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