Blowin' Across the Lake- Geek Challenge

[Jimmychunga]

Not sure if anyone out there is a big geek but when I saw this challenge question on the web I immediately thought of this forum. I had no idea. The answer just came out yesterday.

Question:

You are in the middle of a quiet lake, 250 feet from the shore, when your boat engine stops working. There is no wind, but you raise the sail of your boat and use an electrical blower to supply force to the sails. The blower power is 30,000 cfm (cubic feet per minute). How long will it take you to reach the shore? You can assume the dynamic coefficient of friction between the boat and the water to be 0.1. The weight of the boat with you inside is 750 lb.

(Update: April 3, 8:35 AM) And the Answer is...

Under these ideal conditions and with the power of the blower alone you will never reach the shore, because the boat will never move. According to Newton's Third Law in order to have the action-reaction effect one of the forces has to be external to the system. In this case, the force of the wind from the blower has to come from outside the boat. Because the blower is on the boat, the force from the blower is opposed by a force in the opposite direction.

This is the reason why you cannot move the boat by pushing the mast of the sails if you are standing inside the boat. You could move it by pushing the mast or the boat itself if you are standing on the shore (be careful, you might fall to the lake when the boat moves). This is also the reason why the air coming from the turbine of a jet is directed toward something that is not part of the plane.

Now, having said the above, we should add the clarification that the conditions described are extreme and very difficult to achieve. I consulted with a friend about this question; he considers that only in very ideal conditions will the boat not move. If, for example, the wind from the blower and the sails are not exactly perpendicular to each other, the net force on the boat will not be zero. The net force on the boat will be zero if, and only if, the sail effectively stops the movement of the air - i.e., the momentum the fan imparts to the air is simply cancelled by the air being stopped by the sails. Of course, it is only the average momentum of the air post-sail that would need to be zero.

[johnbaker17]

My first thought was: Well, forget the sail. Stow it. Point the blower straight back and down into the water at a 45 degree angle and off you go. That could get you to shore faster than a 5mph wind.
John

[tyson]

wind from the blower and the sails are not exactly perpendicular to each other

Even if the sail was completely perpendicular to the blower, you'd still have a net force. Air has inertia, and as such, the blower taking the still air and accelerating it (regardless of where the air is being pushed -- into the sail or not, as friction will prevent the sail from counteracting the wind force completely) will result in a net force in the direction from which the blower is sucking air.

[ice_kmauve]

You guys could send that question to the show "Mythbusters" and I bet they'd make a pretty convincing test rig to get a conclusive answer. (My bet's on Tyson's logic, the sail essentially reverses the thrust of the fan and makes the boat into an inefficient version of one of the Florida everglades fan boats).

[Woody]

As I started reading "the dynamic coefficient of friction between the boat and the..." I quickly wondered why I was so thirsty....

...hmmmm Homer likes BEER!

[Denis]

Why would anyone want to be on the water when there is no wind?

[Protege Menace]

I'ts kinda like trying to fly by pulling up on your shoes.

[johnbaker17]

Again, I still think pointing that sucker down into the water will make for a pretty decent propulsion system.