# I Potential energy loss related to force applied?

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1. Jun 1, 2018

### Joey Wilson

How can I calculate the loss of potential energy when forces are applied but no motion in the system occurs? Here's an example:

Let's say I build a battery operated car that is set to drive forward, but I put it right in front of a wall. It attempts to drive forward, but instead it just pushes into the wall and nothing moves. The battery will continue to drain, and thus potential energy is being lost, yet no work is happening. The car and the wall do not move. Let's assume that the car is able to push the wall with a consistent force of 1 newton.

If I know how long the car has been pushing (let's say for one hour), can I calculate the potential energy loss based on the fact that the car has been pushing with 1 newton, for one hour? The work is zero because if W=fd, the distance is 0, so the work is zero. Yet, there definitely is a loss of potential energy in the battery. How can I calculate that?

2. Jun 1, 2018

### kuruman

If there is no motion, then all the energy loss of the battery goes into heating the coils in the motor. You can calculate that if you know the current $I$ that the stalled motor draws. Then $E = IVt$ where $V$ is the battery voltage and t = 3600 s. That's assuming that the battery voltage stays constant and the motor doesn't burn out.

3. Jun 1, 2018

### Joey Wilson

Thank you for the reply. I'm wondering if there is a way to directly calculate the energy loss based on the force applied over time, rather than calculating from internal workings. The reason is we can measure the force applied over time, but measuring the internal flows is not possible.

4. Jun 1, 2018

### sophiecentaur

If no work is done (no motion) then there is no mechanical "energy loss". A Force X Zero Distance involves No Work. When a motor is stalled, there is no back emf to restrict the current through the armature and energy is lost only in the resistance of the wires - and, of course, in the Power source (internal resistance of a battery for instance). The lost Power has to be measured with electrical meters.

5. Jun 1, 2018

### Joey Wilson

OK - so you're saying there is no equation that relates potential energy loss to an integral of force and time?

6. Jun 1, 2018

### kuruman

That is correct. ∫Fdt is impulse which is equal to change in momentum. If nothing is moving, there is no change in momentum. Besides, impulse and energy have different dimensions.