of the Henson Science Hall. One lands on the sidewalk and the other lands on the grass. Which one of the following statements is true of the force and impulse on the pumpkins as their fall was stopped? • Both of the pumpkins experienced the same force and the same impulse. • Both of the pumpkins experienced the same impulse, but the pumpkin that hit the sidewalk experienced a greater force. • Both of the pumpkins experienced the same force, but the pumpkin that hit the grass experienced a smaller impulse. • The pumpkin that hit the sidewalk experienced a greater force and a greater impulse than the pumpkin that hit the grass. • The relationship between the impulses and forces on the pumpkins can not be determined without knowing the height of the building. Dr. Joseph W. Howard ©Spring 2008 Two water slides sit side by side at the water amusement park and these both sit near a high dive tower, as shown below. Your annoying little brother wants to do the ride that promises the fastest attainable speed at the bottom. What recommendation can you make to your brother about which ride should he should choose? Assume that there is no friction on the slides and that air resistance is negligible. Water slide A High dive Water slide B Water slide B Water slide B or the High Dive High Dive Water slide A Any of the rides