• From: Jason Li
  • Date: 16 Feb 1999
  • Subject: Is there a difference between Force and Power?

I can't even do the first question of my mechanics homework, which is to do with power:

A truck of mass 2800kg is accelerating along a straight road at 2.5 m s-2
Resistance forces amount to 1200N.
Calculate the power developed by the engine at the instant when the lorry is travelling at 10m/s.

I think that the force developed by the engine is 8200 Newtons. Is this the same as the power, or not?

Maths Help suggests:

Power and Force are not the same thing.

Power is the rate at which work is done.

Power, for constant forces, is calculated using
P = Fv
providing that the velocity is in the same direction as the force.

To analyse this problem, draw a diagram:

Applying Newton's 2nd Law ("F=ma") gives
F - 1200 = 2800×2.5
from which F = 8200

In your case, the Force is indeed 8200N.
To work out the power, multiply by the velocity of 10 m/s to give 82000 Watts, or 82kW

Return to the Mechanics subject list, or read on for a more detailed explanation...

We know "Work Done = Force × Distance", or
W = F s

Power is the rate of doing work, so
P = d/dt(Fs)

And if the force is constant, this simplifies to
P = F ds/dt
which leads to the formula
P = Fv
as before.

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