5. Derive a relationship between power, force
and velocity
Answers
Explanation:
Consider your simple example: a car with a fixed power output of 1000 W accelerating against a constant frictional force of 5 Newtons (Even better, assume that there is no friction, but the car is climbing a very gentle slope, such that gravity exerts 5 Newtons of force back along the slope.)
Assume that it has reached a stable top speed, V m/s. In one second, the car will travel Vmetres. In doing this, it must exert a constant force of 5 Newtons, since there is no acceleration, and thus the friction force must be exactly balanced. In doing this, exerting this force through this distance, the car does (V×5) joules of work.
But in 1 second, at a power output of 1000 W, the car produces 1000 joules of energy. This energy goes into driving the car, so
(V×5) joules=1000 joules
More generally:
W=F×d
Dividing by t, time:
Wt=F×dt
or:
P=F×v
Answer:
Power=Work done×velocity
Explanation:
we have,power=work/time
work=force×displacement
substituting ,
power=work×velocity