Chapters 10/11 Work, Power, Energy, Simple Machines
10.1 Energy and Work • Some objects, because of their • Composition • Position • movement Possess 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 Motion • Called Kinetic Energy… here’s the derivation…starting with an acceleration equation…
Left side contains terms that describe energy of a system …where the change in velocity is due to work being done.
Kinetic Energy Kinetic energy is the energy of motion. By definition kinetic energy is given by: KE = ½ mv2 Derive the unit for Energy, the Joule!!!! • The equation shows that . . . • . . . the more kinetic energy it has. • the more mass a body has • or the faster it’s moving K is proportional to v2, so doubling the speedquadruples kinetic energy, and tripling the speed makes it nine times greater.
SI Kinetic Energy Units The formula for kinetic energy, KE = ½ m v 2 shows that its units are: kg · (m/s)2 = kg · m 2 / s 2 = (kg · m / s 2 ) m = N · m = Joule So 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 Work Right Side of out earlier equation implies that a force, applied through a distance, causes changes in KE
Work-Energy Theorem Looking at both sides of the equation….. Simply says that by doing work on a system, you increase the kinetic energy
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 an object if the force causes the object to move in the direction of the force. Objects that are at rest may have many forces acting on them, but no work is done if there is no movement.
Work The simplest definition for the amount of work a force does on an object is magnitude of the force times the distance over which it’s applied: W = Fd • This formula applies when: • the force is constant • the force is in the same direction as the displacement of the object F d
Big Heavy Mass 50 N 10 m Work Example A 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 is W = 50 N·10 m = 500 N·m= 500 J In this problem, work is done to change the kinetic energy of the box….
Negative Work A 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 BHM fk = 20 N 7 m
When zero work is done As 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. N BHM 7 m mg
Work done in lifting an object • If 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 Work The 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 Note that (Fnet )(distance) = (30 N)(4 m) = 120 J. Therefore, Wnet = Fnet d N BHM FA = 50 N fk = 20 N 4 m mg
Net Work done???? • Is work done in… • Lifting a bowling ball??? • Carrying a bowling ball across the room??? • Sliding a bowling ball along a table top???
If the force and displacement are not in the exact same direction, then work = Fd(cosq), where q is the angle between the force direction and displacement direction. F =40 N d = 3.0 m The work done in moving the block 3.0 m to the right by the 40 N force at an angle of 35 to the horizontal is ... W = Fd(cos q) = (40N)(3.0 m)(cos 35) = 98 J
B. Energy of Position • Called Potential Energy
Potential Energy energy of position or condition Ug = m g h • The equation shows that . . . • . . . the more gravitational potential energy it has. • the more mass a body has • or the stronger the gravitational field it’s in • or the higher up it is
SI Potential Energy Units From the equation Ug = mgh 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 forUis arbitrary Example: 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.
Law of Conservation of Energy In Conservation of Energy, the total mechanical energy remains constant In any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant.
Law of Conservation of Energy Energy 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 Conserved • Conservation of Energy is different from Energy Conservation, the latter being about using energy wisely • Don’t we create energy at a power plant? • That would be cool…but, 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) • Doesn’t the sun create energy? • Nope—it exchanges mass for energy • E=mc2
pivot K.E. = 0; P. E. = mgh K.E. = 0; P. E. = mgh h height reference P.E. = 0; K.E. = mgh Energy Exchange • Though the total energy of a system is constant, the form of the energy can change • A simple example is that of a simple pendulum, in which a continual exchange goes on between kinetic and potential energy
Perpetual Motion • Why won’t the pendulum swing forever? • It’s hard to design a system free of energy paths • The pendulum slows down by several mechanisms • Friction at the contact point: requires force to oppose; force acts through distance work is done • Air resistance: must push through air with a force (through a distance) work is done • Gets some air swirling: puts kinetic energy into air (not really fair to separate these last two) • Perpetual motion means no loss of energy • solar system orbits come very close
h Law of Conservation of Energy PE = mgh KE = 0 The 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.
h Law of Conservation of Energy PE = mgh KE = 0 If the ball rolls off the shelf, the potential energy becomes kinetic energy PE = 0 KE = ½ mv2
Law of Conservation of Energy Since the energy at the top MUST equal the energy at the bottom… PEtop + KEtop = PEbottom + KEbottom Notice that the MASS can cancel!
Example 1 A 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?
Energy at A? Energy at B? Energy at C? Where is the ball the fastest? Why? 3.0 kg ball Calculate the energy values for A-K
Bouncing Ball • Superball has gravitational potential energy • Drop the ball and this becomes kinetic energy • Ball hits ground and compresses (force times distance), storing energy in the spring • Ball 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 bit • In the end, all is heat
Power, by definition, is the rate of doing work . P=W/t Unit=????
Power • US 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 bills • This is a unit of energy, not power
Simple Machines Ordinary machines are typically complicated combinations of simple machines. There are six types of simple machines: Simple Machine Example / description • Lever • Incline Plane • Wedge • Screw • Pulley • Wheel & Axle 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 & Work A machine is an apparatus that changes the magnitude or direction of a force. Machines often make jobs easier for us by reducing the amount of force we must apply. However, simple machines do not reduce the amount of work we do! The force we apply might be smaller, but we must apply that force over a greater distance.
Force / Distance Tradeoff Suppose a 300 lb crate of silly string has to be loaded onto a 1.3 m high silly string delivery truck. Too heavy to lift, a silly string truck loader uses a handy-dandy, frictionless, ramp, which is at a 30º incline. With the ramp the worker only needs to apply a 150 lb force (since sin30º = ½). A little trig gives us the length of the ramp: 2.6 m. With the ramp, the worker applies half the force over twice the distance. Without the ramp, he would apply twice the force over half the distance, in comparison to the ramp. In either case the work done is the same! continued on next slide 150 lb Silly String 300 lb 1.3 m 1.3 m Silly String 30º
Force / Distance Tradeoff (cont.) So why does the silly string truck loader bother with the ramp if he does as much work with it as without it? In fact, if the ramp were not frictionless, he would have done even more work with the ramp than without it. answer:Even though the work is the same or more, he simply could not lift a 300 lb box straight up on his own. The simple machine allowed him to apply a lesser force over a greater distance. This is the “force / distance tradeoff.” A simple machine allows a job to be done with a smaller force, but the distance over which the force is applied is greater. In a frictionless case, the product of force and distance (work) is the same with or without the machine.
Fout M.A. = Fin Mechanical Advantage Mechanical advantage is the ratio of the amount of force that must be applied to do a job with a machine to the force that would be required without the machine. The force with the machine is the input force, Fin and the force required without the machine is the force that, in effect, we’re getting out of the machine, Fout which is often the weight of an object being lifted. Note: a mechanical advantage has no units and is typically > 1.