Show that power is equal to product of force & velocity
Answers
Answer:
In the straightforward cases where a constant force moves an object at constant velocity, the power is just P = Fv. In a more general case where the velocity is not in the same direction as the force, then the scalar product of force and velocity must be used.
Answer:
In the straightforward cases where a constant force moves an object at constant velocity, the power is just P = Fv. In a more general case where the velocity is not in the same direction as the force, then the scalar product of force and velocity must be used.
Explanation:
Derivation :
Power output is defined as the rate of doing work with respect to time.
Power = \dfrac{Work}{time}Power=
time
Work
Work can be expressed as the scalar product of force vector and displacement.
\implies Power = \dfrac{ \vec{F }. \vec{d }}{time}⟹Power=
time
F
.
d
\implies Power = \dfrac{ F \times d \times \cos( \theta) }{time}⟹Power=
time
F×d×cos(θ)
(d/time) can be written as velocity .
\implies Power = F \times v \times \cos( \theta)⟹Power=F×v×cos(θ)
\boxed{ \implies Power = \vec{F}. \vec{v}}
⟹Power=
F
.
v
[Hence derived]
So, power can be written as dot product of force and velocity vectors.