# How does a stop-start-stop car conserve momentum?

1. Jan 26, 2012

### stephenn

If I am to consider these three points as true:
1. A stationary car has NO momentum
2. A moving car HAS momentum
3. As momentum is a conserved property.......

So I am wondering where the momentum is conserved when
A. The car goes from say 0 to 60 mph .... from none to some p
B. The car goes from 60 to 0 mph ... from some to none p

Does the car dial in momentum to itself through two drive wheels via the road attached to the planet... ie from the planet
And visa versa on slowing down ie dial it back out from four braking wheels into the road attached to the planet... ie into the planet

any thoughts on this one would be most appreciated

2. Jan 27, 2012

### Michael C

Yes, if the momentum of the car changes then the momentum of something else must change. You're correct in thinking that this "something else" is the planet on which the car is running: when the velocity of the car changes, so does the velocity of the Earth. The car exerts a force on the Earth and the Earth exerts an equal and opposite force on the car, and both car and Earth are accelerated by the respective forces.

If you know the masses of both car and Earth, you can work out how much the velocity of the Earth changes when the car accelerates from 0 to 60 mph.

3. Jan 27, 2012

### meldraft

Conservation of momentum depends on the boundaries of your system, and assumptions.

In your case, the car's momentum (or kinetic energy may help you visualise it better) is slowly being dissipated as heat through the car's brakes and friction with the air and the ground.

Momentum is generally conserved in a system where you assume no losses, thus only conservative forces acting into the system. Real-world phenomena always involve non-conservative forces, such as friction. Btw, the energy provided by the engine into the system also messes things up (non-conservative moment).

4. Jan 27, 2012

### Delta Kilo

Sorry but what you said is just plain wrong. Momentum should not be confused with kinetic energy, these are different things. Momentum IS conserved in presence of friction and other non-conservative forces. It most certainly does NOT dissipate as heat.

Precisely. The car propels itself forward and at the same time pushes the earth backward.

Imagine a car on top of a moving platform such as railway flatcar. Driving the car would cause the platform to move the other way so that their combined center of mass would remain stationary (or if it was moving before, contionue moving at the same speed).

5. Jan 27, 2012

### meldraft

$$E_{kinetic}=\frac{momentum^2}{2 mass}$$

One is derived from the other.

Quote from an old post:
https://www.physicsforums.com/archive/index.php/t-70566.html

The conservation of momentum holds ONLY in an isolated system. If there are forces dissipating energy, and are not within the boundary of the system, momentum cannot possibly be conserved, except instantaneously. This is most certainly depicted by the flow of energy.

6. Jan 27, 2012

### Michael C

You cannot derive the momentum of a system from its KE only, nor the KE from the momentum only.

As Delta Kilo pointed out, momentum cannot be dissipated as heat. KE, however, can be dissipated as heat.

To go into the OP's example in a bit more detail:

- In the isolated system composed of the car and the Earth, momentum is always conserved. When the car starts, the change in momentum of the car is equal and opposite to the change in momentum of the Earth.
- In this same system, total energy is conserved, but the chemical energy of fuel may be converted into KE, or KE may be lost by being converted into heat. When the car starts, fuel is converted into KE. Practically all this KE goes into the car: the change in KE of the Earth is negligible compared to the change in KE of the car.
- When the car stops, the change in momentum of the car is once more exactly balanced by the change in momentum of the Earth. The car's KE is dissipated at heat and the change in KE of the Earth is again negligible compared to that of the car.