What can you remember from P3 in year 11?What can you remember from P3 in year 11?

•DefinitionDefinition•FormulaFormula•Derived UnitsDerived Units•Actual unitsActual units

1.1. To understand how to successfully To understand how to successfully complete mechanical power problemscomplete mechanical power problems

2.2. To apply these skills to the slightly more To apply these skills to the slightly more involved questions at ASinvolved questions at AS

Book Reference : Pages 153-154Book Reference : Pages 153-154

Some thoughts on work done from last Some thoughts on work done from last lesson....lesson....

Two people each shifting boxes up a flight of Two people each shifting boxes up a flight of stairs... One at a full sprint, while the other stairs... One at a full sprint, while the other takes all day. Currently, through our view of takes all day. Currently, through our view of work done, we would calculate the work done work done, we would calculate the work done by each to be the sameby each to be the same

Clearly this conflicts with our everyday Clearly this conflicts with our everyday definition of working harddefinition of working hard

Definition :Definition :

Power is defined as the rate of energy transferPower is defined as the rate of energy transfer

Formula : Formula :

Power = Power = EnergyEnergyTimeTime

And when energy is transferred by a force doing work...And when energy is transferred by a force doing work...

Power = Power = Work doneWork donetime taken to do that worktime taken to do that work

Units:Units:Derived : J/s = called Derived : J/s = called Watts (capital W)Watts (capital W)

Worked Example:Worked Example:

A person with a mass of 48kg (480N) climbs a flight A person with a mass of 48kg (480N) climbs a flight of stairs with a height of 10m in 12sof stairs with a height of 10m in 12s

Power = Power = Work doneWork donetime taken to do that worktime taken to do that work

Power = Power = 480N x 10m480N x 10m12s12s

Power = 400WPower = 400W

Looking at the power Equation again:Looking at the power Equation again:

Power = Power = Work doneWork donetime taken to do that worktime taken to do that work

Power = Power = Force x distance moved etc...Force x distance moved etc... tt

However, d/t is a very familiar concept.....However, d/t is a very familiar concept.....

Power = Power = Force x velocityForce x velocity

Engines produce motive power. A powered Engines produce motive power. A powered vehicle can be found in different scenarios:vehicle can be found in different scenarios:

1.1. Moving at constant speed & heightMoving at constant speed & height

2.2. Moving & gaining speedMoving & gaining speed

3.3. Moving & gaining heightMoving & gaining height

No reason why we couldn’t mix and match!No reason why we couldn’t mix and match!

Moving at constant speed & heightMoving at constant speed & height

All of the resistive forces, (friction, air All of the resistive forces, (friction, air resistance etc) are resistance etc) are equalequal and opposite to the and opposite to the motive force. motive force.

The work done by the engine is lost to the The work done by the engine is lost to the surroundings (heat, sound etc)surroundings (heat, sound etc)

PowerPowerEngineEngine = Force = ForceResistiveResistive x velocity x velocity

Moving & gaining speedMoving & gaining speed

The motive force from the engine exceeds the The motive force from the engine exceeds the resistive forces. We have an unbalanced force resistive forces. We have an unbalanced force and so we accelerateand so we accelerate

The work done by the engine is the sum of the The work done by the engine is the sum of the energy lost to surrounding and the gain in energy lost to surrounding and the gain in kinetic energy due to the increase in speed kinetic energy due to the increase in speed

PowerPowerEngineEngine = Force = ForceResistiveResistive x velocity + K.E gain x velocity + K.E gain

Note K.E. = ½mvNote K.E. = ½mv2 2 coming soon.....coming soon.....

Moving & gaining heightMoving & gaining height

If we are driving up an incline we are gaining If we are driving up an incline we are gaining height.... If we are gaining height we are height.... If we are gaining height we are gaining gravitational potential energy (GPE)gaining gravitational potential energy (GPE)

The work done by the engine is the sum of the The work done by the engine is the sum of the energy lost to surrounding and the gain in energy lost to surrounding and the gain in gravitational potential energygravitational potential energy

PowerPowerEngineEngine = Force = ForceResistiveResistive x velocity + GPE gain x velocity + GPE gain

Note G.P.E. = mgh coming soon.....Note G.P.E. = mgh coming soon.....

Show that a juggernaut lorry with an output power of Show that a juggernaut lorry with an output power of 264kW moving at a constant speed of 70 mph (31 m/s) 264kW moving at a constant speed of 70 mph (31 m/s) experiences resistive forces of 8.5kNexperiences resistive forces of 8.5kN

PowerPowerEngineEngine = Force = ForceResistiveResistive x velocity x velocity

ForceForceResistiveResistive = Power = PowerEngineEngine / velocity / velocity

ForceForceResistiveResistive = 264,000 / 31 = 264,000 / 31

ForceForceResistiveResistive = 8516N = 8516N

Power is the rate of energy transfer and can be calculated Power is the rate of energy transfer and can be calculated using:using:

Power = Power = Work doneWork donetime taken to do that worktime taken to do that work

When powered motion is involved we can use:When powered motion is involved we can use:

Power = Power = Force x velocityForce x velocity

This can be applied to scenarios with either constant level This can be applied to scenarios with either constant level velocity or where there are gains in kinetic energy and/or velocity or where there are gains in kinetic energy and/or potential energy due to increases in velocity and height potential energy due to increases in velocity and height respectively.respectively.