Power - Learn - ScienceFlip

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)

$P=12.3\quad KW$