Chapter 4: Energy

1. Chapter 4: Energy • Energy ~ an ability to accomplish change • Work: a measure of the change produced by a force • Work = force through the displacement • portion of the force along displacement * displacement • W = F cos qx F F F F F cos q F cos q F F x x F cos 90 = F0 W = F cos qx W = Fx x W = 0 Units: 1Newton . 1 meter = 1 joule = 1J

2. A person pulls a crate 20 m across a level floor using a rope 30° above the horizontal, exerting a 150 N force on the rope. How much work is done? F F x W = F cos qx

3. Work done against gravity: • Work = force through the displacement W = F cos qx • force * portion of displacement along force • gravity • force is always vertical => work = weight* height lifted • W = mgh • Work depends on height only • Work does not depend upon path h Eating a banana enables a person to perform about 4.0x104 J of work. To what height does eating a banana enable a 60-kg woman to climb?

4. Power: the rate at which work is done An electric motor delivers 15 kW of power for a 1000 kg loaded elevator which rises a height of 30m. How much time does it take the elevator to reach the top floor from the ground floor?

5. Force, speed and power Efficiency: how effective is power delivered

6. Energy: the capacity to do work • Kinetic Energy: energy associated with motion • Potential Energy: energy associated with position • Rest Energy, Thermal Energy, ... • Kinetic Energy, from motion in a straight line

7. Potential Energy • energy associated with position • gravitational potential energy • Work done to raise an object a height h: W = mgh • = Work done by gravity on object if the object descends a height h. • identify source of work as Potential Energy • PE = mgh • other types of potential energy • electrical, magnetic, gravitational, compression of spring ...

8. Conservation of Energy • Conservation Principle: For an isolated system, a conserved quantity keeps the same value no matter what changes the system undergoes. • Conservation of Energy: The total amount of energy in an isolated system always remains constant, even though energy transformations from one form to another may occur. • Usually consider initial and final times: • Ei = Ef

9. Example: A skier is sliding downhill at 8.0 m/s when she comes across an icy patch (negligible friction) 10m high. What is the skier’s speed at the bottom of the patch? h

10. Conservative and Nonconservative Forces • Conservative forces are forces whose work can be expressed as a change in PE. • Conservative forces are the forces which give rise to PE. • The work done by a conservative force is independent of the path of the object, and depends only on the starting point and the ending point of the objects path. • When considering forces and energies • Work-Energy Theorem • how “outside world” interacts with an object • Work done on an object = change in object’s KE • + change in object’s PE • + work done by object

11. F = 120N 3.0m 20m Example: A 25-kg box is pulled up a ramp 20 m long and 3.0 m high by a constant force of 120 N. If the box starts from rest and has a speed of 2.0 m/s at the top, what is the force for friction between the box and ramp? W = Wf + DKE + DPE W = F s Wf = Ff s

12. Problem 41: In the operation of a pile driver, a 500 kg hammer is dropped from a height of 5m above the head of a pile If the pile is driven 20 cm into the ground with each impact, what is the force of the hammer on the pile when struck. • hammer: PE -> KE • does this much work on pile • work is through a distance of 20 cm.