8.8 Efficiency

The ideal machine has 100% efficiency.

Work output = work input

In the real world, no machine is 100% efficient:  some work energy is dissipated (“wasted”) as heat or, more properly, as “thermal” energy

Question:

If 100 J of work is put into a lever and 98 J of work is output, how much energy is “lost” as heat and what is the efficiency of the lever?

In a pulley system, if we do 100 J of work and only 60 J of work is output, how much energy is “lost”?  Why is more energy lost in a pulley system?  What is the efficiency of the pulley?

The lower the efficiency of a machine, the greater is the amount of energy wasted as heat.

Equation for efficiency:

Efficiency = useful work output

                     Total work input

See figure 8.14

Efficiency = actual mechanical advantage

                     Theoretical mech. advantage

Question:

What is the theoretical mechanical advantage of an inclined plane in which a block of ice is slid 5 m to raise it 1 m?

If the plane is only 25% efficient, what is the actual mechanical advantage?

An auto jack is really an inclined plane wrapped around a cylinder.

See fig 8.15 on p 115

Question:

A child on a sled (total weight 500 N) is ppulled up a 10 m slope that elevates her a vertical distance of 1 m

[See picture on p 116]

1. What is the theoretical mechanical advantage of the slope?
2. If the slope is without friction, and she is pulled up the slope at constant speed, what will be the tension in the rope?
3. Considering the practical case where friction is present, suppose the tension in the rope were actually 100 N.  What is the actual mechanical advantage of the slope?  What would the efficiency be?

Automobile Efficiency

An automobile engine transforms chemical energy stored in fuel into mechanical energy.  How efficient is an auto engine?

Fuel Energy in = Cooling water losses + Engine Output + Exhaust Heat

     100%                        35%                               30%                35%

Posted by physicscp at 10:38 AM EST

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8.7 Machines

Machine

q       Device used to multiply force

q       Change direction of force

Lever:  if work output equals work input, then

less force times greater distance = greater force times less distance

Distance is the distance from the fulcrum, which is the pivot point

Mechanical advantage is the ratio of output force to input force:

Mechanical Advantage = Output Force

                                         Input Force

Question:

What is the Mechanical Advantage in figure 8.10?

See figures 8.11 on p 112 for illustrations of 3 types of levers.

Pulley:  a type of lever that can change the direction of the force

See fig 8.12 on p 113 for illustrations of 3 types of pulleys

The Rule for determining Mechanical Advantage for simple pulley systems:

When pulleys are the same size:

The Mechanical Advantage = the number of strands of rope that support the load

Also,

Mechanical Advantage = Input distance

                                         Output distance

q       No Machine can ever put out more energy than is put into it.

q       No Machine can create energy

q       A Machine can only

o       Transfer energy from one place to another or

o       Transform energy from one form to another.

Posted by physicscp at 10:35 AM EST

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8.6 Conservation of Energy

Law of Conservation of Energy

q       Energy cannot be created nor destroyed

q       Energy can be transformed from one form to another

q       Total amount of energy never changes

Energy Transformation in the pendulum (see fig 8,8 on p 110)

PE  transforms into KE  transforms into PE and back again

In fig 8.7, the total PE at the top equals the KE at the bottom

Fig 8.6 shows the conversion of PE to KE + heat.

Question:

Suppose a car with a miracle engine is about to covert into work 100% of the energy released when gasoline burns (40 million joules per liter).  If the air drag and overall frictional forces on the car traveling at highway speed is 500 N, what is the upper limit in distance per liter of gasoline the car could cover at high way speed?

Posted by physicscp at 7:29 PM EST

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Chap 8 Conceptual Physics Notes 8.1 to 8.5

 8.1    Work 

Work = Force x distance

Work requires two things:

q       The application of a force

q       The movement of something by that force

Units of work:

Newton * meter = Joule

Or

Nm = J

One Joule of work is done when 1 Newton of force is exerted over a distance of 1 meter.

 Question: The movers move one load up one storey.If the same load is lifted two stories, how much work is done?If two loads are lifted up one storey, how much work is done? 

8.2    Power 

Power is how fast the work is being done or the rate of doing work

Power = Work Done / Time interval

Unit of Power is the Watt or W

One watt of power is expended when one joule of work is done in one second.

750 watts = 1 horsepower or

750 W = 1 HP

 Question: If a forklift is replaced with a new forklift that has twice the power, how much greater a load can it lift in the same amount of time?Or, if it lifts the same load, how much faster can it operate? 

8.3    Mechanical Energy 

Energy enables an object to do work.

All forms of Energy are measured in Joules.

Mechanical Energy is the Energy due to

q       The position of something or

q       The movement of something

8.4 Potential Energy

Potential Energy is energy

q       that is stored

q       due to the position of the object

q       that the object has because it has the potential for doing work

Examples

Stretched or compressed spring

Stretched rubber band

Fossil fuels

Batteries

food we eat

Gravitational Potential Energy

Potential energy due to elevated position

Gravitational Potential Energy = Weight x height

                        Or

PE = mgh

The height, h is a measurement from the height to some reference level.

The PE does not depend on the path taken to get to h.

(See picture on p 107)

1. How much work is done on a 100 N boulder that you carry horizontally at constant velocity across a 10 m room?

1. a.  How much work is done on a 100 N boulder when you lift it 1 m?

1. What power is expended if you lift the boulder a distance of 1 m in 1 s?
2. What is the gravitational PE of the boulder in the lifted position?
3. How much work are you doing on the boulder to hold it in this position?

8.4    Kinetic Energy

Kinetic Energy is the Energy of Motion

The formula to find Kinetic Energy is:

KE = ½ mv²

Where m is mass and v is velocity

The KE of a moving object is equal to the work required to bring it to that speed.

So,

Fd = ½ mv²

Note:

Speed is squared, so if the speed of an object is doubled, Energy is quadrupled.  (See picture on P 108)

Question:

When the brakes of a motorcycle traveling at 60 km/h become locked, how much farther will the motorcycle skid than if it were traveling at 20 km/h?

Posted by physicscp at 5:43 PM EST

Updated: Saturday, 2 December 2006 5:50 PM EST

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