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Power(P)=Force(F) . Velocity(V)

"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." Source-Hyperphysics

The question here is, since the velocity is constant, there is no acceleration, then where does the force come from?

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  • $\begingroup$ More precisely, $P=Fv\cos \theta$ or $P=\mathbf{F} \cdot \mathbf{v}$. That's the power delivering by specific $F$ which doesn't mean $F$ is the only force acting on the moving object. By the way, $F$ does zero work on the object when it's perpendicular to the object's movement. Imagine a satellite orbiting about a planet, the gravity alters the direction of motion only, not the kinetic energy which depends on speed. $\endgroup$ Feb 9, 2017 at 14:51
  • $\begingroup$ Force doesn’t “come from” acceleration, that is a weird unintuitive idea. In your situation there must be another force like friction exactly cancelling an impressed force to get the situation of no acceleration and thus constant velocity. Only if there is a total resultant force on the object that will make it accelerate. (Note newton action and reaction act between two different bodies and do not therefore cancel in their action on any one body.) $\endgroup$
    – blanci
    Mar 29, 2021 at 21:21

3 Answers 3

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The question here is, since the velocity is constant, there is no acceleration, then where does the force come from?

  • What happens when you stop giving the force?

The object eventually stops.

  • Why does it stop?

Well, there must be some deceleration acting on the object, essentially a dissipative force like friction or, in some cases, viscosity.

So the initial constant force acting on the object is necessary to oppose and cancel out this dissipative force, so that the object has a net constant velocity.

Hope this helps you.

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  • $\begingroup$ I had this exact thought, but again i got to imagine a situation where no opposing force acts. So the conclusion is, the above equations holds only for the situation where opposing forces are present. $\endgroup$
    – Sahil
    Feb 9, 2017 at 14:35
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    $\begingroup$ @ManishYadav Yes, your equation is the power required by, say, a car engine to maintain a constant velocity and balance the resisting forces F (friction from the ground, air resistance, friction of the moving parts in the engine..) $\endgroup$ Feb 9, 2017 at 14:39
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    $\begingroup$ @ManishYadav If you don't have any opposing force, why would you require power? You require energy to perform some work aganst some barrier. Else the object will move with constant velocity without the application of any external force as per Newton's First Law. And if you still give force in such a scenario, the object will accelerate. $\endgroup$ Feb 9, 2017 at 14:40
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Imagine a body falling at the terminal (constant) speed.
The force of gravitational attraction (weight of the body $W$) is doing work at a rate (power) $Wv$ and this work is dissipated as heat due to the equal but opposite force of friction acting upwards on the body.

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The formula applies to the sum total of all involved forces. A box drifting through empty space requires no power because no force is required to maintain the velocity; pushing a box across the ground requires a motor or laborer to apply constant force because friction applies an opposing force. If you consider only the motor there is a non-zero force - and thus non-zero power - but if that force is equal to the friction force, the net acceleration is zero and the velocity is constant.

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