Relative velocity of the wind making a flag move

[Crystal037]

Homework Statement

When you are standstill holding a flag, the flag flutters in the direction of wind. When you start running the direction of fluttering of the flag changes to the direction of the wind relative to you. In all case a flag flutters in the direction of the wind relative to the flag

Relevant Equations

V(w,f)=V(w)-V(f)
Where V(w,f) is the velocity of wind w.r.t ship

Here it is given that the flag flutters in the direction of wind w.r.t. to man. But why would the direction of fluttering of flag would change without any tangential acceleration. Is there a pseudo force acting on it. I think the direction if fluttering should remain same.

 

[jbriggs444]

Homework Statement:: When you are standstill holding a flag, the flag flutters in the direction of wind. When you start running the direction of fluttering of the flag changes to the direction of the wind relative to you. In all case a flag flutters in the direction of the wind relative to the flag
Relevant Equations:: V(w,f)=V(w)-V(f)
Where V(w,f) is the velocity of wind w.r.t ship

Here it is given that the flag flutters in the direction of wind w.r.t. to man. But why would the direction of fluttering of flag would change without any tangential acceleration. Is there a pseudo force acting on it. I think the direction if fluttering should remain same.

There is a problem here. You have spoken of two scenarios. In one there is a man holding a flag in a wind. In the other there is a man on a ship holding a flag in the wind. Since these are two different scenarios, there is no meaningful sense in which acceleration applies. We did not change from one wind velocity to another over a change in time. We changed from one wind velocity to another over a change in scenarios.

If we are to bring acceleration into this, we have to put the two situations together in a single scenario. So...

A man stands on the deck of a ship that is stationary in the middle of a large expanse of ocean. There is a 10 knot wind blowing from the right (starboard). The man holds a flag aloft. Unsurprisingly, the flag flutters to the left (port).

The captain signals full speed and the engine room responds. The ship accelerates until it is moving at 10 knots. The man has been holding the flag aloft this whole time. Unsurprisingly, the flag now flutters at 45 degrees back from straight left (4 points off the port stern) in a 14 knot relative wind.

You ask about the torque that could produce such a change in the flag's orientation. Can you find one?

 

[haruspex]

... and "When you start running" should read "When you are running". It is to do with the two different states, not the transition from one to the other.

 

[Crystal037]

There is a problem here. You have spoken of two scenarios. In one there is a man holding a flag in a wind. In the other there is a man on a ship holding a flag in the wind. Since these are two different scenarios, there is no meaningful sense in which acceleration applies. We did not change from one wind velocity to another over a change in time. We changed from one wind velocity to another over a change in scenarios.

If we are to bring acceleration into this, we have to put the two situations together in a single scenario. So...

A man stands on the deck of a ship that is stationary in the middle of a large expanse of ocean. There is a 10 knot wind blowing from the right (starboard). The man holds a flag aloft. Unsurprisingly, the flag flutters to the left (port).

The captain signals full speed and the engine room responds. The ship accelerates until it is moving at 10 knots. The man has been holding the flag aloft this whole time. Unsurprisingly, the flag now flutters at 45 degrees back from straight left (4 points off the port stern) in a 14 knot relative wind.

You ask about the torque that could produce such a change in the flag's orientation. Can you find one?

Yeah V(w, f) is the velocity of wind w.r.t flag.
But we can take the ship also. So you said that after the ship reaches a speed of 10 knot the direction of fluttering of flag changes. I don't understand why. I think it should flutter in its original direction after the ship attains a constant speed. Since no acceleration is taking place. But you say that it turned 45 degrees even after the ship attained a constant speed and acceleration stopped. And what do you mean by 4 points off the stern and how come the relative velocity of wind is 14 knot and it is relative to what.

 

[Crystal037]

... and "When you start running" should read "When you are running". It is to do with the two different states, not the transition from one to the other.

What if we take the point of transition from one state to other.

 

[haruspex]

Yeah V(w, f) is the velocity of wind w.r.t flag.
But we can take the ship also. So you said that after the ship reaches a speed of 10 knot the direction of fluttering of flag changes. I don't understand why. I think it should flutter in its original direction after the ship attains a constant speed. Since no acceleration is taking place. But you say that it turned 45 degrees even after the ship attained a constant speed and acceleration stopped. And what do you mean by 4 points off the stern and how come the relative velocity of wind is 14 knot and it is relative to what.

It is not to do with acceleration.
Do you understand relative velocities and frames of reference? To an observer on the ship, the ship is stationary. What does the observer think the wind is doing? What is the flag expected to do in response?

 

[Crystal037]

Then for an observer outside the ship the direction of fluttering remains the same?

 

[haruspex]

Then for an observer outside the ship the direction of fluttering remains the same?

The direction of the flag looks the same to all observers.

 

[Crystal037]

E

The direction of the flag looks the same to all observers.

Even the observer inside the ship?

 

[haruspex]

E
Even the observer inside the ship?

The flag will flutter in a specific direction. Everyone can see what direction that is, no matter how those people are moving.

 

[Crystal037]

The flag will flutter in a specific direction. Everyone can see what direction that is, no matter how those people are moving.

So let's say the flag was on the ship and the direction of wind was towards west when the ship wasn't moving then the flag will flutter in the west direction for both a man on the ship and a man outside the ship. But when ship starts moving towards the North then the flag flutters towards South West both for a man outside and a man inside the ship

 

[jbriggs444]

So let's say the flag was on the ship and the direction of wind was towards west when the ship wasn't moving then the flag will flutter in the west direction for both a man on the ship and a man outside the ship. But when ship starts moving towards the North then the flag flutters towards South West both for a man outside and a man inside the ship

At the risk of confusing you further.

An individual flutter in the flag will slowly move down the length of the flag from its pole in the northeast to its tip in the southwest. From the point of view of a sailor on the ship, nothing fancy is going on. The flutter moves from northeast to southwest. Similarly, from the sailor's point of view, a feather floating in the wind moves from northeast to southwest.

From a landlubber's point of view, the flag is moving north while the flutter is moving southwest relative to the flag. The flutter ends up propagating in a more or less westward direction from this point of view. Similarly, a feather floating in the wind moves from east to west.

 

[haruspex]

So let's say the flag was on the ship and the direction of wind was towards west when the ship wasn't moving then the flag will flutter in the west direction for both a man on the ship and a man outside the ship. But when ship starts moving towards the North then the flag flutters towards South West both for a man outside and a man inside the ship

Yes.