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**Work Work = Force x Distance The force must be in the direction**

No Work Work = Force x Distance The force must be in the direction of the motion, or no work is done. Work W F D

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**The unit of work is the Joule**

Force x Distance = Work 1 Newton x 1 meter = 1 Newton meter 1 Newton meter = 1 Joule James Prescott Joule

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Example 1: A high jumper weighs 700 newtons. What work does the jumper perform in jumping over a bar 2.0 meters high? Answer: W = F x d W = 700N x 2.0 m = 1400 nm = 1400 Joules

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**No work is done if there is no distance!**

The statue of liberty has been holding up her torch for an awfully long time. How much work has she done? Answer: 0! Although it takes a force to hold the torch against the force of gravity, there is no motion so no work is done.

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**Which does more work? Frictionless**

The net work is the force (weight) of the cart X the vertical distance. This is the same in all three cases. In the first, the force is less, but distance is greater to reach the same vertical height.

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Example 2 A force of 200N is required to push a lawn mower. If 4000 J of work is performed on the lawnmower, how far does it move? Answer 4000Nm ÷ 200N = D = 20m W F D 4000J D 200N

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Remember For work to happen the force has to be applied in the SAME direction as the motion.

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**Power = Force x distance**

Work done per unit of time Power = Work Time Power = Force x distance P T

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Power An object that has more power than another object does more work in the same time. You need more power to run up the stairs than to walk because it takes you less time to do the same work.

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**The SI unit of power is the WATT (W)**

Power = Work Time 1 watt = Joule 1 Second

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**A Watt is small! Usually measured in kilowatts(kW)= 1,000W**

Another unit of power: Horsepower (not an SI unit) 1horsepower= 746 watts

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Example 3 A crane lifts a car into a junk pile in 10 seconds. What is the crane’s power if 120,000 J of work are performed? Answer: Power = Work Time 120,000J = 10 sec 12,000 Watts

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**Power = Force x distance**

Example 4 A 750 N diver does a somersault off a 10m platform. It takes her 1.5 seconds to hit the water. What is her power? Since work is Force x distance, the power formula can be written as Power = Force x distance Time

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**Answer: Power = 750N x 10m Power = 7500N m Time 1.5 sec = 5000 Watts**

Power = Force x distance Time Power = 750N x 10m 1.5 sec Power = N m = Watts

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**Other units of power 1 kilowatt = 1000 watts 1 horsepower = 746 watts**

In the previous example, how many kilowatts power was generated? How much horsepower? Answer: 5000 watts ÷ 1000 kw/w = 5 kilowatts 5000 watts ÷ 746 hp/w = 6.7 horsepower

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What is a Machine? A device that allows you to do work in a way that is easier. It changes at least one of 3 factors: The amount of force you exert The distance over which you exert your force The direction in which you exert your force.

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**Input & Output Force Input force- The force you exert on the machine.**

The input force moves the machine a certain distance, called the input distance. Output force- The force the machine exerts on an object. The machine does work by exerting a force over another distance, called the output distance.

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**Input & Output Work Input work= input force x input distance**

Output work= Output force x Output distance The amount of output work can never be greater than the amount of input work.

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Changing Force In some machines, the output force is greater than the input force This is possible by increasing the distance. What kind of machine allows you to exert a smaller input force? Ramp, faucet knob.

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Changing Distance In some machines, the output force is less than the input force Why would you use a machine like this? Hockey stick, chopsticks, riding a bike on a high gear.

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Changing Direction Some machines don’t change either the force of the distance. What is the advantage of using a machine like this? It is easier to pull down then to push up.

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Mechanical Advantage A machine's mechanical advantage is the number of times a machine increases a force. Formula: mechanical advantage (MA) = Output Force Input Force There is no unit for MA.

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Mechanical Advantage (IMA) Ideal MA: This is the MA of a machine in a world with no friction, and no force is lost anywhere. (AMA) Actual MA: This is simply the MA of a machine in the world as we know it. - Force is lost due to friction. - It is transferred into thermal energy. Can we have an ideal machine?

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Increasing Force When the output force is greater than the input force, the MA is greater than 1. Suppose you exerted a force of 10 N on a hand-held can opener and the can-opener exerts a force of 30 N on the can. What is the MA of the can opener? MA= Output force Input Force MA= 30N 10N MA= 3

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Increasing Distance For a machine to increase distance, the output force is less than the input force. The MA is less than 1 Suppose you applied a force of 20N and the machine applied a force of 10 N. What is the MA? MA= Output force Input Force MA= 10N 20N MA= 0.5 The MA is less but the machine would exert the force over a longer distance.

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Changing Direction What can you predict about the MA of a machine that changes the direction of the force? If ONLY the direction is change the input force will be the same as the output force so the MA will always be 1

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Efficiency In real world situations, the output work is always less than the input work because some work is wasted overcoming friction. Efficiency compares the output work to the input work. Efficiency= Output work x100% Input work Efficiency is expressed as a percent

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Try it out You do 20 J of work while using a hammer. The hammer does 18J of work on the nail. What is the efficiency of the hammer? Efficiency= Output work x100% Input work Efficiency= 18J x100% 20J Efficiency= .9 x100% = 90%

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**You do 250,000J of work to cut a lawn with a hand mower**

You do 250,000J of work to cut a lawn with a hand mower. If the work done by the mower is 200,000J, what is the efficiency of the lawn mower? Efficiency= Output work x100% Input work Efficiency= 200,000J x100% 250,000J Efficiency= .8 x100% = 80%

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**Is there a machine with 100% efficiency?**

Unfortunately, there is no such machine. In all machines some work is transferred into thermal energy due to friction. Ideal vs. Actual All machines have an efficiency of less than 100%

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