Work and Power

Work and PowerYour science teacher has just given you tonight’s homework assignment. You have to read an entire chapter by tomorrow! That sounds like a lot of work!

Actually, in the scientific sense, you won’t be doing much work at all! How can that be? In science, work is done when you exert a force that causes an object to move in the direction of the force for some distance. In the example above, you may have to put a lot of mental effort into doing your homework, but you won’t be using force to move anything. So, in the scientific sense, you will not be doing work—except the work to turn the pages of your book!

WorkHow do you know if it is work? The object has to move. No Work

Without Motion. To do work on an object, the object must move some distance as a result of force. If you lift and object work is done with upward force. However, if you then carry that same object no work is done. Remember, force must be exerted in the same direction for it to be work.

Work or Not Work?

Calculating Work How do you calculate work? The amount of work (W) you do

depends on both the amount of force (F) exerted and the distance (D) the object moves. Multiply force times distance.

W= f x d

Calculating Work How do you calculate work? Force is expressed in newtons, and

meters is the unit for length or distance. The unit of used to express work is the newton x meter (N·m), which is simply called a joule. One joule (J) is the amount of work you do when you exert a force of 1 newton to move an object a distance of 1 meter.

W = WORK in JOULES (J)f= FORCE in NEWTONS (N)d= DISTANCE in METERS (M)

Calculating Work How do you calculate work? You can use this formula to calculate

the amount of work you do to lift the plant. To lift the plant you use 50 Newtons and you move it 0.5 meters.

W= f x d W = 50 N x 0.5 m = 25 J or 25 N . m

PowerWhat is power? Is the rate at which energy is

transferred. Power equals the amount of work done on an object in a unit of time. To do a set amount of work in a shorter period of time, you need more power.

PowerHow do you calculate power? Power (P) is calculated by

dividing the amount of work (W) by the amount of time (t) required to do the work.

Since work is force times distance, you can also rewrite the equation.

Power UnitsWhat are power units? The unit to express power is joules

per second (J/s), also called the watt (W). 1W = 1 J/s

A watt is a small unit and often measured in larger units. One kilowatt (kW) equals 1,000 watts.

Power measures how fast work happens, or how quickly energy is transferred.

Power UnitsWhat are power units? When more work is done in a given

amount of time, the power output is greater. Power output is also greater when the time it takes to do a certain amount of work is decreased. For example, sanding by hand or using an electric sander.

Power UnitsWhat are power units? When talking about engines for

vehicles, they use another power unit instead of watts. This unit is the horsepower. One horsepower equals 746 watts. (Note: horsepower is not an SI unit)The term horsepower was developed to quantify power. A strong horse could move a 750 N object one meter in one second

750 N

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Machines

What Is a Machine?You are in the car with your mom on the way to a party when suddenly—KABLOOM hisssss—a tire blows out. “Now I’m going to be late!” you think as your mom pulls over to the side of the road.

She opens the trunk and gets out a jack and a tire iron. Using the tire iron, she pries the hubcap off and begins to unscrew the lug nuts from the wheel. She then puts the jack under the car and turns the jack’s handle several times until the flat tire no longer touches the ground. After exchanging the flat tire with the spare, she lowers the jack and puts the lug nuts and hubcap back on the wheel.

“Wow!” you think, “That wasn’t as hard as I thought it would be.” As your mom drops you off at the party, you think how lucky it was that she had the right equipment to change the tire.

How Machines Do WorkWhat is a machine? It is a device that allows you to do work

that is easier or more effective by changing the size or direction of a force. It can be complex as a motor or as simple as a shovel.

It does not decrease the amount of work you do but changes the way you do work.

How Machines Do WorkMachines A machine makes work easier by

changing at least one of three factors. • The amount of force you exert• The distance over which you exert

your force• The direction in which you exert your

force

How Machines Do WorkWhat forces are exerted? Work is done when a force is applied

through a distance.•The work that you on a machine is called work input.

•The work done by the machine on an object is called work output.

•The force you exert on the machine is called input force.

•The force exerted by the machine is called output force.

•The input force multiplied by input distance is input work.

•The output force multiplied by the distance is called output work.

3 Factors The amount of force you exert

In some machines, the output force is greater than the input force. How can this happen? Recall the formula for work: Work = Force x Distance. If the amount of work stays the same, a decrease in force must mean an increase in distance. So if a machine allows you to use less input force to do the same amount of work, you must apply that input force over a greater distance.

What kind of machine allows you to exert a smaller input force? Think about a ramp. Suppose you have to

lift a heavy box onto a stage. Instead of lifting the box, you could push it up a ramp. Because the length of the ramp is greater than the height of the stage, you exert your input force over a greater distance.

However, when you use the ramp, the work is easier because you can exert a smaller input force. The faucet knob in changes force in the same way .

3 Factors The distance over which you exert forceIn some machines, the output force is less than the input force. Why would you want to use a machine like this? This kind of machine allows you to exert your input force over a shorter distance. In order to apply a force over a shorter distance, you need to apply a greater input force.

When do you use this kind of machine? Think about taking a shot with a hockey stick. You move our hands a short distance, but the other end of the stick moves a greater distance to hit the puck. When you use chopsticks to eat your food, you move the hand holding the chopsticks a short distance. The other end of the chopsticks moves a greater distance, allowing you to pick up and eat food. When you ride a bicycle in high gear, you apply a force to the pedals over a short distance. The Bicycle, meanwhile, travels a much longer distance.

3 Factors The direction in which you exert forceSome machines don’t change either force or distance. What could be the advantage of these machines? Well, think about a weight machine. You could stand and lift the weights. But it is much easier to sit on the machine and pull down than to lift up. By running a steel cable over a small wheel at the top of the machine, as seen below, you can raise the weights by pulling down on the cable. This cable system is a machine that makes your job easier by changing the direction in which you exert your force.

How Machines Do WorkWhat is mechanical advantage?

It is the number of times a machine multiplies force.

A machine works easier by multiplying either force or distance, or by changing the direction of the force.

Mechanical AdvantageIncreasing Force. When the output force is greater than the input force, the mechanical advantage of a machine is greater than 1. Suppose you exert an input force of 10 newtons on a hand-held can opener, and the opener exerts an output force of 30 newtons on a can. The mechanical advantage of the can opener is The can opener triples your input force!

Increasing Distance. For a machine that increases distance, the output force is less than the input force. So in this case, the mechanical advantage is less than 1. For example, suppose your input force is 20 newtons and the machine’s output force is 10 newtons. The mechanical advantage is The output force of the machine is half your input force, but the machine exerts that force over a longer distance.

Changing Direction. What can you predict about the mechanical advantage of a machine that changes the direction of the force? If only the direction changes, the input force will be the same as the output force. The mechanical advantage will always be 1.

Math Skills

Efficiency of MachinesWhat is mechanical efficiency?

How do you calculate efficiency?

Mechanical efficiency (muh KAN I kuhl e FISH uhn see) is the comparison of a machine’s work output to the work input. It is expressed as a percent (%). The higher the percentage, the more efficient the machine

Divide the output work by the input work and multiply the result by 100 percent.

Math Skills

Efficiency of MachinesReal and Ideal Machines If you could find a machine with an efficiency of

100%, it would be an ideal machine. Unfortunately, an ideal machine, such as the one on the left does not exist. In all machines, some work is wasted due to friction. So all machines have an efficiency of less than 100%. The machines you use every day, such as scissors, screwdrivers, and rakes, lose some work due to friction.

A machine’s ideal mechanical advantage is its mechanical advantage with 100% efficiency. However, if you measure a machine’s input force and output force, you will find the efficiency is always less than 100%. A machine’s measured mechanical advantage is called actual mechanical advantage.

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Simple Machines

Lever PulleyWheel and Axle

Wedge ScrewInclined Plane

Types of MachinesImagine that it’s a hot summer day. You have a whole ice-cold watermelon in front of you. It would taste cool anddelicious—if only you had a machine that could cut it!

The machine you need is a knife. But how is a knife a machine? A knife is actually a very sharp wedge, which is one of the six simple machines. The six simple machines are the lever, the inclined plane, the wedge, the screw, the pulley, and the wheel and axle. All machines are made from one or more of these simple machines. They are machines that make work easier and has few or no moving parts.

LeversWhat is a lever and how does it works?

It is a simple machine that has a rigid bar that is free to pivot, or rotate, about a fixed point called a fulcrum.

Think about using a paint can opener. The opener rests against the edge of the can, which acts as the fulcrum. When you push down, you exert an input force on the handle, and the opener pivots on the fulcrum. Resulting in the opener pushing up exerting an output force on the lid.

Three classes of levers based on the location of the fulcrum, the load, and the input force.

Levers Mechanical Advantage

What is the mechanical advantage for a lever?

The ideal mechanical advantage of a lever is determined by dividing the distance from the fulcrum to the input force by the distance from the fulcrum to the output force.

Ideal = input arm length/output arm lengthinput arm = distance from input force to the fulcrumoutput arm = distance from output force to the fulcrum

First-Class of LeversWith a first-class lever, the fulcrum is located between the input force and the load. They always makes work easier by changing direction of the input force and can be used to increase force or increase distance.

Second-Class of LeversWith second-class levers, the load is located between the fulcrum and the input force. They do not change the direction of the input force. But they allow you to apply less force than the force exerted by the load. Because the output force is greater than the input force, you must exert the force over a greater distance.

Third-Class of LeversWith third-class levers, the input force is located between the fulcrum and the load. They do not change the direction of the input force. IN addition, they do not increase the input force and the output force is always less than the input force.

PulleyWhat is a pulley and how it works?

It is a simple machine that has a grooved wheel that holds a rope or a cable. A load is attached to one end of the rope or cable, and an input force is applied to the other end.

You use a pulley by pulling down on one end of the rope. This is the input force. At the other end of the rope, the output force pulls up on the object you want to move.

Types of PulleysWhat are the two types of pulleys?

A fixed pulley is attached to something that does not move. By using a fixed pulley, you can pull down on the rope to lift the load up. The pulley changes the direction of the force. Example – elevator.

Movable pulleys are attached to the object being moved. A movable pulley does not change a force’s direction. Movable pulleys do increase force, but they also increase the distance over which the input force must be exerted.

Types of PulleysWhat is a combination of the two types of pulleys?

A combination of the fixed and movable pulleys is called block and tackle.• The effort needed to lift the load is

less than half the weight of the load.

• The main disadvantage is it travels a very long distance.

Pulley Mechanical AdvantageWhat is the mechanical advantage for a pulley?

The ideal mechanical advantage of a pulley is equal to the number of sections of rope that support the object. Count the number of ropes that apply an upward force (note the block and tackle!)

Wheel and AxleWhat is a wheel & axle and how it works?

It is a simple machine consisting of two circular or cylindrical objects of different sizes that are fastened together and that rotate about a common axis. The object with the larger diameter is the wheel. The smaller diameter is the axle.

When you use the screwdriver, you apply an input force to turn the handle, or wheel. Because it is larger than the shaft, or axle, the axle rotates and exerts a large output force. The wheel and axle increases your force, but you must exert your force over a long distance.

Wheel and AxleHow it works? What would happen if the input force

were applied to the axle rather than the wheel? The example is a facet.

When a small input force is applied to the wheel, the wheel rotates through a circular distance.

As the wheel turns, so does the axle. But because the axle is smaller that the wheel, it rotates a smaller distance, which makes the output force force larger than the input force.

Wheel and Axle Mechanical AdvantageWhat is the mechanical advantage for a wheel and axle?

You can find the ideal mechanical advantage (MA) of a wheel and axle by dividing the radius (the distance from the center to the edge) of the wheel by the radius of the axle. Turning the wheel results in a mechanical advantage of greater than 1 because the radius of the wheel is larger than the radius of the axle.

Suppose the radius of a screwdriver’s wheel is 15 cm and its axle radius is 3 cm. The ideal mechanical advantage would be 15 cm divided by 3 cm, or 5.

Wheel & Axle and Gears

The axle is stuck rigidly to a large wheel. Fan blades are attached to the wheel. When the axel turns, the fan blades spin.

Each gear in a series reverses the direction of rotation of the previous gear. The smaller gear will always turn faster than the larger gear.

Inclined PlaneWhat is an inclined plane and how does it work?

It is a straight, flat, slanted surface with one end higher than the other.

It allows you to exert your input force over a long distance. As a result, the input force needed is less than the output force.

An inclined plane can be used to alter the effort and distance involved in doing work, such as lifting loads. The trade-off is that an object must be moved a longer distance than if it was lifted straight up, but less force is needed.

Inclined Plane - ExampleThe Egyptians used simple machines to build the pyramids. One method was to build a very long incline out of dirt that rose upward to the top of the pyramid very gently. The blocks of stone were placed on large logs (another type of simple machine - the wheel and axle) and pushed slowly up the long, gentle inclined plane to the top of the pyramid.

Inclined Plane Mechanical AdvantageWhat is the mechanical advantage for an inclined plane?

The ideal mechanical advantage (MA) of an inclined plane can be calculated by dividing the length of the incline by its height to which the load is liftedWhile the inclined plane produces a mechanical advantage, it does so by increasing the distance through which the force must move.

IMA = 3 meters / 1 meter or 3.This means the inclined plane increases the force you exerted by three times.

Wedge What is a wedge and how does it work?

It is a pair of inclined planes that moves and is thick at one end and tapers to a thin edge at the other end.

It applies an output force that is greater than your input force, but you apply the input force at a greater distance. Instead of moving an object along the inclined plane. They are used to split things. Force pushes down into wood.

Wedge - Mechanical AdvantageWhat is the mechanical advantage for a wedge?

It is similar to the inclined plane. The ideal mechanical advantage of a wedge is determined by dividing the length of the wedge by its width. Another method is dividing the slope (S) by its thickness (T).• The longer and thinner the wedge is,

the greater its mechanical advantage.

• Mechanical advantage is increased by sharpening it.

Wedge - Mechanical AdvantageAssume that the length of the slope is 8cm and the thickness is 2 cm. The mechanical advantage is equal to 8/2 or 2cm. As with the inclined plane, the mechanical advantage gained by using a wedge requires a corresponding increase in distance.

ScrewWhat is a screw and how it works?

It is an inclined plane wrapped around a central cylinder, forming a spiral.

When a screw is turned, a small force is applied over the long distance along the inclined plane. The threads act like an inclined plane to increase the distance over which you exert the input force. As the screw turns they exert output force and friction between the screw and wood hold it in place.

Most commonly used as fasteners.

Screw Mechanical Advantage

What is the mechanical advantage for a screw?

The ideal mechanical advantage of a screw is the length around the threads divided by the length of the screw.

• The closer the threads, the greater the mechanical advantage. The closer the threads the faster the screw goes into the wood.

• The mechanical advantage of an screw can be calculated by dividing the circumference by the pitch of the screw.

• Pitch equals 1/ number of turns per inch.

Combination MachinesWhat are combination machines and how it works?

They are a combination of simple machines. One that utilizes two or more simple machines. A block and tackle is an example because it consists of two or more pulleys.

A can opener may seem simple, but it is actually three machines combined. It consists of a second-class lever, awheel and axle, and a wedge. When you squeeze the handle, you are making use of a second-class lever. The blade of thecan opener acts as a wedge as it cuts into the can’s top. The knob that you turn to open the can is a wheel and axle.

Combination Machines Mechanical EfficiencyWhat is the mechanical efficiency of combination machines?

The mechanical efficiency of a compound machine low because the compound machines have more moving parts then the simple machines and more friction.

Simple Machines in the BodyYou probably don’t think of the human body as being made up of machines. Believe it or not, machines are involved in much of the work that y our body does.

Simple Machines in the BodyLiving Levers Most of the machines in your body are levers that consist of bones and muscles. Every time you move, you use a muscle. Your muscles are attached to your bones by connecting structures called tendons. Tendons and muscles pull on bones, making them work as levers. The joint, near where the tendon is attached to the bone, acts as the fulcrum. The muscles produce the input force. The output force is used for doing work, such as lifting your hand.

Working Wedges When you bite into an apple, you use your sharp front teeth, called incisors. Your incisors are shaped like wedges to enable you to bite off pieces of food. When you bite down on something, the wedge shape of your front teeth produces enough force to break it into pieces, just as an ax splits a log. The next time you take a bite of a crunchy apple, think about the machines in your mouth!

Rube Goldberg Machines• Rube Goldberg machines are

examples of complex machines.• All complex machines are made up

of combinations of simple machines.

• Rube Goldberg machines are usually a complicated combination of simple machines.

• By studying the components of Rube Goldberg machines, we learn more about simple machines

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