028 Can you blow your own sail?

It should be obvious to everyone that the cart receives both a forward and backward force: The forward force comes from the wind hitting the sail. The backward force comes from the reaction force to the fan blowing air forward.

fancart0

Basically, the air gave the cart a backward impulse when they “pushed themselves off” the fan, but a forward impulse when they collide into the sail. If the air became still and stuck to the sail after collision (perfectly inelastic collision), then the two impulse are equal in magnitude. And the cart will stay at rest. However, if the air rebound backward after collision (elastic collision), then the forward impulse on the sail will be larger than the backward impulse on the fan. And the cart will move forward.

The principle of conservation of momentum can make the analysis even easier. Just use the fact that the total momentum of the cart plus the air as a system must remain as zero!

With the original sail, the air got pushed out around the sides of the sail. Since the net change in momentum of the air is zero, the cart cannot have any change in momentum.

fancart1

With the improvised sail, the air got turned around and back. Since the air have acquired a backward momentum, the cart must acquire a forward momentum.

fancart2

In practice of course it will be silly to blow your own sail forward. It is much easier (and more efficient) to simply blow backward.

2 thoughts on “028 Can you blow your own sail?

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