Power


The rate at which work is done is power (P). Power is the rate at which energy is transferred, or transformed from one form into another.

 P=\cfrac { \Delta W }{ t } =\cfrac { \Delta E }{ t } =\cfrac { Fs }{ t }}

Power is measured in  \cfrac { J }{ s } . This unit is commonly referred to as the watt (W)


Example 1:

A crate with a mass of 5kg is carried up a hill that is 4m high in 10s. Calculate the required power needed to complete this task:

Using  P=\cfrac { \Delta E }{ t } and W=Fs ;

The applied force is = to the weight of the crate;

 F_{ g }=mg

 F_{ g }=5\times 9.8

 F_{ g }=49\quad N

Calculate the work done;

 W=Fs

 W=49\times 4

 W=196\quad J  

Calculate the power;

 P=\cfrac { \Delta E }{ t }

 P=\cfrac { 196 }{ 10 }

 P=19.6\quad W


Energy changes also occur when an object changes velocity or height. This requires power.

Example 2: 

A 350kg motorbike accelerates from rest to a velocity of 15  \cfrac { m }{ s } in 3.2s. Calculate the power required to achieve this velocity:

Using  P=\cfrac { \Delta E }{ t } and  W=\Delta KE=\cfrac { 1 }{ 2 } m({ v }^{ 2 }-{ u }^{ 2 })

 W=\Delta KE=\cfrac { 1 }{ 2 } \times 350({ 15 }^{ 2 }-{ 0 }^{ 2 })

 W=39375\quad J

Calculate the power;

 P=\cfrac { \Delta E }{ t }

 P=\cfrac { 39375 }{ 3.2 }

 P=12304.7\quad W

Often it is useful to convert power values into KW (divide W by 1000)

 P=12.3\quad KW

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