# Blowing Into Your Own Sail

• rosedog09
rosedog09
Homework Statement
An ice sail craft is stalled on a frozen lake on a windless day. A large fan blows air into the sail. If the wind produced by the fan strikes and bounces backward from the sail the sail craft will move

a. to the left (forwards)
b. to the right (backwards)
c. not at all
Relevant Equations
Conservation of Momentum

C. There is no net change in force, momentum, or velocity of the sail craft because the fan exerts a forward force on the air; however due to Newton's third law the air exerts an equal and opposite force on the fan. This air then exerts a forward force on the sail which cancels out the rearward force of the fan.

Take the sail down, turn the fan around and you have an airboat.

berkeman

rosedog09 said:
Homework Statement: An ice sail craft is stalled on a frozen lake on a windless day. A large fan blows air into the sail. If the wind produced by the fan strikes and bounces backward from the sail the sail craft will move

a. to the left (forwards)
b. to the right (backwards)
c. not at all
Relevant Equations: Conservation of Momentum

View attachment 344016
C. There is no net change in force, momentum, or velocity of the sail craft because the fan exerts a forward force on the air; however due to Newton's third law the air exerts an equal and opposite force on the fan. This air then exerts a forward force on the sail which cancels out the rearward force of the fan.

View attachment 344017
You are overlooking "and bounces backward from the sail"

haruspex said:
You are overlooking "and bounces backward from the sail"
I understand that the sail will enact a forward force on the cart due to newtons third law from bouncing the air back, but I dont understand why this force would not be counteracted by the force which air exerts on the fan (Newtons third law).

Orodruin said:

Ok I can see that this works, but I want to understand why. I am not understanding how the air could possibly enact a greater change in momentum on the cart after bouncing back than it did when it hit the blade of the fan (pushing the cart backwards) initially.

rosedog09 said:
I understand that the sail will enact a forward force on the cart due to newtons third law from bouncing the air back, but I dont understand why this force would not be counteracted by the force which air exerts on the fan (Newtons third law).
Newton’s third law does not apply to the latter part. The forces you are talking about do not form a third law pair.

The third law partner of the force of the air on the sail is the force from the sail on the air.

The fan accelerates the air from essentially standstill to some velocity. The sail reflects the air from that velocity to some velocity in the back direction. What is the net momentum change of the air? Is whatever velocity the air had between fan and sail even relevant?

rosedog09 said:
I understand that the sail will enact a forward force on the cart due to newtons third law from bouncing the air back, but I dont understand why this force would not be counteracted by the force which air exerts on the fan (Newtons third law).
Would the two cancel if the sail merely stopped the air, thus returning it to its initial state?

haruspex said:
I have wondered whether Braindead is an Iranian-Russian-North Korean-Chinese plot to undermine western science.
To me it looks like artificial intelligence coming to the aid of natural stupidity.

rosedog09 said:
Ok I can see that this works, but I want to understand why. I am not understanding how the air could possibly enact a greater change in momentum on the cart after bouncing back than it did when it hit the blade of the fan (pushing the cart backwards) initially.
Imagine the cart is stationary and so is an air molecule near the fan. We start the engine and the molecule gets hit by a fan blade and accelerated to some speed ##v##. Then it hits the sail. If it imparts the opposite momentum to the cart as it got from the fan then there is no net force on the vehicle. What is its final speed in this case? Is that how bouncing off something works in your experience?

Ibix said:
Imagine the cart is stationary and so is an air molecule near the fan. We start the engine and the molecule gets hit by a fan blade and accelerated to some speed ##v##. Then it hits the sail. If it imparts the opposite momentum to the cart as it got from the fan then there is no net force on the vehicle. What is its final speed in this case? Is that how bouncing off something works in your experience?
Ok so what your suggesting is that the momentum change (impulse) on the sail is greater than the fan because the particle is reversing directions. I can understand this, but I still find it hard to understand how there is enough momentum from the fan for it to transfer more momentum to the sail than the fan transferred to the air.

rosedog09 said:
Ok so what your suggesting is that the momentum change (impulse) on the sail is greater than the fan because the particle is reversing directions. I can understand this, but I still find it hard to understand how there is enough momentum from the fan for it to transfer more momentum to the sail than the fan transferred to the air.
For an ideal reflection, you get twice as much momentum from the sail as you lose from the fan.

Ibix said:
Imagine the cart is stationary and so is an air molecule near the fan. We start the engine and the molecule gets hit by a fan blade and accelerated to some speed ##v##. Then it hits the sail. If it imparts the opposite momentum to the cart as it got from the fan then there is no net force on the vehicle. What is its final speed in this case? Is that how bouncing off something works in your experience?
Ok. I think I've figured it out. The sail is reflecting the air (in this case with an unrealistic level of efficiency) such that momentum goes from p to -p, a total change of -2p. Since the fan initially transferred p to the air we are left with -p, so it is essentially the same as having the fan pointing backwards. I think my confusion is coming from the sail because I dont understand what would cause the sail to enact enough force on the air to reverse its direction.

jbriggs444
rosedog09 said:
I dont understand what would cause the sail to enact enough force on the air to reverse its direction.
What causes the basketball court to enact enough force on a basketball to reverse its direction?

If you engineer the "sail" carefully to channel the air through a semicircular path, you can do a decent job of reflection. As experiment shows, even a cardboard box is good enough to do more than a halfway job.

jbriggs444 said:
What causes the basketball court to enact enough force on a basketball to reverse its direction?

If you engineer the "sail" carefully to channel the air through a semicircular path, you can do a decent job of reflection. As experiment shows, even a cardboard box is good enough to do more than a halfway job.
I dont know. It bothers me, but I dont know.

rosedog09 said:
I dont know. It bothers me, but I dont know.
Are you intuitively thinking of momentum like energy, and therefore that the sum of the ##|\vec p|## should be conserved? That's not correct, but it's an easy thing to thing ought to be correct.

rosedog09 said:
I dont know. It bothers me, but I dont know.
Personally, I like to ignore the details and consider the big picture. We have air flowing into the craft from all directions (Feynman reverse sprinkler anyone?) and being expelled in a rearward direction. That is a net increase in rearward momentum of the air. So a required increase in forward momentum of the cart. Ignore the folderol with the fan and sail. The mechanism behind the external momentum flows is irrelevant. Only the flows themselves matter.

Ibix
Ibix said:
Are you intuitively thinking of momentum like energy, and therefore that the sum of the ##|\vec p|## should be conserved? That's not correct, but it's an easy thing to thing ought to be correct.
Ok I think I am having trouble because I keep bouncing between force, momentum energy, etc

The fan "adds" (yes I know its a conversion) energy to the system, so Energy final =/= Energy Initial within the system.

Since the objects of momentum come from outside the system (air) momentum is not conserved

What I don't understand/bothers me is the forces in this system. To me it seems like the force of the air on the fan and the force of the air on the sail would cancel, but they dont as we can see from the change in momentum. Im confused as to where that extra "force" is coming from.

rosedog09 said:
The fan "adds" (yes I know its a conversion) energy to the system, so Energy final =/= Energy Initial within the system.
Never assume mechanical energy is conserved without a good reason.
rosedog09 said:
Since the objects of momentum come from outside the system (air) momentum is not conserved
The system is what you define it to be. It can include the air that interacts with the craft.
rosedog09 said:
What I don't understand/bothers me is the forces in this system. To me it seems like the force of the air on the fan and the force of the air on the sail would cancel,
You can't compare forces like that. If I hit a ball with a bat, the bat exerts quite a large force for a short time on the ball. If you catch it, you will exert a smaller force for a longer time. The momentum changes cancel but the forces don’t.

haruspex said:
Never assume mechanical energy is conserved without a good reason.

The system is what you define it to be. It can include the air that interacts with the craft.

You can't compare forces like that. If I hit a ball with a bat, the bat exerts quite a large force for a short time on the ball. If you catch it, you will exert a smaller force for a longer time. The momentum changes cancel but the forces don’t.
This makes sense. I didnt think about the timing of it.

rosedog09 said:
To me it seems like the force of the air on the fan and the force of the air on the sail would cancel
Why? There is no reason they should. They are not a third law pair.

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