Work and Energy (part I): Question: How do you raise an object? Answer: Apply an upward force to it. The force must be at least as large as the weight of the object. less force applied more force applied applied force 1 meter 1 meter Weight force applied force more weight less weight in order to lift box Which one makes a louder “bang” if dropped? Obviously the big one…… Weight
Question: But what is the difference between lifting the box by • a height of, say 2 meters as opposed to 1 meters? • Answer: The force is the same in each case BUT: • force is applied to the box over different amount of distance • box makes louder “bang” when dropped on the floor • We say that the applied force does the WORK on the box: • Question: But what if we compare the process of lifting a “big” box to • that of lifting a “small” box? • Answer: Now the forces are different, it takes more force to lift a big • box than to lift a small box
Summary of our observations: 1) More WORK is done ON a system (the box) when a LARGER force is applied to it. 2) More WORK is done ON the system when the force applied causes the system to move through a larger distance 3) In order to do any work, applied force must be in the same direction as motion Work Done by Force Distance Moved by Force = X The Force Joules Newtons Meters
Work Done by Force Distance Moved by Force = X The Force Joules Newtons Meters 1 Joule = (1 Newton) X (1 meter) 1 J = 1 N X m F and d Along the same line!! W = F X d
quick-examples: • An 800 N person steps up onto a 1 meter tall stool, how much • work ? What force does this work? force applied by legs on body lifts the weight of the person 1 meter Work = W = 800N X 1 meter force lift of lifting = 800 N X 1 m = 800 Joules 800 Joules = 191.2 calories NOTE : 1 joule = 0.239 cal 4186 J = 1 kcal
Work and Energy 2) You pull a box along the floor. How much work is done in moving the box 10 m? x = 10 x = 0 20 Newtons friction 10 meters which force does the work? The 20 N applied force! W = (20N) X (10 m) = 200 Nm = 200 Joules Work – Force Graphs: If we plot the Force that was applied to the box as a function of distance we can find the total work done! 20 N The area under the plot represents the total Work done!!!!! Force Area = length x height = (10 m) x (20 N) = 200 Joules x = 10 Position
These graphs are great for more complex forces: What’s the work done from x =0 to x = 4m? Area of a triangle is ½ base x height = ½ (4 m) x (10 N) = 20 Joules! Spring force proportional to the stretch distance 10 N Force x = 4 m Position Calculate the work done from x =0 to x = 6 m. 10 N 8 N Force 3 N x = 6m x = 1m x = 3m Position
When a force does work on an object it gives the object Energy of one form or another. Energy is the ability to do work. But, what does this mean, really? Now mass can do work resulting in a flying monkey 2 1 do work on mass work = mass x 10 m/s2 Mass h = height of mass How? Drop it! Mass speeds up as it falls maximum speed upon impact 3 4 h Look at frame 2: The mass CAN do work (but hasn’t) by virtue of its position or “configuration” Look at frame 4: The mass CAN do work (but hasn’t) by virtue of its speed and impact
Energy The ABILITY to do WORK e.g. A “raised” mass has the potential to pop a monkey up into the air! How to actually do the work is not the issue. The issue is simply that “it” CAN. • Two types of energy: • Kinetic Energy: energy by virtue of motion • Potential Energy: energy by virtue of • position (configuration
Forms of Energy • Kinetic (KE): energy by virtue • of motion • Translational • KE = ½ x mass x (speed)2 • 2. Rotational • 3. Thermal • remember: • motion temperature of • “atoms” • Potential (PE): energy by virtue • of position (configuration) • Gravitational • PE = (mass x 10 m/s2) x height • = Weight x height • 2. Elastic (spring) • 3. Chemical • 4. Nuclear • 5. Electromagnetic
Work Energy relationship • Work = Force x Distance • Work changes energy (work = change in energy) • Energy increases when work is done on or to an object • Energy decreases when work is done by an object
Spring • Work is done to compress a spring a distance Dx. • The change in the potential energy is identical to the work done. W = DP.E. P.E. = 1/2 k Dx2 k is the spring constant (a characteristic of the spring) • The spring can now do work on something else.
Potential Energy • The motor pulls the cart up against gravity WORK = Force x distance mg x height • Muscles do work against the tension in the bow string • Muscles do work against gravity to lift the axe above the ground
Potential Energy • The roller coaster cart, the bow and the axe were all given potential energy. The change in the potential energy is identical to the work done. W = DP.E. • These objects now have the potential to do work and convert that stored potential energy.
Kinetic Energy • The energy associated with an objects motion. K.E. = 1/2 m v2 m = mass v = velocity Without velocity, there is no KE Chop, Chop
Law of Conservation of Energy (The 1st Law of Thermodynamics) Energy is never created nor is it destroyed. Energy can be transformed from type to type, BUT When you add up all of the energy AFTER a process you will have the exact same amount as BEFORE the process Example Let’s look at the simple pendulum: • The pendulum swings to and fro, • where it stops, conservation of energy knows. • TOTAL ENERGY = Potential Energy + Kinetic Energy
The Simple Pendulum The total energy of this system is zero. This simple pendulum could be the sway in a grandfather clock, a child on a swing, a hypnotists watch, etc Suppose someone does work against gravity to give it some potential energy?
The Simple Pendulum Suppose someone does work against gravity to give it some potential energy? The work done = Force x Distance Force = m g Distance = h The work done = potential energy gained (DPE) W = m g h The total energy of the system is now (m g h), reflecting the work done to the system. h
To and Fro The pendulum swings until it has reached the same height on the other side, before pausing to swing (oscillate) back. h
Energy Exchange When paused, the pendulum has its maximum potential energy (mg h) and zero kinetic energy. Total energy = mgh + 0 When at the bottom of its swing its height is zero, therefore it has its minimum potential energy (0) and its maximum kinetic energy. It travels the fastest at the bottom of its swing. Total energy = 0 + 1/2 m v2 EVERYWHERE the TOTAL energy remains unchanged.
Energy Exchange The energy sloshes from PE to KE and back again. A pendulum weighing 5 kg is lifted against gravity to a height of 2 m from its equilibrium position. What is its speed at the bottom of its swing?
Energy Exchange The energy sloshes from PE to KE and back again. A pendulum weighing 5 kg is lifted against gravity to a height of 2 m from its equilibrium position. What is its speed at the bottom of its swing? TOTAL Energy = PE + KE = mg h + 0 = 5 kg 10 m/s2 2 m = 100 Joules
Energy Exchange At the bottom of its swing the total energy is still 100 Joules. 100 Joules = TOTAL Energy = 0 + KE = 1/2 m v2 = 1/2 5 kg v2
Energy Exchange At the bottom of its swing the total energy is still 100 Joules. 100 Joules = TOTAL Energy = 0 + KE = 1/2 m v2 100 = 1/2 5 kg v2 2(100)/5 = v2 40 = v 6.3 m/s = velocity
Drum Roll Diver The platform diver does work against gravity by climbing the pole to the platform at height h. This gives him potential energy PE = mg h. At the bottom, he is traveling the maximum speed and has traded his potential energy into the energy of motion, kinetic energy. TOTAL Energy is conserved at every point along the way!
Drum Roll Diver If the idiot climbed to a height of 20 meters, how much is his mass? PE = 10,000 = mg h
Drum Roll Diver If the idiot climbed to a height of 20 meters, how much is his mass? PE = 10,000 = mg h m = 10,000/gh = 10,000/10(20) = 50 kg
The Curved Track: Q1: How did the ball get to the “starting position” in the first place? Q2: What forms of energy does the ball possess at each point of its journey? Where did it get the energy?
The Curved Track: “Ideal Case”: no friction, no rolling no sound no air resistance “Real Case”:friction sound air resistance, etc.
The Curved Track: Some of the energy appears to be “lost” in the transfer. Where does it go?
In the track example. Reversible Part: some of…… gravitational PE rotational KE gravitational PE translational KE Irreversible Part: Remainder of Thermal (friction) gravitational PE Sound lost to the surroundings
By building a curved track, we can get some of the energy back….. but never all of it. The ball gives up its gravitational energy not only to rotational and translational kinetic forms but also to thermal forms and to sound (another example of translational Kinetic) Point: We can “get back” the ordinary rotational and translational KE We cannot “get back” the thermal, sounds, etc… Actual Efficiency (AE) of a process: “what percentage of the INPUT produces useful OUTPUT” Or, since POWER is the rate of energy flow (or work performance)
Example Lift a 2 kg brick to height of 2 meters. Drop it and do 15 Joules of work in driving a nail. What is this processes actual efficiency? The energy (or Power) which is NOT converted to a useful form is called exhaust for the process….. Common Examples: Thermal Energy Output (friction, air resistance, etc.) Sound (friction, collisions) Light (friction, “dissipative atomic processes
Example continued: The brick does 15 Joules of useful work, thus the process has an exhaust of 40 Joules – 15 Joules = 25 Joules input useful output scattered, non-useful output [thermal, sound, etc.]