Energy, Work, and Energy, Work, and MachinesMachines

What is work?What is work?

Put a book over your head, are you Put a book over your head, are you working?working?

Hold a pencil out straight from your body, Hold a pencil out straight from your body, are you working?are you working?

From a physics standpoint, no. Work is From a physics standpoint, no. Work is the product of the force and the objects the product of the force and the objects distance, W = Fddistance, W = Fd

Force x Time changes momentumForce x Time changes momentum Force x Distance changes energyForce x Distance changes energy

What are we doing then?What are we doing then?

Energy is being expended, a force is being Energy is being expended, a force is being exerted but, without any net displacement, exerted but, without any net displacement, no work is done, no energy is changed.no work is done, no energy is changed.

What about a planet orbiting the sun? Is What about a planet orbiting the sun? Is work being performed?work being performed?

Remember, a force perpendicular to an Remember, a force perpendicular to an object does not change its speed, only its object does not change its speed, only its direction.direction.

What if?What if?

What if you push against a wall?What if you push against a wall? What if you push a flat cart along the What if you push a flat cart along the

ground at a constant speed?ground at a constant speed? What if you say forget it, jump out of a What if you say forget it, jump out of a

plane and are in free fall?plane and are in free fall? Ultimately, work can be defined as a Ultimately, work can be defined as a

change in kinetic energy where change in kinetic energy where KE = ½ mvKE = ½ mv22

Kinetic EnergyKinetic Energy

From the equation we can see that an From the equation we can see that an increase in mass or speed results in an increase in mass or speed results in an increase in kinetic energy, similar to increase in kinetic energy, similar to momentum. momentum.

Notice that velocity is squared, therefore a Notice that velocity is squared, therefore a small increase in speed results in a large small increase in speed results in a large increase in kinetic energy.increase in kinetic energy.

So?So? The definition of energy is the ability to cause The definition of energy is the ability to cause

change, in relation to an object either in itself or change, in relation to an object either in itself or its surroundings. Kinetic energy is the energy of its surroundings. Kinetic energy is the energy of motion, potential energy at rest. Energy is motion, potential energy at rest. Energy is measured in quanta, we’ll get to that later.measured in quanta, we’ll get to that later.

The work energy theorem states that work is a The work energy theorem states that work is a change in kinetic energy or W = KEchange in kinetic energy or W = KE

This states that work is accomplished when This states that work is accomplished when there is a net change in kinetic energythere is a net change in kinetic energy

Work is accomplished with any change in Work is accomplished with any change in energy, W = E energy, W = E

James Prescott JouleJames Prescott Joule

English Dude, 1800’s, discovered English Dude, 1800’s, discovered relationship between work and the change relationship between work and the change in energy. in energy.

Joule, also known as a Newton - Meter is Joule, also known as a Newton - Meter is equal to a force of 1 Newton acting over a equal to a force of 1 Newton acting over a distance of 1 meter. It is a unit of energydistance of 1 meter. It is a unit of energy

Lifting an apple a distance of 1 meter is Lifting an apple a distance of 1 meter is approximately 1 Jouleapproximately 1 Joule

What if?What if?

What if I am pushing a car at an angle of What if I am pushing a car at an angle of 25 degrees from the horizontal. 25 degrees from the horizontal.

Remember a force acting in the direction Remember a force acting in the direction of motion does work. A force acting of motion does work. A force acting perpendicular to the direction of motion perpendicular to the direction of motion does no work.does no work.

In this case work is a function of the angle.In this case work is a function of the angle.

Still What ifStill What if

W = Fdcos0 W = Fdcos0 The sine of the angle is the y component The sine of the angle is the y component

and vertical or perpendicular forces do no and vertical or perpendicular forces do no workwork

Gravity and normal forces do not Gravity and normal forces do not contribute to work. The cosine of 90 is 0contribute to work. The cosine of 90 is 0

Friction opposes motion and 180 degrees Friction opposes motion and 180 degrees would be opposite of motion, the cosine of would be opposite of motion, the cosine of 180 is -1 180 is -1

More workMore work

It should be noted that the area under a It should be noted that the area under a graph of force versus displacement curve graph of force versus displacement curve illustrates work.illustrates work.

What about time?What about time?

You lift 100lbs over your head but take 60 You lift 100lbs over your head but take 60 seconds to get it there. Your buddy lifts seconds to get it there. Your buddy lifts the same weight the same distance in 1 the same weight the same distance in 1 second. Work performed is the same. second. Work performed is the same. However your buddy is obviously stronger However your buddy is obviously stronger or he has more power.or he has more power.

Power is work done divided by the time it Power is work done divided by the time it takes to do it of P = w/ttakes to do it of P = w/t

PowerPower

Power is measured in watts, 1 joule of Power is measured in watts, 1 joule of energy in 1 second. Watts are typically energy in 1 second. Watts are typically measured in kilowatts measured in kilowatts

Energy and power are not the same thing Energy and power are not the same thing the smallest device can use a tremendous the smallest device can use a tremendous amount of energy given enough time. amount of energy given enough time. Power is how fast a device can use or Power is how fast a device can use or transfer energytransfer energy

More Power!!!!!More Power!!!!!

If power is equal to work divided by time If power is equal to work divided by time then it can also be said that:then it can also be said that:

P = Fd/t of P = Fv since v equals d/tP = Fd/t of P = Fv since v equals d/t

Machines incorporate these variables to Machines incorporate these variables to maximize power. You need the proper maximize power. You need the proper amount of force and speedamount of force and speed

MachinesMachines

A machine is any device that changes A machine is any device that changes either the direction or magnitude of the either the direction or magnitude of the applied force or both.applied force or both.

If the machine increases the magnitude of If the machine increases the magnitude of the applied force it gives us a mechanical the applied force it gives us a mechanical advantage, the resistance force divided by advantage, the resistance force divided by the effort force.the effort force.

MA = FMA = Frr/F/Fee

Mechanical AdvantageMechanical Advantage

If the MA is greater than 1, the machine If the MA is greater than 1, the machine provides a mechanical advantage or provides a mechanical advantage or increase in the applied force.increase in the applied force.

Machines can increase force but it cannot Machines can increase force but it cannot increase energy. All machines lose increase energy. All machines lose energy through heat, friction, etc.energy through heat, friction, etc.

An ideal machine transfers all the energyAn ideal machine transfers all the energy

Ideal Mechanical AdvantageIdeal Mechanical Advantage

While MA can be written as resistance While MA can be written as resistance force over effort force it can also be written force over effort force it can also be written as output work Wo / input work Wi or as output work Wo / input work Wi or

FFrrDDrr / F / FeeDDee Ideal mechanical advantage is calculated Ideal mechanical advantage is calculated IMA = dIMA = dee/d/drr

Notice, MA is Fr/Fe and IMA is de/drNotice, MA is Fr/Fe and IMA is de/dr

MachinesMachines

Machines are never ideal, this is a Machines are never ideal, this is a measure of the maximum possible amount measure of the maximum possible amount of work. of work.

Efficiency of machines can be measured Efficiency of machines can be measured in two ways:in two ways:

Efficiency = Wo/Wi x 100 orEfficiency = Wo/Wi x 100 or Efficiency = MA/IMA x 100Efficiency = MA/IMA x 100

More MachinesMore Machines

A simple machine is one that does work with A simple machine is one that does work with only one movement.only one movement.

There are six basic types: Lever, inclined plan, There are six basic types: Lever, inclined plan, wedge, screw, pulley, and wheel & axle.wedge, screw, pulley, and wheel & axle.

Lever, increases applied force Le/Lr and Lever, increases applied force Le/Lr and changes directionchanges direction

3 types 13 types 1stst class fulcrum in the middle class fulcrum in the middle 22ndnd class, fulcrum resistance and effort class, fulcrum resistance and effort 33rdrd class, fulcrum effort and resistance class, fulcrum effort and resistance The human body is composed of several levers.The human body is composed of several levers.

Simple machinesSimple machines

Pulleys, single pulley changes direction, a Pulleys, single pulley changes direction, a movable pulley or multiple pulleys movable pulley or multiple pulleys decrease the effort force, increasing the decrease the effort force, increasing the applied force.applied force.

Wheel and axle, similar to a lever attached Wheel and axle, similar to a lever attached to a shaft, increases your applied forceto a shaft, increases your applied force

IMA = Rw/RaIMA = Rw/Ra

More simple machinesMore simple machines

Inclined plane, allows you to cover more Inclined plane, allows you to cover more distance with less force.distance with less force.

IMA = length of slope/height of slopeIMA = length of slope/height of slope Screw, is an inclined plane wrapped Screw, is an inclined plane wrapped

around a postaround a post Wedge, is an inclined plane with two or Wedge, is an inclined plane with two or

more sloping sides, change the direction more sloping sides, change the direction of the forceof the force

Machines, Machines, MachinesMachines, Machines, Machines

A compound machine is a combination of A compound machine is a combination of any two or more simple machinesany two or more simple machines

Most “machines” are compoundMost “machines” are compound The MA for a compound machine is the The MA for a compound machine is the

combination of MA’s for each simple combination of MA’s for each simple machine MA = MA1 + MA2machine MA = MA1 + MA2