What is the power if a force is applied on a body and it moves with a velocity V?

Answer 1

P=v/f

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Well, let's see.

Force = newton

Work = force x distance = newton-meter

Power = work/time = (newton-meter)/(second)

The first answer above says Power = (Velocity)/(force). Let's check it out.

Speed= length/time = meter/second

Force = newton

V/f = (meter)/(newton-second)

Power = (newton-meter)/(second)

We don't know what kind of monstrosity V/f is, but it's not power.

How about (force) x (speed) = (newton) x (meter/second) = (newton-meter)/(second).

That's a lot nicer.

In all its glory, Power = F · V .

You, the questioner, said 'velocity', not 'speed', so you're going to have to

face this for what it is ... the product of two vectors. Force is a vector, and

so is velocity, but power is not. The way you multiply two vectors and get

a scalar is by means of the 'vector dot-product'. The dot-product of force

and velocity is:

(magnitude of the force) times (magnitude of the velocity) times (cosine of the angle between them).

The reason for this is: If the force isn't pushing in the same direction as the velocity,

then not all of it produces power, only the part of it that points in the right direction.

If you're trying to push a heavy wagon and it's not moving fast enough, what

do you do ? You let your feet get farther behind the wagon, and you crouch

down so that your shoulders are lower and more in line with the wagon. The

reason you do that is: Only the part of the force that lines up with the motion

helps with the motion, so if you want to push faster, you get the force down to

where it lines up better with the motion. You reduce the angle between the

force and the motion. That makes the cosine of the angle greater, so the dot

product is greater. Even though the magnitude of the force hasn't changed,

the component of the force in the direction where you need it has become

greater, by reducing the angle between them.