Question:

Can the fan cart blow itself forward?

Answer:

There are two forces acting on the cart.

1. The forward force resulting from the air (wind) pushing the sail forward.

2. The backward force resulting from the air (wind) pushing the fan backward.

Must these two forces cancel each other out? These two forces are often mistaken as an action-reaction pair but they are not! (The AR-pair to the forward force is the sail pushing the air backward, and the AR-pair to the backward force is the fan pushing the air forward.) Since they are not action-reaction pair, they need not have the same magnitude and therefore need not cancel each other out.

–

So whether the cart successfully blows itself forward depends on whether the wind pushes the sail harder than the fan pushed the air. And the analysis is easier if we approach using PCOM.

So let’s use the fact that the total momentum of the cart plus the air as a system must remain as zero!

With the original flat sail, the air got pushed out roughly around the sides of the sail, with no forward velocity. Since the net change in forward momentum of the air is zero, the cart cannot have any change in momentum (forward or backward).

–

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.

–

In practice, natural wind provides an external force to blow a sail boat forward. If you really must use an on-board fan, it is much easier (and more efficient) to simply blow it backward, instead of blowing into a sail.

• Uncategorized