Why Doesn't Momentum Conservation Apply to a Cart with a Sail?

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Homework Help Overview

The discussion revolves around the application of momentum conservation in a scenario involving a cart with a sail and a fan blowing air into the sail. Participants explore why the cart does not move despite the apparent lack of external forces acting on the system, referencing a specific example from a physics resource.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the reasoning behind momentum conservation in the context of the cart and the fan, comparing it to a different scenario involving tennis balls and a cart. There is a focus on the forces exerted by the air on both the fan and the sail, and whether these forces result in any net movement of the cart.

Discussion Status

The discussion is active, with participants offering insights into the mechanics of the system and questioning the assumptions made by the original poster. Some participants suggest that the forces involved may not lead to the expected outcome, while others highlight the need for further clarification on the mechanics at play.

Contextual Notes

There is an emphasis on the idealized nature of the scenarios being discussed, with participants considering the implications of air movement and forces in a real-world context. The original poster's understanding of momentum conservation is being critically examined, particularly in relation to the behavior of the cart and the air. The discussion also touches on the concept of center of mass remaining constant.

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Homework Statement


http://www.physics.umd.edu/lecdem/outreach/QOTW/arch3/a046.htm
According to the site, when a fan is blowing air into a sail, the entire cart system remains motionless.
Why doesn't the following approach work:
Since there are no net external forces acting on the entire cart, momentum is conserved. The air particles are bombarding the sail and are bouncing back with a momentum of p_f. Since momentum is conserved, the cart must then move in the opposite direction with a momentum of p_0+p_f. Because the sail is attached to the car, the car itself moves in the direction in which the fan is blowing.

What's wrong with this?

Also, in another example where a person throws tennis balls leftward at a rigid surface that is perpendicularly attached to a cart, the cart itself moves leftward.

What is the difference here?
Thanks

Homework Equations


p_i = p_f
F_{net}\Delta t=m\Delta v


The Attempt at a Solution


(Essentially given in part 1)
 
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#H34N1 said:

Homework Statement


http://www.physics.umd.edu/lecdem/outreach/QOTW/arch3/a046.htm
According to the site, when a fan is blowing air into a sail, the entire cart system remains motionless.
Why doesn't the following approach work:
Since there are no net external forces acting on the entire cart, momentum is conserved. The air particles are bombarding the sail and are bouncing back with a momentum of p_f. Since momentum is conserved, the cart must then move in the opposite direction with a momentum of p_0+p_f. Because the sail is attached to the car, the car itself moves in the direction in which the fan is blowing.

What's wrong with this?

Also, in another example where a person throws tennis balls leftward at a rigid surface that is perpendicularly attached to a cart, the cart itself moves leftward.

What is the difference here?
Thanks

Homework Equations


p_i = p_f
F_{net}\Delta t=m\Delta v


The Attempt at a Solution


(Essentially given in part 1)

Can you please re-assess the second system so I know exactly what's happenin'?

And, as for the first part, the fan exerts a force on the air the drives the air to the right, while the force exerted by the air on the fan drives the fan and, consequently, the cart to the left. But, this propelled air then strikes the sail, exerting a force equal and opposite that it imposed on the fan during part (1) of motion. So, essentially, the cart will stay where it begins.
 
Last edited by a moderator:
asleight said:
And, as for the first part, the fan exerts a force on the air the drives the air to the right, while the force exerted by the air on the fan drives the fan and, consequently, the cart to the left. But, this propelled air then strikes the sail, exerting a force equal and opposite that it imposed on the fan during part (1) of motion. So, essentially, the cart will stay where it begins.
But the OP makes the very good point that if the wind bounces off the sail and goes backward then isn't this equivalent to having the fan pointing backward?

Imagine it with tennis balls - if you sit inside a car and throw balls at the windscreen and they bounce off and go out of the back of the car with the same velocity - this is the same as throwing the balls backward with that velocity.
 
asleight said:
Can you please re-assess the second system so I know exactly what's happenin'?

And, as for the first part, the fan exerts a force on the air the drives the air to the right, while the force exerted by the air on the fan drives the fan and, consequently, the cart to the left. But, this propelled air then strikes the sail, exerting a force equal and opposite that it imposed on the fan during part (1) of motion. So, essentially, the cart will stay where it begins.
This assumes a perfect coupling of the force of the air from the fan blades and the sail. Does any of the air moved by the fan have a tangential component? If so, won't the cart experience a net force tending to move it toward the left?
 
mgb_phys said:
But the OP makes the very good point that if the wind bounces off the sail and goes backward then isn't this equivalent to having the fan pointing backward?

Imagine it with tennis balls - if you sit inside a car and throw balls at the windscreen and they bounce off and go out of the back of the car with the same velocity - this is the same as throwing the balls backward with that velocity.

Center of mass must remain constant.

Removed so OP can try.
 
Last edited:
Yes that's why the paradox is wrong - the fan is 'sucking' the air from behind the cart and then blowing it back at the same velocity. I hoped the OP would contribute something before we revealed that.
 

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