Exploring Momentum Conservation in Cart Motion

[#H34N1]

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)

 

[asleight]

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.

 

[mgb_phys]

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.

 

[turbo]

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?

 

[asleight]

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.

 

[mgb_phys]

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.