## Perpetual Motion

Is it possible to use the energy of the wind to propel a cart directly against the wind? Or the energy of flowing water to propel a boat upstream?

Perpetual motion machines have been proposed and ridiculed for centuries. In this question, we separate engineering fantasy from physical reality.

The common theme connecting all perpetual motion machines is that they propose to use the motion of an object as the means to keep it going. For example, the perpetual weight wheel purports to use the kinetic energy of weights falling on one side to drive the rise of the weights on the other.

The reason that this and other such motion machines fail is because no machine is perfect—there’s always some loss of energy. If the energy we need to put in is the same as the energy we get out, then even a slight loss means there’s not enough energy to keep it going.

Left: the kinetic energy gained by the falling weight is used to offset the rise in the potential energy of the weights on the left. Right: the energy produced by the combustion engine is in excess of the energy needed to accelerate a car.

This is the dividing line between working machines and fantasies: engines must consume energy in excess of what they produce.

Varied though they are, all our machines are bound by a few simple rules:

1. All forces have to be balanced.
2. All energy flows have to be accounted for.

For example, the forward force from an accelerating car is greater than the frictional forces it experiences, and the power from the engine accounts for the increase in the kinetic energy of the car as well as the energy lost to friction. When it reaches constant velocity, the forces are exactly equal and 100% of the engine’s energy goes into fighting friction.

How much energy? If the car suffers a force of friction and it moves through distance  then the energy lost to friction is  If it moves at speed  then it will lose energy per second.

Just because something is a friction to be overcome in one power-flow doesn’t mean that it can’t be a power source in another. For example, if we slide a box across the floor, then friction will bring it to rest, and it will lose its energy at a rate of  per second. However, if we drop a box onto a moving conveyor belt, it will gain speed at the rate  until it moves at the same speed as the conveyor belt.

In this light, let’s confront two proposed vehicles:

Energy flows from the wind through the propeller down the crankshaft and into the wheels, which propel the cart upwind. Energy flows from the water in front of the boat into the turbine through mechanical gearing in the boat to the propeller in back, which propels the boat upstream.

# Today’s Challenge

Consider the following proposed vehicles:

One is a boat that, on a calm day (no wind), uses the energy of a flowing river to propel itself upstream: water flows through the turbine in front, which in turn spins propellers that power it upstream.

The other is a wind cart that uses the energy of the wind to propel itself upwind: wind flows through the turbine, which in turn spins the wheels to propel it into the wind.

One of these is impossible (the boat) while the other (the wind cart) has been successfully built and operated. What is the crucial difference between them?