# How to calculate motor force from power?

• Ockonal

#### Ockonal

There is car, that has motor with power P. From power I can calculate motor work per time:
$A = P*\Delta t$

P - power, A-work, $\Delta t$ - time interval.

$\Delta t$ and P are known (calculations are performing by discrete time steps).

Now, I want to calculate force F, that will produce car's moving. I.e. I need some function $F=tadam(A)$.

My attempts to solve

If motor will change only kinetic energy $E_k$, calculations can be like this (assuming, that body not moving yet, i.e. $v_1 = 0$):

$A = \Delta E_k = m*v_2^2/2 - m*v_1^2/2 = m*v_2^2/2$

$v_2 = \sqrt{2*A/m}$

$a = \frac{v_2-v_1}{\Delta t} = \frac{v2}{\Delta t} = \frac{\sqrt{2*A/m}}{\Delta t}$

$F = m*a = \frac{m*\sqrt{2*A/m}}{\Delta t} = \frac{\sqrt{2*A*m}}{\Delta t}$

If motor will change only potential energy $E_p$, calculation can be like this:

$A = \Delta E_p = m*g*\Delta h$

$A = F*\Delta h$

$F = m*g$

But, these calculations are not that I need, because I feel, that F should not depend on mass. What difference for motor, which mass has the car? I think, that force should be equal in any case. Is my feeling wrong? Why?

Context: I am developing a game, using physics engine Box2D. There I know motor power, and need force, that I will apply to the car body, by call
Code:
car->applyForce(force)
.

What difference for motor, which mass has the car?

Put a 1 litre engine in a Mini and it will accelerate to 100km/hr fairly quickly.
Put the same 1 litre engine engine in a Kenworth truck and it will hardly move.
The mass has a huge effect on acceleration.

Power = force x velocity
This gives you the relationship for a car moving at steady velocity.

Hello all, I am another author of the question.

Put a 1 litre engine in a Mini and it will accelerate to 100km/hr fairly quickly.
Put the same 1 litre engine engine in a Kenworth truck and it will hardly move.
The mass has a huge effect on acceleration.

DesmondD, yes, mass has a huge effect on acceleration, but what effect it has on motor force? If I put force 10H to body with mass = 1, it will has acceleration $10m/s^2$ and if I put same force 10H to body with mass = 100, it will has acceleration $0.1m/s^2$. I think, that motor *force* should not depend on mass. Am I wrong?

Power = force x velocity
This gives you the relationship for a car moving at steady velocity.

technician, I believe that this formula is right, when motor changing only potential energy.

$P = A/t = F*\Delta l / t = F * v$

This formula based on fact, that work is $F * \Delta l$. But if body moving without resistance and without impact of another forces, motor will change velocity, i.e. kinetic energy. After that, body can pass billions of kilometers by inertia, and no work will be done at all. So, in this case $F*v$ is meaningless.

p.s. In my case motor can change both, potential (moving car up) and kinetic (moving car forward) energies.

So far you have calculated the power and force required to accelerate the car or go up hills.

For a motor

Power = Torque x angular velocity.

You can choose:

Large torque & small angular velocity
or
Small torque & large angular velocity.

To resolve you need data on the motor, wheels gearbox etc.

So far you have calculated the power and force required to accelerate the car or go up hills.

For a motor

Power = Torque x angular velocity.

You can choose:

Large torque & small angular velocity
or
Small torque & large angular velocity.

To resolve you need data on the motor, wheels gearbox etc.

Thanks, CWatters, that's the answer. Question is closed.