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Work & Energy WORK WORK: It is used by physicists to measure something that is accomplished. So it results in the equation: Work = Force x displacement The symbol for work is the variable = W W=(F)(d) You must move something (d) with a force (F) to accomplish work. Is work being done? Pushing a car. Attempting to lift 2,000,000 N. A snowflake dropping from the sky. Swimming in a rip current. WORK UNITS: Force is measured in Newtons, N, and displacement is measured in meters, m. BUT WAIT… we just did torque… and they were measured in Nm… So scientists named Nm that measure Work and Energy, and called them Joules (J). 1 Nm of work or energy = 1 Joule NOW DO IT! Calculate the work done if a 52.9 Kg brick is dropped 5.0 meters. SO WHAT IF I PUSH ON A WALL THAT DOES NOT MOVE? HAVE I DONE WORK?… NO! HAVE I USED ENERGY?... YES! WHAT IS ENERGY? UH OH… another definition coming… ENERGY ENERGY: is the ability to do work… measured in Joules (J)… AND it comes in two kinds: POTENTIAL ENERGY: stored up energy . KINETIC ENERGY: moving energy Potential or Kinetic? Water behind a dam Wound rubber band Falling raindrops The battery while listening to your IPod POTENTIAL ENERGY How do you “store up energy?... There are two kinds we study… GPE - GRAVITY POTENTIAL ENERGY: If you put an object up in the air… gravity will pull it down and make it move some distance… WORK will be done… an object is moved some displacement… GPE = mgh… mg=force gravity, h=height… the heavier the object is, the more force on it, the higher it is, the further down it moves… GPE = mgh EPE - ELASTIC POTENTIAL ENERGY: This is stored in a spring or rubber band. The stronger the spring, or the further you stretch it, the more work it can do. So, the EPE=(1/2)(k)(x2) … k = how strong the spring is, and x= how far you stretch it… EPE=(1/2)(k)(x2) KINETIC ENERGY KINETIC ENERGY = KE: This is moving energy. Something that is moving will collide and crash into another object, and move it a distance,… SO, the energy that it has, will be equal to how BIG it is, m (mass), and how FAST, v (velocity), it is moving…. KE = (1/2)(m)(v2) NEW FORMULAS W=(F)(d) EPE=(1/2)(k)(x2) GPE=(m)(g)(h) KE=(1/2)(m)(v2) ENERGY is what you “can do”……… WORK is what you “do do”……… and isn’t work doo-doo? Calculating Work F d m A mass is being pulled to the right by a force, F , it is moving to the right so that the displacement is d… BUT is ALL of the force, F , doing work?.... NO…. because some of the force is lifting up in the positive +y direction AND the box is not moving upward in that direction… so (F)(sinϴ) does NO WORK This means that the part of F that is pulling to the right in the +x direction is doing work, because that is the way the box is moving… so work W = (F)(cos ϴ)(d) Calculating Work F d m What about the other forces on the box like weight, mg, pulling down, or the F-normal, of the ground pushing up…. NO… they do NO WORK, because the box is not moving up or down…. Calculating Work F d m What about F-friction, is it doing work?... YES… BUT WAIT… THE FRICTION FORCE IS NOT IN THE SAME DIRECTION THE BOX IS MOVING!! IT IS TO THE LEFT!! This force is fighting the work being done by F. It is doing what we call negative work because it is being done in the OPPOSITE DIRECTION THAT THE OBJECT IS MOVING… so the work done by friction is W = -(Wf)(d) = -(µ)(F-normal)(d) So now go back in your notes to the NET FORCE UNIT, and look up how to find the force normal on a box with the force F at an angle… F-normal = [(mg) – (F)(sinϴ)] Calculating Work F d m FINALLY, we can find the TOTAL WORK, Wt, done on the box…. It is the positive work done by F plus the negative work done by friction Ff… Wt = W - Wf QUICK OVERVIEW ON WORK…. 1) Work equals Force x displacement… W = (F)(d) 2) Work is measured in Nm called Joules, or J 3) Work is positive if the force, F, is in the same direction as the displacement 4) If ALL of the force is not in the same direction as the displacement, find the component of F that is in the same direction as d… W = (F)(cosϴ)(d) 5) Any force that pushes on the object, but does not move the object in the direction it is pushing… does NO work 6) Any force that pushes in the opposite direction that the object is moving, (especially friction), does negative work POWER POWER… What is it? There seems to be political power, military power, personal power, and automobile engine power to mention a few…. Physics will concern itself with mechanical power… So what is that?.... In words it means “how fast you do work”….. So the formula for power is P = W/t Let’s see if this makes sense…. W, work is in the numerator, so if you do more work in the same amount of time, it takes more power… t, time is in the denominator, so if you do the same amount of work in less time, it takes more power… finally, if you do more work in less time, you need a lot more power! Units of POWER UNITS: If P = W/t… This means that units of power will be Joules/second or J/s… We call a J/s a Watt or W Another unit of power is horsepower, hp…. Since a Watt, W, is in metric units…. To convert to horsepower…. Use 1.00 hp = 755W We have seen in the previous notes how to find work… W = (F)(cosϴ)(d) But how will we find time, t ?... The most common way will be to use kinematics and the kinematic equations: (vi, vf, d, a, t)’s…. So keep those equations handy Finally… If we go back to the other uses of power like political or military power…. They all seem to mean that if you can get a lot done, in a short amount of time…. This takes POWER. Work Done by a Spring Work done by a spring is different… WHY?... Because the more you displace it, the MORE force it takes to do it… SO… you can not just multiply F x d, because F gets bigger as you stretch it…. F IS CHANGING!... OK… so how do you handle this? Work Done by a Spring Let’s take a spring that is not stretched or compressed, we will call its length, Lo. So Lo is how long the spring is when it is not stretched or compressed. Look at the diagram…. x is called the deformation, it is how far you stretch or compress the spring from its original length, measured in meters, m. Work Done by a Spring If we are going to write a formula for the work done by a spring, or the potential energy stored in a spring, we have to know HOW STRONG IS THE SPPRING? How do you measure this? In words it is “how much force does it take to stretch or compress the spring”…. The scientist Hooke gave us a formula: F = kx Simply, if we rearrange this formula: k = F/x…. What does this mean in words?.... The strength of a spring, k, is measured by HOW MANY NEWTONS OF FORCE, F, it takes to stretch (or compress) a spring, divided by the AMOUNT YOU STRETCH OR COMPRESS IT, x (the deformation)… Work Done by a Spring k, the strength of a spring is measured in units of N/m…. An example in words is: k = 150N/m… It takes 150 Newtons of force to stretch (or compress) this spring a deformation of 1.00 meter…. THAT is how strong the spring is…. So if we had a spring, how could we measure how strong it was… its k?... Let us hang it down from a post… measure how long it is… this is Lo, its original length without any force on it… NOW let’s add a force, F… If it is hanging down the force will be equal to the weight of the mass we hang on the spring, mg… What is the deformation, x, or the amount it stretches?.... This is x, measured in meters… Put a larger mass on the spring, and again measure, x, the deformation…. Keep doing this and graph it…. Work Done by a Spring You will get a graph like this one at the left… the force, F, will be equal to the weight, mg, of the mass hanging on the spring. The deformation (stretch) can be measured in meters, m. The Hooke’s Law constant, k, will be equal to the slope of the line… k = ΔF/Δx…. HOW STRONG is the spring in N/m… The Elastic Limit is the point when you stretch a spring, like the one in a ballpoint pen past the point where it can return to its original length…. The Breaking Point is where the spring or rubber band breaks…. Work Done by a Spring SO…. How much WORK is done on a spring?... Or How much ENERGY is stored in a spring?... They are the same!... The area under the triangle, AREA = (1/2)(F)(x)…. WORK on a spring, OR ENERGY stored in a spring…. Wspring = EPE (Elastic Potential Energy) = (1/2)(k)(x2) CONSERVATION OF ENERGY The Law of Conservation of Energy: ENERGY CAN NOT BE CREATED OR ELIMINATED…IT CAN ONLY BE CHANGED FROM ONE FORM TO ANOTHER… This is one of the most important concepts put forward by scientists of the last 250 years… It has been used in physics, chemistry, biology, environmental science, space technology, cosmology, atomic particle theory and ALL levels of science… BUT what does it really mean? The total energy of an object at point a… + the work done on it by a (+force)… - the work done on it by a (-force)… will equal the total energy of an object at point b…. or point c…. or point d…. (etc…) CONSERVATION OF ENERGY FORMULA ΣEA + WF – Wf = ΣEB = ΣEC = ΣED = etc. CONSERVATION OF ENERGY FORMULA ΣEA + WF – Wf = ΣEB How do you solve this equation? ΣEA= This is the TOTAL Energy at Point A…. 1) Is there any GPE, gravity potential energy, mgh 2) Is there any EPE, elastic potential energy, (1/2)(k)(x2) 3) Is there any KE, kinetic energy, (1/2)(m)(v2) 4) ADD UP ALL THE ENERGY AT POINT A…. CONSERVATION OF ENERGY FORMULA If an outside force is applied that moves the object in the same direction that the object moves… ADD WFA If an outside force like friction acts on an object in the opposite direction that it is moving… SUBTRACT Wf **ATTENTION** DO NOT ADD OR SUBTRACT THE WORK DONE BY GRAVITY OR A SPRING IN THIS FORMULA!... BUT WHY NOT?... BECAUSE WE ALREADY DO THAT BY MEASURING THE GPE & EPE AT THE START AND AT THE END OF THE MOTION CONSERVATION OF ENERGY FORMULA ΣEA + WF – Wf = ΣEB If an outside force is applied that moves the object in the same direction that the object moves… ADD WFA If an outside force like friction acts on an object in the opposite direction that it is moving… SUBTRACT Wf **ATTENTION** DO NOT ADD OR SUBTRACT THE WORK DONE BY GRAVITY OR A SPRING IN THIS FORMULA!... BUT WHY NOT?... BECAUSE WE ALREADY DO THAT BY MEASURING THE GPE & EPE AT THE START AND AT THE END OF THE MOTION CONSERVATION OF ENERGY FORMULA ΣEA + WF – Wf = ΣEB ΣEB= This is the TOTAL Energy at Point B So let us check: 1) Is there any GPE, gravity potential energy, mgh 2) Is there any EPE, elastic potential energy, (1/2)(k)(x2) 3) Is there any KE, kinetic energy, (1/2)(m)(v2) 4) ADD UP ALL THE ENERGY AT POINT B…. Now, solve for any of the variables you don’t know……