Chapter 5: Work and Energy

5-1 What is Work Is any work done in these situations? You hold a heavy chair at arm’s length for several minutes… You carry a bucket of water along a horizontal path while walking at constant velocity. According to the scientific definition of work… no work is done. If these are not work, then when is work done on an object?

5-1 Work The force must cause the displacement Work is done on an object when some forces cause a displacement of the object (a change in position). Imagine that your car runs out of gas, and you need to push it to the side of the road. You exert some force on the car to change its position. That means that you are doing work on the car. The work that you do on the car is equal to the magnitude of the force times the magnitude of the displacement of the car. W = Fd The unit for work is the joule (J) named after James Joule. 1 J = 1 Nm

Work Work is done only when the force is parallel to the displacement. If the force is perpendicular to the displacement of an object, work is not done on the object. When the force on an object and the object’s displacement are in different directions, only the component of the force that is parallel to the object’s displacement does work. If θ is the angle between the displacement and your applied force, we can calculate the work done on the object by using the equation: W = Fdcosθ

Net Work (Wnet) If many forces are applied to an object, we can find the net work being done on the object by using the equation: Wnet = Fnetd(cos θ) To calculate work, use the following equations: W = Fd W = Fdcosθ

Concept check Decide whether any work is being done in each situation. If so, identify the object (s) on which work is being done. A teacher applies a force to a wall and becomes exhausted A book falls off a table and free falls to the ground A rocket accelerates through space.

Concept Check answers A teacher applies a force to a wall and becomes exhausted NO. this is not work. The wall is not displaced. A force must cause a displacement in order for work to be done. A book falls off a table and free falls to the ground YES. This is work, there is a force (gravity) which acts on the book which causes it to be displaced in a downward direction. A rocket accelerates through space. Yes. There is a force (expelled gases push on the rocket) which causes the rocket to be displaced through space.

Work Work is a scalar quantity (force that has magnitude but no direction) Can be + or – Is + when force is in the same direction as displacement Is - when the force is opposite the displacement Cosθ is negative for angles greater than 90⁰ Cosθ is positive for angles less than 270 ⁰ If  = 0⁰, then cos  ⁰ = 1 ( work is done) If  = 90⁰, then cos  ⁰ = 0 (W=0)

Work and speed If the work done on an object results only in a change in the object’s speed, the sign of the net work tells you if the speed is increasing or decreasing Net work +, the object speeds up and the net force does work on the object Net work -, the object slows down and work is done by the object on another object

Sample 5A How much work is done on a vacuum cleaner pulled 3.0m by a force of 50.0 N at an angle of 30⁰ above the horizontal? * Only the horizontal component of the applied force is doing work on the vacuum cleaner. HW: Practice 5A 1-4

5-2 Energy Kinetic Energy

(kinetic energy is measured in joules (J), like work) Kinetic energy is the energy associated with an object in motion. Kinetic energy depends on the speed and mass of an object. To find the kinetic energy of an object, we use the equation: KE = ½ mv2 (kinetic energy is measured in joules (J), like work)

Work-Kinetic Energy Theorem The Work-Kinetic Energy Theorem tells us the work that is done on an object while the object changes speed. ΔKE = Wnet KEf – KEi= Wnet ½ mvf2 – ½ mvi2 = Wnet Velocity is sometimes ΔV which equals Vf - Vi When net work > 0, speed is increasing When net work < 0, speed is decreasing

Sample 5B A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball have? How fast must a 2.45 g table-tennis ball move in order to have the same kinetic energy as the bowling ball? Is this speed reasonable for a table-tennis ball? Do practice 5B

Potential Energy The stored energy of an object is called potential energy. Gravitational potential energy is the potential energy due to an object’s elevated position. The amount of g.p.e. possessed by an object is equal to the work done against gravity in lifting it. PE = mgh Where h is the height - the distance above some chosen reference level, such as the ground or the floor of a building

Elastic Potential Energy The potential energy stored in a compressed or stretched object is called elastic potential energy. PEelastic = ½ kx2 When an external force compresses or stretches the spring, elastic potential energy is stored in the spring. x is the distance that the spring is stretched or compressed; units for x is meters (m). The amount of energy depends on the distance that the spring is compressed or stretched from its natural length. k is the spring constant, which is the spring’s resistance to being stretched or compressed; units for k are Newtons per meter (N/m)

5-2 Sample Problem 5D Classwork :Practice 5D 1,2,3 Homework: Section Review 1-5

Conservation of energy 5-3 Conservation of energy

Conservation of Energy If a ball is suspended in the air how much kinetic energy does it have? If we drop the ball, how much potential energy does it have the instant before it hits the ground? When the ball is halfway down, can you predict what the PE would be?

Mechanical Energy ME = KE + SPE The Energy changes form but the TOTAL energy remains the same. What kind of Energy is PE & KE? Mechanical Energy is the TOTAL energy ME = KE + SPE

Types of Energy Energy Mechanical Kinetic Potential Gravitational Elastic Non-Mechanical Chemical internal electrical

Conservation of Mechanical Energy Principle Without any friction the total mechanical energy remains the same. Friction does negative work and decreases the amount of energy If Friction is present the law of MEC does not apply. The Law of MEC occurs even when acceleration varies

ME = KE + SPE MEi = MEf Initial mechanical energy = final mechanical energy (in the absence of friction) The formula used depends on the form of Energy in the problem. If the only force acting on an object is the force due to gravity, then (KE=1/2 mv2 and PE=mgh) ½ mvi2 + mghi = ½ mvf2 + mghf If other forces (besides friction) are acting on an object, add the appropriate potential energy formula. (ie Pee )

Example 5E Starting from rest, a child zooms down a frictionless slide with 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. Homework Practice 5E 1-5 & Section Review 1-3

5-4 Power

Power Power is the rate at which work is done. The time it takes to do work is just as important as the amount of work that is done. Take 2 identical cars Car #1 can go 0-27 m/s (60 mph) in 4 seconds Car #2 takes 8 seconds to get up to the same speed What’s the difference?

P = W/Dt or F d/Dt (the def. of work) Power Car # 1 has a ‘souped up’ engine. Each engine does work to accelerate the car, but the ‘souped up’ one does it MORE QUICKLY. Power is work done per unit of time P = W/Dt or F d/Dt (the def. of work) P=FV (force x speed) P=mgd/Dt

Power The unit is Watt (W) 1 horsepower = 746 W * remember, the distance moved per unit of time is just the speed! Machines with different power ratings (lawnmowers, etc) do the same work in different amounts of time. The total amount of the work is the same.

Sample 5F A 193kg curtain needs to be raised 7.5m, at constant speed, in as close to 5.0s as possible. The power ratings for three motors are listed as 1.0kW, 3.5kW and 5.5kW. Which motor is best for the job?

Homework Practice 5F 1, 3,4,5 Section Review 1-3

Mechanical Energy Conserved quantity Mechanical energy is the sum of the kinetic energy and all the forms of potential energy in an object (remember that an object can have elastic potential energy and gravitational potential energy). ME = KE + ΣPE

Conservation of Mechanical Energy When friction is absent, the amount of mechanical energy remains constant, or is conserved. The initial amount of mechanical energy will equal the final amount of mechanical energy. MEi = MEf KEi + ΣPEi = KEf + ΣPEf KEi + PEelastic, i + PEg, i = KEf + PEelastic, f + PEg, f ½ mvi2 + ½ kxi2 + mghi = ½ mvf2 + ½ kxf2 + mghf

Power Power is the rate at which work is done. P = Work = W time interval Δt P = Fd Δt P = Fv (Force x speed) Power is measured in Watts (W). Horsepower (hp) is another unit of power that is sometimes used; 1 hp = 746 watts