Chapters 10/11Work, Power, Energy, Simple Machines
10.1 Energy and WorkSome objects, because of theirCompositionPositionmovementPossess the ability to cause change, or to do Work. Anything that has energy has the ability to do work.In this chapter, we focus on Mechanical Energy only.Old Man on the Mountain (before and after)
A. Energy of Things in MotionCalled Kinetic Energy heres the derivationstarting with an acceleration equation
Substitute F/m for a
Multiply by m
Lets look at each side of this equation, one side at a time.
Left side contains terms that describe energy of a systemwhere the change in velocity is due to work being done.
Kinetic EnergyKinetic energy is the energy of motion. By definition kinetic energy is given by: KE = m v 2The equation shows that . . .
. . . the more kinetic energy it has. the more mass a body has or the faster its moving
K is proportional to v2, so doubling the speed quadruples kinetic energy, and tripling the speed makes it nine times greater.Derive the unit for Energy, the Joule!!!!
SI Kinetic Energy UnitsThe formula for kinetic energy, KE = m v 2shows that its units are: kg (m/s)2 = kg m 2 / s 2 = (kg m / s 2 ) m = N m = JouleSo the SI unit for kinetic energy is the Joule, just as it is for work. The Joule is the SI unit for all types of energy.
Sample Calculations.What is the kinetic energy of a 75.0 kg warthog sliding down a muddy hill at 35.0 m/s?
What is the kinetic energy of a 50.0 kg anvil after free-falling for 3.0 seconds?
Mechanical WorkRight Side of out earlier equation implies that a force, applied through a distance, causes changes in KE
Work-Energy TheoremSimply says that by doing work on a system, you increase the kinetic energyLooking at both sides of the equation..
Work is done when..Work done against a force, including friction, or gravity (no net work is done however)Work done to change speed (momentum)(net work is done)
Work is only done by a force on anobject if the force causes the objectto move in the direction of the force.Objects that are at rest mayhave many forces acting on them,but no work is doneif there is no movement.
WorkThe simplest definition for the amount of work a force does on an object is magnitude of the force times the distance over which its applied: W = F dThis formula applies when: the force is constant the force is in the same direction as the displacement of the objectFd
Work ExampleA 50 N horizontal force is applied to a 15 kg crate of BHM over a distance of 10 m. The amount of work this force does isW = 50 N 10 m = 500 N m = 500 JIn this problem, work is done to change the kinetic energy of the box.
Negative WorkBHM7 mfk = 20 NA force that acts opposite to the direction of motion of an object does negative work. Suppose the BHM skids across the floor until friction brings it to a stop. The displacement is to the right, but the force of friction is to the left. Therefore, the amount of work friction does is -140 J.v
When zero work is doneBHM7 mNmgAs the crate slides horizontally, the normal force and weight do no work at all, because they are perpendicular to the displacement. If the BHM were moving vertically, such as in an elevator, then each force would be doing work. Moving up in an elevator, the normal force would do positive work, and the weight would do negative work.Another case when zero work is done is when the displacement is zero. Think about a weight lifter holding a 200 lb barbell over her head. Even though the force applied is 200 lb, and work was done in getting over her head, no work is done just holding it over her head.
Work done in lifting an objectIf you lift an object at constant velocity, there is no net force acting on the object.therefore there is no net work done on the object.However, there is work done, but not on the object, but against gravity
Net WorkThe net work done on an object is the sum of all the work done on it by the individual forces acting on it. Net Work is a scalar, so we can simply add work up. The applied force does +200 J of work; friction does -80 J of work; and the normal force and weight do zero work.So, Wnet = 200 J - 80 J + 0 + 0 = 120 J BHMFA = 50 N4 mfk = 20 NNmgNote that (Fnet ) (distance) = (30 N) (4 m) = 120 J.
Therefore, Wnet = Fnet d
Net Work done????Is work done inLifting a bowling ball???Carrying a bowling ball across the room???Sliding a bowling ball along a table top???
If the force and displacement are notin the exact same direction, thenwork = Fd(cosq),where q is the angle between the forcedirection and displacement direction.F =40 Nd = 3.0 mThe work done in moving the block 3.0 mto the right by the 40 N force at an angleof 35 to the horizontal is ...W = Fd(cos q) = (40N)(3.0 m)(cos 35) = 98 J
B. Energy of PositionCalled Potential Energy
Ug = m g hThe equation shows that . . .
. . . the more gravitational potential energy it has. the more mass a body has or the stronger the gravitational field its in or the higher up it is
SI Potential Energy UnitsFrom the equation Ug = m g h the units of gravitational potential energy must be:= m g h= kg (m/s2) m = (kg m/s2) m = N m = J What a surprise!!!!!
This shows the SI unit for potential energy is still the Joule, as it is for work and all other types of energy.
Reference point for U is arbitraryExample: A 190 kg mountain goat is perched precariously atop a 220 m mountain ledge. How much gravitational potential energy does it have?Ug = mgh = (190kg) (9.8m/s2) (220m) = 410 000J
This is how much energy the goat has with respect to the ground below. It would be different if we had chosen a different reference point.
Conservation and Exchange of Energy
Law of Conservation of EnergyIn Conservation of Energy, the totalmechanical energy remains constant In any isolated system of objects interactingonly through conservative forces, the totalmechanical energy of the system remainsconstant.
Law of Conservation of EnergyEnergy may neither be created, nor destroyed, but is transformed from one form to another.Example: kinetic energy of flowing water is converted into electrical energy using magnets.
Energy is ConservedConservation of Energy is different from Energy Conservation, the latter being about using energy wiselyDont we create energy at a power plant?That would be coolbut, no, we simply transform energy at our power plants, from one form to another(fossil fuel energy or nuclear energy or potential energy of water to electrical energy)Doesnt the sun create energy?Nopeit exchanges mass for energyE=mc2
Energy ExchangeThough the total energy of a system is constant, the form of the energy can changeA simple example is that of a simple pendulum, in which a continual exchange goes on between kinetic and potential energy
Perpetual MotionWhy wont the pendulum swing forever?Its hard to design a system free of energy pathsThe pendulum slows down by several mechanismsFriction at the contact point: requires force to oppose; force acts through distance work is doneAir resistance: must push through air with a force (through a distance) work is doneGets some air swirling: puts kinetic energy into air (not really fair to separate these last two)Perpetual motion means no loss of energysolar system orbits come very close
Law of Conservation of EnergyThe law says that energy must be conserved. On top of the shelf, the ball has PE.Since it is not moving, it has NO kinetic energy.PE = mghKE = 0
Law of Conservation of EnergyIf the ball rolls off the shelf, the potential energy becomes kinetic energyPE = mghKE = 0PE = 0KE = mv2
Law of Conservation of EnergySince the energy at the top MUST equal the energy at the bottom
PEtop + KEtop = PEbottom + KEbottom
Notice that the MASS can cancel!
Example 1A large chunk of ice with mass 15.0 kg falls from a roof 8.00 m above the ground. Find the KE of the ice when it reaches the ground.What is the velocity of the ice when it reaches the ground?
Where is the ball the fastest? Why?3.0 kg ballCalculate the energy values for A-K
Bouncing BallSuperball has gravitational potential energyDrop the ball and this becomes kinetic energyBall hits ground and compresses (force times distance), storing energy in the springBall releases this mechanically stored energy and it goes back into kinetic form (bounces up)Inefficiencies in spring end up heating the ball and the floor, and stirring the air a bitIn the end, all is heat
Power,by definition, isthe rate of doing work.P = W / tUnit=????
PowerUS Customary units are generally hp (horsepower)Need a conversion factor
Can define units of work or energy in terms of units of power:kilowatt hours (kWh) are often used in electric billsThis is a unit of energy, not power
Simple MachinesOrdinary machines are typically complicated combinations of simple machines. There are six types of simple machines: Lever Incline Plane Wedge Screw Pulley Wheel & Axle Simple Machine Example / description crowbar ramp chisel, knife drill bit, screw (combo of a wedge & incline plane) wheel spins on its axle door knob, tricycle wheel (wheel & axle spin together)
Simple Machines: Force & WorkA machine is an apparatus that changes the magnitude or direction of a force. Machines often make jobs easier for us by