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Chapter 6Work and Machines

6.1 Work vs. Impulse

It takes Energy to push something and make it move.

• 2 conditions

1.) Force Exerted.

2.) How long force is exerted.

For…

Impulse = “how long” means time.

Work = “how long” means distance

What is Work?Work makes something move!

• Work-the transfer of energy that occurs when a force makes an object move.

• 2 conditions

1.) Force must make the object move.

2.)Movement must be in the same direction as force.

Is this work?

Examples: Lifting a barbell? Holding a barbell steady?Carrying barbell across the gym?

• Why?

Formula to calculate work

Work(J)=Force(N)*distance (m)

Or: W= Fd

Try this!Alexander has a mass of 70 kg.

His apartment is on the second floor, 5 meters from the ground level. How much work does he do against gravity each time he climbs the stairs to his apartment?

1. W=fd2. W= (70 kg x 10 m/s2) (5 m) 3. W= 3500 J

Try this!How much additional work does

Alexander have to do if he is carrying 5 kg of groceries?

1. W=fd2. W= (75 kg x 10 m/s2) (5 m) 3. W= 3750 J

Try this!A car engine does 50,000 J of

work to accelerate at 10 m/s2 for 5 m. What is the mass of the car?

• F = W ÷ d• F = 50,000 J ÷ 5 m • F = 10,000 N• F = m x a• 10,000 N = 10 m/s2 x m• Mass = 1000 kg

POWER!Power-amount of work done in one second.

• Rate at which work is done• SI unit = Watts (W)• 1 kilowatt = 1000 WFormulaPower (Watts) = Work (Joules) / Time(seconds)

P = W/t

Problem

A roller coaster is pulled up a hill by a chain attached to a motor. The roller coaster has a total mass of 10,000 kg. If it takes 20 s to pull the roller coaster up a 50 m hill, how powerful is the motor?

• P = W/t; W = Fxd• W = (10,000 kg x 10 m/s2) x 50 m • P = 5,000,000 J ÷ 20 s = 250 kW

ANOTHER PROBLEM…

What would the motor’s power be if it took 40 s to pull the same roller coaster up the hill?

P = W/tP = 5,000,000 J / 40 sP = 125 kW

YET ANOTHER PROBLEM…

What is the power of a 70 kg person who climbs a 10-meter high hill in 45 s?

P = W/t; W=FdP = (70 kg x 10 m/s2) x 10 m / 45 s

P = 156 W

TIEING IT ALL TOGETHER

Power is also the rate at which energy is transferred.

Power (Watts) = Energy transferred (Joules)

time (seconds)

P= E/tEX: Power used by lightbulb is the amount of electrical E used each second.

Work and Energy

Energy-the ability to cause change or to do work

Types of energy:Potential = energy of position.m x g x h or F x h.

Kinetic = energy of motion½ m x v2

• transfer of energy always occurs when work is done!

Mechanical Energy

Includes both Potential and Kinetic Energy

The sum of the kinetic and potential energy in a system.

Work – Energy TheoremWork is equal to change in Energy (could be potential or kinetic)

Work = ΔKE or ΔPE

Work – Energy TheoremEnergy is required to change the motion of an object (speed up or slow down)

The more motion an object has, the more KE the object has.

Work = Δ KE, therefore the more KE the more work required to change the object’s motion.

Work and EnergyHeight of the weight, Δ y = distance the tractor travels, d.

Ideal situation: constant speed and negligible friction - therefore Ftractor = Fweight

PE is given by FΔ y, & Wtractor on the weight equals Fd

So W = ΔE

Try this!How much work is needed to lift

an object that weighs 500 N to a height of 4 m? How does this work compare to the change in PE for that object?

1. W=fd or PE = m x g x h2. W= (500N) (4m) or PE = 500 N

x 4 m3. W= 2000 J or PE = 2000 J4. They are the same!

Try this!A tractor accelerates a 100 kg

trailer from rest to a velocity of 5 m/s over a distance of 1.25 m. How much work is required and how does this work compare to the change in KE for that object? What is the acceleration of the trailer?

• W=fd or KE = ½ m x v2

• W= (100 kg x 10 m/s2) (1.25 m) or KE = ½ 100 kg x 52

• W= 1250 J or KE = 1250 J• They are the same!• F = ma; a = 10 m/s2

Try this!A car traveling along a level road at

speed “v” slams on the brakes and skids to a stop. If the force of friction on the car is half the car’s weight, how far does the car slide?

1. W=Fd or ΔKE = ½ m x v2

2. Fd = ½ m v2 3. d = ½ m v2 ÷ F; F = ½ m g4. d = v2 ÷ g5. Stopping distance is proportional

to v2

6.8 Machines

Machine- a device that makes doing work easier.

• ↑ force that can be applied on an object.

• ↑ the distance over which a force can be applied.

• Changing the direction of the force applied

Work done by Machines

Input force-force that is applied to the machine. Fin

Output force- force applied by the machine. Fout

Energy is always conserved!• Your energy is transferred to machine• Machine transfers energy to the object.

• Some energy changes to heat due to friction

•Wout is never greater than Win

Conserving Energy

Work done by Machines

If Friction is negligible, meaning not present, then we can say the following:

Work input = Work output(Fd)in = (Fd)out

Simple Machines

• 6 classes of machines: Lever Inclined planePulley Wheel & axleWedgeScrew

1. Lever

Lever- A bar that is free to pivot or turn around a fixed point.

Parts of a Levers

Fulcrum- fixed pointInput Arm- Distance from fulcrum to part where input force is applied.

( E =effort force)Output arm-Distance from fulcrum to part where output force is applied.

(R =resistance Force)

First Class levers

• Fulcrum is between the output ( R ) & input force (E).

• Forces move in opposite directions

• Ex: See saw

INPUT FORCE

OUTPUT FORCE

Second Class Levers

• Output force between the input force & fulcrum.

• EX: Car door, wheelbarrow

OUTPUT FORCE

INPUT FORCEFULCRUM

Third Class Lever

• The input force is between output force and fulcrum.

• EX: Your arm, hockey stick, baseball bat.

OUTPUT FORCE

FULCRUM

INPUT FORCE

Mechanical Advantage

Mechanical advantage-the ratio of the output force to the input force

MA = output force (N) input force (N)

• The mechanical advantage of a machine without friction is the ideal mechanical advantage. (IMA)

Ideal MA (lever)

IMA= Length of input arm (m) Length of output arm (m)

IMA = Linput ÷ Loutput

Example Problem

A lever has a mechanical advantage of 4. Its input arm is 60 cm long. How long is its output arm?

1. MA = Lin ÷ Lout2. 4 = 60 ÷ Lout3. Lout = 15 cm

Example Problem

What is the mechanical advantage of a lever with an input arm of 25 cm and an output arm of 100 cm?

1. MA = Lin ÷ Lout2. MA = 25 cm ÷ 100 cm3. MA = 0.25

Example Problem

A lever has an input arm of 100 cm and an output arm of 10 cm. What is the mechanical advantage of this lever? Given the mechanical advantage, how much input force is needed to lift a 100-N load?

1. MA = Lin ÷ Lout2. MA = 100 cm ÷ 10 cm = 104. MA = Fout ÷ Fin; 10 = 100-N ÷ Fin5. Fin = 10 N

Example Problem

You want to use a lever to lift a 2000 N rock. The maximum force you can exert is 500 N. Draw a lever that will allow you to lift the rock. Label the input force, output force, fulcrum, input arm and output arm. Specify measurements for the input and output arms.

2. PulleysPulley – grooved wheel w/ a rope or chain, or cable running along a groove.

Modified 1st class lever

Can change direction of input force or increase output force

Three types!

PULLEYS

1.Fixed Pulley- Changes only direction of force.

IMA = 1 EX: Elevator

cable

OUTPUT FORCE

INPUT FORCE

FULCRUM

PULLEYS

2. Moveable pulley- one end of the rope is fixed & wheel is free to move.

Multiplies force Force required = weight ÷ IMA

Output force = 8 NInput force = 4 NIMA = 2

String attached to ceiling is another

person who can support ½ weight of

the load.

If the weight of the load is equal to 8 N, you only need to exert a force of 4 N in order to support and lift the load.

8N

PULLEYS

3. Block & Tackle- System of fixed & moveable pulleys

IMA= # of ropes that support the weight.

Force required = weight ÷ IMA

Fixed Pulley

Moveable Pulley

IMA = 2

Efficiency

Efficiency- a measure of how much of the work put into a machine is changed into useful output work by the machine.

efficiency ( %) = output work (J)

input work (J) X 100

• ↑ Efficiency by reducing friction– Lubrcant ex: oil or grease, ball bearings, etc…

Work & EnergyWork - the transfer of energy that occurs when a force makes

an object move.• 2 conditions

1.) Force must make the object move.

2.)Movement must be in the same direction as force.

W = F x d

Work & EnergyWork - the transfer of energy that

occurs when a force makes an object move.

Types of energy:Potential = energy of position.m x g x h or F x h.Kinetic = energy of motion½ m x v2

Work must equal CHANGE IN ENERGY!

Work & EnergyPower-amount of work done in one second.

• Rate at which work is done

FormulaP = W/t

Work & Energy

Machine- a device that makes doing work easier.

• ↑ force that can be applied on an object.

• ↑ the distance over which a force can be applied.

• Changing the direction of the force applied

•Win = Wout or (Fd)in = (Fd)out

Simple Machines

• 6 classes of machines: Lever Inclined planePulley Wheel & axleWedgeScrew

Mechanical Advantage

Mechanical advantage-the ratio of the output force to the input forceMA = output force (N) input force (N)MA lever = Lin/LoutMA pulley = # ropes supporting weight

Efficiency

Efficiency- a measure of how much of the work put into a machine is changed into useful output work by the machine.

efficiency ( %) = output work (J)

input work (J) X 100

• ↑ Efficiency by reducing friction