Work Energy and Power What is Work Work

Work, Energy and Power

What is Work? • Work is the product of the magnitudes of the components of a force along the direction of displacement and the displacement W = Fd • A force that causes a displacement of an object does work on the object

Hey! I’m working here! • Work requires motion • Work is done only when components of a force are parallel to a displacement • SI Unit = Joule (J) or N*m – Lifting a Big. Mac to your mouth ~1 J – Three push-ups ~1000 J

A weight lifter lifts a set of weights a vertical distance of 2. 00 m. If a constant net force of 350 N is exerted on the weights, what is the net work done on the weights? W = Fd W = (350 N)(2. 00 m) W = 700 J

The sign of work is important

Homework p. 170 • 1. A tugboat pulls a ship with a constant net horizontal force of 5000 N and causes the ship to move through a harbor. How much work is done on the ship if it moves a distance of 3000 m?

• 2. A weight lifter lifts a set of weights a vertical distance of 2. 00 m. If a constant net force of 350 N is exerted on the weights, what is the net work done on the weights?

• 3. If 2. 0 J of work is done in raising a. 18 kg apple, how far is it lifted?

Homework p. 171 • 1. For each of the following statements, indicate whether the everyday or the scientific meaning of work is intended. • a. Jack had to work against time as the deadline neared. • b. Jill had to work on her homework before she went to bed. • c. Jack did work carrying the pail of water up the hill.

• 2. If a neighbor pushes a lawnmower four times as far as you do but exerts only half the force, which one of you does more work and by how much?

• 3. Determine whether or not work is done in each of the following examples: • a. a train engine pulling a loaded boxcar initially at rest. • b. a tug of war that is evenly matched. • c. a crane lifting a car.

Power • Power is the rate at which energy is transferred • Since W = Fd, we can also say: • And since d/t is velocity, we can say:

Power, cont. • SI Unit of power = Watt (W) = J/s • Also will see horsepower (hp) 1 hp = 746 watts • Machines with different power ratings do the same work in different time intervals – Or, said another way, machine with different power ratings will do different amounts of work in the same time interval

Example • A tractor moves a 193 kg hay bale 7. 5 m in 5. 0 seconds. How powerful is the tractor? How many horsepower does the tractor use? • m=193 kg; d=7. 5 m; t=5. 0 s; P=? • *Remember Fw=mg

Example • Fw=mg • Fw = (193)(9. 81)=1893. 33 N • • P=1893. 33 N x 7. 5 m/5. 0 s P = 2840 W 1 Hp = 746 W 2840 W x 1 Hp/746 W = 3. 8 Hp

Homework • 1. A rain cloud contains 2. 66 x 107 kg of water vapor. How long would it take for a 2. 00 k. W pump to raise the same amount of water to the cloud’s altitude, 2000 m?

• 2. How long does it take a 19 k. W steam engine to do 6. 8 x 107 J of work?

• 3. A 1. 50 x 103 kg car accelerates uniformly from rest to 10. 0 m/s in 3. 00 s. – a. What is the work done on the car in this time interval? – b. What is the power delivered by the engine in this time interval?

5. 2 - Energy • Kinetic Energy – the energy of an object due to its motion – Depends on speed and mass – SI unit = Joule • A 7 kg bowling ball moves at 3 m/s. How much KE does the bowling ball have? • Answer = 31. 5 J

Work-Kinetic Energy Theorem • The Net Work equals the change in Kinetic Energy

A 75 kg bobsled is pushed along a horizontal surface by two athletes. After the bobsled is pushed a distance of 4. 5 m starting from rest, its speed is 6. 0 m/s. Find the magnitude of the net force on the bobsled. • • • m= 75 kg d= 4. 5 m vi= 0 vf= 6. 0 m/s F= ? • F x d = ½ mvf 2 – ½ mvi 2 • F = (½ mvf 2 – ½ mvi 2)/d • F = [½ 75*(6. 0)2 – ½ 75* (0)2]/4. 5 • F= 300 N

Kinetic Energy problems Homework • 1. Calculate the speed of an 8. 0 x 104 kg airliner with a kinetic energy of 1. 1 x 109 J. • 2. Two bullets have masses of. 003 kg and. 006 kg respectively. Both are fired with a speed of 40. 0 m/s. Which bullet has more kinetic energy? • 3. A car has a kinetic energy of 4. 32 x 105 J when traveling at a speed of 23 m/s.

Work Kinetic Energy Theorem problem • 1. A student wearing frictionless in-line skates on a horizontal surface is pushed a friend with a constant force of 45 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 352 J?

Hi • You need a calculator • Grab out your Energy, Work and Power notes packet

Potential Energy • Potential Energy – stored energy due to the position of an object – Several types of Potential Energy • Gravitational Potential Energy (PEg) • Elastic Potential Energy (PEe) • Chemical Potential Energy (PEc)

Gravitational Potential Energy • The potential energy associated with an object due to the position of the object relative to the Earth or some other gravitational source • We can set our “zero level” wherever we want to make our calculations easy.

Example Problem An 80. 0 kg climber climbs 8848 m to the top of Mount Everest. What is the climber’s potential energy? PEg = mgh • m = 80. 0 kg • h = 8848 m • g = 9. 81 m/s 2 • PEg = mgh • PEg = (80. 0)(8848)(9. 81) • PEg = 6. 94 x 106 J

Elastic Potential Energy • The potential energy in a stretched or compressed elastic object (spring) • k is called the spring constant, or force constant. A flexible spring has a small k value, a stiffer spring has a larger k value. – Units are N/m

Example Problem • The staples inside a stapler area kept in place by a spring with a relaxed length of 0. 115 m. If the spring constant is 51. 0 N/m, how much elastic potential energy is stored in the spring when its length is 0. 150 m? • . 031 J

Potential Energy problems 1. A spring with a force constant of 5. 2 N/m has a relaxed length of 2. 45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3. 57 m. Calculate the elastic potential energy stored in the spring.

Potential Energy problems 2. A spoon is raised. 21 m above a table. If the spoon and its contents have a mass of. 030 kg, what is the gravitational potential energy associated with the spoon at that height relative to the surface of the table? Ans. . 06 J

Homework PE • 1. Find the gravitational potential energy of a 60. 0 kg person standing on top of the Eiffel Tower. (tip height is 324 m above ground) • 2. Find the height of the same 60. 0 kg person if they have a gravitational potential energy of 1080 J.

5. 3 – Conservation of Energy • Conserved = remains constant • Mechanical Energy = the sum of kinetic energy and all forms of potential energy • In the absence of friction, mechanical energy is conserved, i. e. the total mechanical energy at the beginning is the same as the total mechanical energy at the end.

Law of Conservation of Mechanical Energy

Conservation of Energy

Energy Conservation for a Skier

Another Example…

KE, PEg and PEe

Energy Conservation in a Pendulum

Example Problem • Starting from rest, a child zooms down a frictionless slide from an initial height of 3. 00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25. 0 kg.

• • • hi=3. 00 m hf=0 m M= 25. 0 kg vi= 0. 0 m/s vf=? • PEi + KEi = PEf + KEf • mgh + 0 = 0 + ½ mvf 2 • (25)(9. 81)(3) = ½ (25)vf 2 • vf= 7. 67 m/s

Conservation of Energy HW 1. A bird is flying with a speed of 18. 0 m/s over water when it accidentally drops a 2. 00 kg fish. If the altitude of the bird is 5. 40 m and friction is disregarded, what is the speed of the fish when it hits the water?

Conservation of Energy HW 2. A 755 N diver drops from a board 10. 0 m above the water’s surface. – Find the diver’s speed 5. 00 m above the water’s surface. – Then find the diver’s speed just before striking the water. – If the diver leaves the board with an initial upward speed of 2. 00 m/s, find the diver’s speed when striking the water.

Conservation of Energy HW 3. An Olympic runner leaps over a hurdle. If the runner’s initial horizontal speed is 2. 2 m/s, how much will the runner’s center of mass be raised during the jump? 4. A pendulum bob is released from some initial height such that the speed of the bob at the bottom of the swing is 1. 9 m/s. What is the initial height of the bob?