Download Physics Chapter 10 – Work, Energy, and Simple Machines What is

Physics Chapter 10 – Work, Energy, and Simple Machines
What is energy? When you have a lot of energy you can run farther or faster; you can jump higher. Objects, as well
as people, can have energy. A stone falling off a high ledge has enough energy to damage a car roof. One way to
summarize the examples of energy above is to say that an object has energy if it can produce a change in itself or
in its surroundings. This may not seem very exact, but there is no more precise definition.
Eureka! Episode 8 - Work
In this chapter, we will concentrate on ways of producing changes in objects or their environment. The human race
has developed many tools and machines that make it easier to produce such changes. A 21-speed mountain
bicycle is a machine that allows the rider to select the speed that makes the bike easiest to ride whether it is going
uphill or along a level path. You will discover the physical principles that make this kind of machine work.
10-1. Work and Energy
If you spend the morning lifting crates from the floor of a warehouse up onto a truck, you will get tired and hungry.
You will need to eat food to "get more energy." By digestion and absorption, the energy in the food will be
transferred into the energy in the raised crates. We use the word work to indicate the amount of energy that was
transferred from food to you to the crates. The word work has both an everyday and a scientific meaning. In the
case of lifting crates, everyone will agree that work was done. In everyday life, however, we use the word when
talking about other activities. For example, everyone says that learning physics is hard work! But in physics, we
reserve the term work to mean a very special form of physical activity.
Work
When lifting crates, or any other object, we do more work when the crate is heavier. The task is even harder if the
crate must be lifted higher. It seems reasonable to use the quantity force times distance to measure the amount of
energy transferred when lifting. For cases where the force is constant, we define work as the product of the force
exerted on an object and the distance the object moves in the direction of the force. In equation form,
W = Fd, where W is the work, F is the magnitude of force, and d is the magnitude of displacement in the direction of
the force. Note that work is a scalar quantity meaning it has no direction. The SI unit of work is the joule [JOOL].
The joule is named after James Prescott Joule, a nineteenth century English physicist and brewer. If a force of one
newton moves an object one meter, one joule of work is done.
1 joule (j) = 1 newton · meter (N · m) - English system foot pounds = .736 ftlbs
Work is done on an object only if the object moves. If you hold a heavy banner at the same height in the same
place for an hour, you may get tired, but you do no work on the banner. Even if you carry the banner at constant
velocity and at a constant height, you do no work on it. The force you exert is upward while the motion is sideways,
so the banner gains no energy. Work is only done when the force and displacement are in the same direction.
A force-displacement graph can give you a picture of the work done. The graph below shows the forcedisplacement graph of a rock being pushed horizontally.
A net force of 20 N is needed to push the rock 1.5 m with constant velocity. The work done on the rock is the
product of the force and the displacement, W = Fd = (20 N)(1.5 m) = 30 J. The shaded area under the curve of the
graph is equal to 20 N x 1.5 m, or 30 J. The area under the curve of a force-displacement graph represents the
work done. If you increase either the width of the rectangle (displacement) or the height (force), you increase the
work done.
Use example problem 10-1 to solve practice problems 10-1
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Work and Direction of Force
Work is done only if a force is exerted in the direction of motion. The person or object that exerts the force does the
work. If a force is exerted perpendicular to the motion, no work is done. What if a force is exerted at some other
angle to the motion? For example, if a man pushes the lawn mower in figure A below, what work would he be
doing?
You know that any force can be replaced by its components. The 125-N force (F) he exerted in the direction of the
handle has two components, figure b. The horizontal component (Fx) is 113 N (cos); the vertical component (Fy)
(sin) is –53 N (downward). The vertical component is perpendicular to the motion. It does no work. Only the
horizontal component does work. The work accomplished when the exerted force is at an angle to a motion is equal
to the component of the force in the direction of the motion times the distance moved. The magnitude of the
component of the force F acting in the direction of motion is found by multiplying the force F by the cosine of the
angle between F and the direction of motion.
W= F(cos θ)d
= Fd cos θ
Other objects exert forces on the lawn mower. Which of these objects do work? Earth's gravity acts downward, and
the ground exerts the normal force upward. Both are perpendicular to the direction of motion. That is, the angle
between the force and direction of motion is 900. Since cos 900 = 0, no work is done.
The lawn exerts a force, friction, in the direction opposite the motion. In fact, if the lawn mower moves at a constant
speed, the horizontal component of the applied force is balanced by the force of friction,F f. The angle between the
force of friction and the direction of motion is 1800. Since cos 1800 = - 1, the work done by the grass is W = - Ffd.
The work done by the friction of the grass is negative. The force is exerted in one direction, while the motion was in
the opposite direction. Negative work indicates that work is being done on the grass by the mower. The positive
sign of the work done by you exerting the force on the handle means you are doing work.
What is the effect of doing work? When you lift a box of books onto a shelf, you give the box a certain property. If
the box falls, it can do work; it might exert forces that crush another object. If the box is on a cart and you push on
it, you will start it moving. Again, the box could exert forces that crush another object. In this case too, you have
given the box energy - the ability to produce a change in itself or its surroundings.
By doing work on the box, you have transferred energy from your body to the box. Thus, we say that work is the
transfer of energy by mechanical means. You can think of work as energy transferred as the result of motion. When
you lift a box, the work you do is positive. Energy is transferred from you to the box. When you lower the box, work
is negative. The energy is transferred from the box to you.
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PROBLEM SOLVING STRATEGY
When doing work problems, you should:
1. Carefully check the forces acting on the object. Draw a diagram indicating all the force vectors.
2. Ask, "What is the displacement? What is the angle between force and displacement?"
3. Check the sign of the work by determining the direction energy is transferred. If the energy of the object
increases, the work done on it is positive.
Use example problem 10-2 to solve practice problems 10-2
Power Physics: Power
Until now, none of the discussions of work have mentioned the time it takes to move an object. The work done
lifting a box of books is the same whether the box is lifted in 2 seconds or if each book is lifted separately, so that it
takes 20 minutes to put them all on the shelf. The work done is the same, but the power is different. Power is the
rate of doing work. That is, power is the rate at which energy is transferred. Power is work done divided by the time
it takes. Power can be calculated using
P = W/t
Power is measured in watts (W). One watt is one joule of energy transferred in one second. A machine that does
work at a rate of one joule per second has a power of one watt. A watt is a relatively small unit of power. For
example, a glass of water weighs about 2 N. If you lift it 0.5 meter to your mouth, you do 1 joule of work. If you do it
in one second, you are doing work at the rate of one watt. Because a watt is such a small unit, power is often
measured in kilowatts (kW). A kilowatt is 1000 watts. Refer to Watts Power – word doc
Use example problem 10-3 to solve practice problems 10-3
10.2 MACHINES
Everyone uses some machines every day. Some are simple tools like bottle openers and screwdrivers; others are
complex objects such as bicycles and automobiles. Machines, whether powered by engines or people, make our
tasks easier. A machine eases the load either by changing the magnitude or the direction of a force, but does not
change the amount of work done.
Simple and Complex Machines
Consider the bottle opener below. (This was before twist offs)
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When you use the opener, you lift the handle, doing work on the opener. The opener lifts the cap, doing work on it.
The work you do is called the input work, W i The work the machine does is called the output work, W 0.
Work, you remember, is the transfer of energy by mechanical means. You put work into the machine. That is, you
transfer energy to the bottle opener. The machine does work on another object. The opener, in turn, transfers
energy to the cap. The opener is not a source of energy, so the cap cannot receive more energy than you put into
the opener. Thus, the output work can never be larger than the input work. The machine simply aids in the transfer
of energy from you to the bottle cap.
Energy Conservation and Mechanical Advantage
The force you exert on a machine is called the effort force, F e. The force exerted by the machine is called the
resistance force, Fr. The ratio of resistance force to effort force, Fr /Fe, is called the actual mechanical advantage
(AMA) of the machine. That is,
AMA = Fr/Fe
Many machines, like the bottle opener, have a mechanical advantage greater than one. When the mechanical
advantage is greater than one, the machine increases the force you apply.
We can calculate the mechanical advantage of a machine using the definition of work. The input work is the product
of the effort force you exert, Fe, and the displacement of your hand, de In the same way, the output work is the
product of the resistance force, Fr, and the displacement caused by the machine, dr. A machine can increase force,
but it cannot increase energy. An ideal machine transfers all the energy, so the output work equals the input work,
W o = W i or Frdr = Fede
This equation can be rewritten Fr / Fe = de /dr . We know that the actual mechanical advantage is given by AMA =
Fr/Fe. For an ideal machine, we also have
IMA = de/dr. Because this equation is characteristic of an ideal machine, the mechanical advantage is called the
ideal mechanical advantage,
IMA = de/dr
Note that you measure distances moved to calculate the ideal mechanical advantage, IMA, but you measure the
forces exerted to find the actual mechanical advantage, AMA.
In a real machine some of the energy is lost to friction, so not all of the input work is available as output work. The
efficiency of a machine is defined as the ratio of output work to input work. That is,
Efficiency =
W o/W i x 100
An ideal machine has equal output and input work, W o/W i = 1, and the efficiency is 100%. All real machines have
efficiencies less than 100%. We can express the efficiency in terms of the mechanical advantage and ideal
mechanical advantage.
Fr /Fe
efficiency = de/dr x 100
efficiency =
AMA
IMA
x l 00
The IMA of most machines is fixed by the machine's design. An efficient machine has an AMA almost equal to its
IMA. A less efficient machine has a smaller AMA. Lower efficiency means that a greater effort force is needed to
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exert the same resistance force.
Simple Machines – 3 types
All machines, no matter how complex, are combinations of up to six simple machines. Although we refer to the six
simple machines there is really only three - the inclined plane, the lever, and the wheel & axle. The wedge, the
pulley, and the screw are modifications of the first three.
http://videos.howstuffworks.com/science-channel/29987-what-the-ancients-knew-archimedes-on-force-video.htm
1. Inclined Planes
The inclined plane (d below) is the simplest of all the machines. A common inclined plane is a ramp. A ramp works
by helping you lift things more easily up to a higher level. The longer the distance of the ramp, the easier it is to do
the work, however, it will take a longer time to do the work. Some examples of incline planes include parking
ramps, ladders, loading docks, car ramps, stairs, and a roller coaster. AMA = Fr/Fe IMA = De/Dr What you gain
in force you lose in distance
The screw and wedge are modifications of the inclined plane.
The screw (f below) is an inclined plane in the round with a wedge at the tip. Think of a typical screw. The wedge is
the pointed end, the inclined plane is the thread that wraps around the screw.
http://videos.howstuffworks.com/science-channel/30585-what-the-ancients-knew-the-archimedes-screw-video.htm
A wedge (e below) is an inclined plane turned on its side, but instead of helping you to move things to a higher
level, a wedge helps you push things apart. Some examples of wedges include nails, pins, teeth, chisels, and wood
splitting wedges.
2. Wheel and axles
The wheel and axle (c below), moves objects across distances. The wheel, the round end, turns the axle, the
cylindrical post, causing movement. Some examples of a wheel and axle include pencil sharpener, doorknobs,
rolling pin, egg beater, bicycle, and a windmill.
The pulley (b below) is really a wheel and axle with a rope or chain attached. The grooved wheel turns around an
axle (fulcrum), and a rope or a chain is used in the grove to lift heavy objects. A pulley makes work seem easier
because it changes the direction of motion to work with gravity. Instead of lifting up, you can pull down using your
body weight against the resistance (load, that you are lifting). There are three types of pulleys the fixed pulley, the
moveable pulley, and the combined pulley. Some of the many uses of pulleys include oil derricks, winches, window
blinds, flagpoles, block and tackles, weight machines. AMA = Fr/Fe IMA =
supporting ropes (not change of direction) What you gain in force you lose in distance
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3. Levers (a) above
The lever is a device that "pivots" (or turns) against a "fulcrum" (or point). Levers come in three basic types - firstclass lever, second-class lever, and third-class lever. AMA = Fr/Fe IMA=Ae/Ar
What you gain in force you lose
in distance
Fr
FIRST CLASS LEVER
The fulcrum is between the load
force (Fr) and the effort force
(Fe). Ex. seesaw, crowbar,
trebuchet, hammer claw, pliers
(double), Scissors (double),
Shoehorn and a Spud bar
Fr
1. SECOND CLASS LEVER
The load force (Fr) is between
the effort force (FE) and the
fulcrum.
Ex: a wheel barrow, wrench,
bottle opener, diving board,
doing push ups
Fr
1.
THIRD CLASS LEVER
The effort force (Fe) is between
the fulcrum and the load force
(Fr). Ex: tweezers, arm baseball
bat, broom, Fishing rod, Hockey
stick, Shovel (the action of
picking or lifting up sand or dirt),
and Hammer
Gears, one of the simple machines used in a bicycle, are really a form of the wheel-and-axle. The IMA of all
machines is the ratio of distances moved.
The figure below shows that for levers and wheel-and-axles this ratio can be replaced by the ratio of the distances
between the places where the forces are applied and the pivot point.
For levers and wheel and axles, the IMA = re/rr
A common version of the wheel-and-axle is a pair of gears on a rotating shaft. The IMA is the ratio of the radii of the
two gears.
Compound Machines
A compound machine consists of two or more simple machines linked so that the resistance force of one machine
becomes the effort force of the second. For example, in the bicycle, the pedal and sprocket (or gear) act like a
wheel-and-axle. The effort force is the force you exert on the pedal, Fop The resistance is the force the sprocket
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exerts on the chain, Foc. The chain exerts an effort force on the rear wheel sprocket, Fbc, equal to the force exerted
on the chain. This sprocket and the rear wheel act like another wheel-and-axle. The resistance force is the force the
wheel exerts on the road, For. By Newton's third law, the ground exerts an equal forward force on the wheel. This
force accelerates the bicycle forward.
The mechanical advantage of a complex machine is the product of the mechanical advantages of the simple
machines it is made up of. For example, in the case of the bicycle,
AMA = (Foc/Fop) x (For/Fbc) = For/Fop
The IMA of each wheel-and-axle machine is the ratio of the distances moved. For the pedal sprocket,
IMA = Pedal radius/ Front sprocket radius
For the rear wheel, we have
IMA = rear sprocket radius/wheel radius
For the bicycle, then
IMA =(Pedal radius/ Front sprocket radius)(rear sprocket/wheel radius)
= (rear sprocket radius/ Front sprocket radius) (pedal radius/wheel radius)
Since both sprockets use the same chain and have teeth of the same size, you can simply count the number of
teeth on the gears and find that
IMA = (teeth on rear sprocket
(Pedal arm length
teeth on front sprocket) X wheel radius)
On a multi-gear bike, the rider can change the mechanical advantage of the machine by choosing the size of one or
both sprockets. When accelerating or climbing a hill, the rider increases the mechanical advantage to increase the
force the wheel exerts on the road. (gear radius small front large back) On the other hand, when going at high
speed on a level road, less force is needed, and the rider decreases the mechanical advantage to reduce the distance the pedals must move for each revolution of the wheel.(gear radius large front small back)
You know that if the pedal is at the top or bottom of its circle, no matter how much force downward you exert, the
pedals will not turn. The force of your foot is most effective when the force is exerted perpendicular to the arm of
the pedal. Whenever a force on a pedal is specified, you should assume that it is applied perpendicular to the arm.
World record bicycle speed - 2008 World's Fastest Bicycle 82.33 mph! Sam Whittingham 2008 World's Fastest
Bicycle 82.33 mph! http://www.youtube.com/watch?v=BlUPjlLFzm0 (background)
http://www.youtube.com/watch?v=PMUNOLwW0io ( 82 mph record)
World's Fastest Bicycle! 58 mph for 1 hour
http://www.youtube.com/watch?v=jUgXtZFdUcs
Use example problem 10-4 to solve practice problems 10-4
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BIOLOGY CONNECTION
The Human Walking Machine.
Movement of the human body is explained by the same principles of force and work that describe all motion.
Simple machines, in the form of levers, give us the ability to walk and run. Lever systems of the body are complex,
but each system has four basic parts: 1) a rigid bar (bone), 2) a source of force (muscle contraction), 3) a fulcrum or
pivot (movable joints between bones), and 4) a resistance (the weight of the body or an object being lifted or
moved), Figure 10-14. Lever systems of the body are not very efficient, and mechanical advantages are low. This is
why walking and jogging require energy (burn calories) and help individuals lose weight.
When a person walks, the hip acts as a fulcrum and moves through the arc of a circle centered on the foot. The
center of mass of the body moves as a resistance around the fulcrum in the same arc. The length of the radius of
the circle is the length of the lever formed by the bones of the leg. Athletes in walking races increase their velocity
by swinging their hips upward to increase this radius.
A tall person has a lever with a lower IMA than a short person. Although tall people can usually walk faster than
short people, a tall person must apply a greater force to move the longer lever formed by the leg bones. Walking
races are usually 20 or 50 km long. Because of the inefficiency of their lever systems and the length of a walking
race, very tall people rarely have the stamina to win.
Do Concept Review 10-2
Put levers, incline planes, and pulleys on board – pass out additional reading.
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