Work & Power

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Work

Work is done on an object when a force is applied and it moves in a direction that is parallel to the force acting on it.

Unit for Work is the Joule

Work = Force x DisplacementJoule Newton Meter

Nm kg m/s2 m

Work is only done on an object if the force is parallel to the object’s displacement.

Work at an angle

cosW F d

The product of the displacement and the force component acting in the direction of displacement

Example 1

Bud, a very large man of mass 130 kg, stands on a pogo stick. How much work is done as Bud compresses the spring of the pogo stick 0.50 m? (remember to find weight first, the force that is acting downwards!)

Example 2

After finishing her physics homework, Sherita pulls her 50 kg body out of the living room chair and climbs up the 5.0-m-high flight of stairs to her bedroom. How much work does. Sherita do in ascending the stairs?

It is important to note that when you are solving for the work done, you need know only the displacement of the body moved. The number of stairs climbed or their steepness is irrelevant. All that is important is the change in position.

Example 3

A car has run out of gas. Fortunately, there is a gas station nearby. You must exert a force of 715 N on the car in order to move it. By the time you reach the station, you have done 2.72 × 104 J of work. How far have you pushed the car?

Example 4

A gardener pushes down on the handle of a lawnmower at an angle of 45 with an applied force of 141 N, while pushing the mower 8.5 m along level ground. Calculate the amount of work done.

Example 5

A building under construction requires an amount of cement to be raised be lifted 76.2 m by a crane. If the net work done on the cement is 1.31 × 103 J, what is the magnitude of the net force exerted on the cement?

PowerPoweris is the rate at which work is donethe rate at which work is done

P=Work/timeP=Work/time =Force x distance/time=Force x distance/time

Power is a scalar quantity.

Force is directly proportional to power. Displacement is directly proportional to power. Time is inversely proportional to power.

Fvt

WP

The SI unit of power is the Watt, named in honor of James WattHe was a Mechanical Engineer who He was a Mechanical Engineer who invented a invented a moremore powerfulpowerful steam steam engine.engine.He also established the system by He also established the system by which we rate the power of an engine.which we rate the power of an engine.

Watt (W) = Joule/sec.Watt (W) = Joule/sec.1 kilowatt kW = 1000W1 kilowatt kW = 1000W

Horsepower

Watt’s compared the performance of the steam engines that he designed and sold to the power of horses which is what steam engines were to replace.

Horsepower (unit = hp) 1 hp = 746 watts

Example 6

Example 7

A runner exerts a force of 225 N against the ground while using 1900 Watts of power. How long does it take the runner to run a distance of 40 m?

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Simple Machines

The six simple machines are:– Lever – Wheel and Axle – Pulley – Inclined Plane – Wedge – Screw

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Simple Machines

A machine is a device that helps make work easier to perform by accomplishing one or more of the following functions: – transferring a force from one place to

another, – changing the direction of a force, – increasing the magnitude of a force, or – increasing the distance or speed of a force.

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Mechanical Advantage

It is useful to think about a machine in terms of the input force (the force you apply) and the output force (force which is applied to the task).

When a machine takes a small input force and increases the magnitude of the output force, a mechanical advantage has been produced.

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Mechanical Advantage

Mechanical advantage is the ratio of output force divided by input force. If the output force is bigger than the input force, a machine has a mechanical advantage greater than one.

If a machine increases an input force of 10 pounds to an output force of 100 pounds, the machine has a mechanical advantage (MA) of 10.

In machines that increase distance instead of force, the MA is the ratio of the output distance and input distance.

MA = output/input

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EfficiencyEfficiency

(Finput) distance = (Foutput) distance

However, some output force is lost due to friction.However, some output force is lost due to friction.

The comparison of work input to work output is called The comparison of work input to work output is called efficiency. efficiency. – Efficiency = (Woutput) / (Winput)

No machine has 100 percent efficiency due to friction. No machine has 100 percent efficiency due to friction.

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No machine can increase No machine can increase bothboth the magnitude and the magnitude and the distance of a force at the distance of a force at the same time.the same time.

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The 3 Classes of Levers

The class of a lever is determined by the location of the effort force and the load relative to the fulcrum.

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The Lever

A lever is a rigid bar that rotates around a fixed point called the fulcrum.

The bar may be either straight or curved. In use, a lever has both an effort (or applied)

force and a load (resistant force).

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Type of Lever Examples Direction of force

Crowbar, scissors, pliers, seesaw

Always changes

Nutcracker, wheelbarrow, door, bottle opener

Never changes; Increases force; increases MA

Tweezers, hammer, shovel

Never changes; Decreases force (gain speed & distance); Decreases MA

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wheel and axle - large wheel rigidly secured to a smaller wheel or shaft, called an axle.

pulley - a grooved wheel that turns freely in a frame called a block.

– can be used to simply change the direction of a force or to gain a mechanical advantage, depending on how the pulley is arranged.

– MA is equal to the number of ropes that support the moveable pulley.

Inclined plane - an even sloping surface that makes it easier to move a weight from a lower to higher elevation by increasing the distance traveled

– MA is equal to the length of the slope divided by the height of the inclined plane.

Simple Machines

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Wedge – modified inclined plane– used as either separating or holding devices.

Screw - modified inclined plane– threads of the screw as a type of circular ramp– MA is equal to dividing the number of turns per

inch

Simple Machines