In mechanics, we can also express power in terms of force and velocity. In this post, we will derive the relation between power and velocity. First, we will follow a simpler method (for class 10). And then we will use the concept of Vector to find out the Force power velocity relationship.
Relation between power and velocity
Consider a vehicle traveling at constant velocity v along a straight, level road. The engine must continue to do work against friction as the vehicle is moving at a constant velocity.
If the frictional force is F, then the engine will supply an equal-sized force in the opposite direction.
The work done by the engine, W, in time t, is Fs, where s is the distance traveled in time t:
So, power = (Fs)/t ………………. (1)
but s/t= v,
therefore: power = Fv
Now, let’s find the above relationship involving vector concepts.
Force power velocity relationship [using vector concept]
Suppose that a force F acts on an object while it undergoes a vector displacement Δs. If F|| is the component of F tangent to the path (parallel to Δs), then the work done by the force is ΔW = F||Δs.
The average power is Pav =(F||Δs)/Δt = F|| (Δs/Δt) = F||vav ……………… (a)
Instantaneous power P is the limit of this expression as Δt ->0
P = F||v ………………(b)
where v is the magnitude of the instantaneous velocity.
We can also express Eq. (b) in terms of the scalar product: P = F.v
Numerical solved using P= Fv equation
A cyclist is travelling along a straight level road at a constant velocity of 27 km h−1 against total frictional forces of 50 N.
Calculate the power developed by the cyclist.
Solution:
First, let’s Convert the velocity from km h−1 into m s−1:
v= 27 km h−1 = 27 ×1000/3600 = 7.5 m s−1.
As the cyclist is moving with uniform velocity, hence Force applied by the cyclist = frictional force
So the power developed by the cyclist = force × velocity = 50 x 7.5 W = 375 W
