Sailboat forces and Newton's 3rd law

[abrenner]

Not sure if this is the correct forum, but I'm sure someone will let me know. My question regards Newton's 3rd law of motion. How does Newton's 3rd law relate to a sailboat moving downwind. (I'm not talking about lift, or Bernoulli's principle, just a simple single sail, let all the way out, with the wind behind it. As I understand the 3rd law, the wind impinges on the sail, and the sail pushes the wind back. So far, the forces cancel. However, if the sail pushes back on the wind and the sail is attached to the boat, the boat moves forward. Am I correct so far? If so, where is the equal and opposing force on the boat? Is it the drag produced by the water? If it is equal, why does the boat move at all?? I suspect it has to do with the 2nd law and unequal masses, i.e., the mass of the boat vs. the mass of the water? If the mass of the water is less, then the boat will accelerate? Am I all wet(pardon the pun) here? If not, how can you possibly determine the mass of the water?

A. Brenner

 

[rcgldr]

The wind impinges on the sail, and the sail pushes the wind back. So far, the forces cancel. However, if the sail pushes back on the wind and the sail is attached to the boat, the boat moves forward. Is it the drag produced by the water? If it is equal, why does the boat move at all?

Acceleration is zero when the forces cancel, but not velocity. If the forces cancel, the sail boat moves at constant velocity. If the sail boat is not moving or moving slower, then the wind force is greater than the water drag, and the sail boat accelerates until the forces cancel.

 

[abrenner]

Let's go back to the 3rd law. Is it the sail pushing back on the wind that propels the boat forward?

 

[DaveC426913]

Let's go back to the 3rd law. Is it the sail pushing back on the wind that propels the boat forward?

Yes. The wind is slowed dramatically.

 

[abrenner]

So what is happening -are we now talking about F= ma, where the acceleration of the wind drops as it is slowed down. Does that mean that the force exerted by the sail pushing back, and therefore the force pushing the boat forward is less than the force of the wind? Or are we talking about different masses,i.e., mass of the wind, mass of the sail, mass of the boat. I'm trying to understand which of Newton's laws makes the boat move, and if it is both 3rd and 2nd laws, when and how they come into play.

 

[sganesh88]

Does that mean that the force exerted by the sail pushing back, and therefore the force pushing the boat forward is less than the force of the wind?

Yes. Its like moving a block by moving another block placed under it. The net force on the upper block(in the form of static friction) will be lesser than the force you apply.

I'm trying to understand which of Newton's laws makes the boat move, and if it is both 3rd and 2nd laws, when and how they come into play.

Rushing wind hits the sail and loses some momentum in the initial direction which is transferred to the sail and through the sail to the boat, the rate at which this momentum is transferred gives the force of the wind. This is the second law. Momentum conservation hides within the third law. Read further on the Newton's laws.

 

[abrenner]

I'm wondering if I could understand the opposite and EQUAL force law without introducing momentum. The wind impinges on the sail with a force F¹= ma¹, where a¹ = the rate of change of the velocity of the wind. Since the velocity is decreasing, the acceleration is negative. So F¹ is negative. The equal and opposite force pushing the sail and therefore the boat forward is F² = -F¹. Is this correct?

 

[sganesh88]

The equal and opposite force pushing the sail and therefore the boat forward is F² = -F¹. Is this correct?

Exactly.

 

[rcgldr]

I'm wondering if I could understand the opposite and EQUAL force law without introducing momentum. The wind impinges on the sail with a force F¹= ma¹, where a¹ = the rate of change of the velocity of the wind. Since the velocity is decreasing, the acceleration is negative. So F¹ is negative. The equal and opposite force pushing the sail and therefore the boat forward is F² = -F¹. Is this correct?

The force exerted by the wind onto the sail is what pushes the sailboat forwards. The drag force from the water is transferred through the boat, and ends up as a force exerted by the sail onto the wind, which is what slows down the wind.

 

[sganesh88]

The drag force from the water is transferred through the boat, and ends up as a force exerted by the sail onto the wind, which is what slows down the wind.

This would be found confusing to the OP who might end up concluding that a third party like water is needed for the reaction force.. Even in the absence of drag force of the water, the sail exerts a reaction to the wind slowing it down.

 

[rcgldr]

If there was no drag, then the sail would move at the same speed as the wind and there would be no force.

 

[abrenner]

If there was no drag, then the sail would move at the same speed as the wind and there would be no force.

Could Jeff's reply be true? Assume there is a wind with nothing to impede it. Now introduce an object (like a catamran gliding onthe water, assume no drag). Wouldn't the sails still impede the wind and create a force? Otherwise, how could the boat begin to move without a force?

 

[rcgldr]

Could Jeff's reply be true? Assume there is a wind with nothing to impede it. Now introduce an object (like a catamran gliding onthe water, assume no drag). Wouldn't the sails still impede the wind and create a force? Otherwise, how could the boat begin to move without a force?

Initially there would be a force because the dragless boat would be moving slower than the wind, with acceleration due to the force from the wind on the slower moving sail. As the dragless boat's speed increased to that of the wind, the force would approach zero. If the dragless boat were moving at the same speed as the wind, the force would be zero.

 

[abrenner]

Initially there would be a force because the dragless boat would be moving slower than the wind, with acceleration due to the force from the wind on the slower moving sail. As the dragless boat's speed increased to that of the wind, the force would approach zero. If the dragless boat were moving at the same speed as the wind, the force would be zero.

That makes sense; thanks to all of you who responded; I'm teaching a middle school class about force and sailboats. While I want to make it understandable, I also want them to grasp the physics of forces. I think I can now do that.

 

[abrenner]

After thinking about it again, I'd like to reopen this thread with a short discussion of momentum. If, as we've said, the wind slows down dramatically when it hits the sail, a collision is taking place. Consider a motionless sailboat (and for the moment a dragless situation). The wind picks up, hits the sail and the boat moves forward (Analagous to a bowling ball hitting a tennis ball?). If momentum is conserved here (no water friction), it suggests the mass of the air is greater than the mass of the sail and boat. This seems intuitively not posssible, because the weight of the air is so negligible. Where have I gone wrong?

 

[DaveC426913]

This seems intuitively not posssible, because the weight of the air is so negligible. Where have I gone wrong?

Air is not neglibile at all. Few things can knock down a tree - or a house - better than a large volume of air.

If a wind were able to apply a mere 1/10 of a atmosphere to a sail on a small boat, that would produce 8 tons of pressure. (85 sq. ft. x 144 x 14.7lbs/in^2 = ~17000lbs)

Is that enough for you?

 

[abrenner]

Momentum = mv. I was looking for the mass of air I should use, not the pressure. At 1.2g/L, I calculate that the mass of air in say, 85 cubic feet, has a mass of 2.94 KG, or 6.5 lbs. My question is what volume of air do I use to calculate the mass of air impinging on the sail?