The Motor Boat

[Motor Daddy]

The water in the pool is moving at 3.27 km/h, because the whole pool is moving at 3.27 km/h. Right?

In the 22.5 seconds it takes the boat to go the length of the pool, the whole pool moves 20.4 metres.
Right?

So in the 22.5 seconds it takes the boat to go the length of the pool, how far does it actually move, if it's moving in the same direction as the ship?
How far does it actually move, if it's moving in the opposite direction to the ship?

We are measuring the time it takes for the toy boat to go from one side of the pool to the other. We are measuring a TIME, not a velocity or a distance. The distance is known, which is the diameter of the pool. If we wanted to measure using light then we would do that, but it still took 22.5 seconds for the toy boat to travel from one side of the pool to the other.

 

[Undefined]

You're missing the point of the current. The current is an opposing force to the boat's motion. The current slows the boat down when it's going upstream against the current. What current is opposing your toy boat's force in the pool?

The water in the pool is moving at 3.27 km/h. Right?

In the 22.5 seconds it takes the boat to go the length of the pool, the whole pool moves 20.4 metres.
Right?

So in the 22.5 seconds it takes the boat to go the length of the pool, how far does it actually move, if it's moving in the same direction as the ship?
How far does it actually move, if it's moving in the opposite direction to the ship?

In my naive reading so far, I think I see what Motor Daddy is getting at, Pete. In the pool on a ship, the toy boat as well as the pool water are already in equilibrium state even before the motor starts (ie the boat is floating and already being taken in the same direction as the pool water at the same rate). Whereas in the river-and-current example, the river water and the boat are not in equilibrium, but the motor must take the initial starting "drag backwards" into account just to remain stationary. And then must add more motor power to make headway against the current as well. So the setup starting and analysis of both scenarios may not be exactly the same? Is that what you mean, Motor Daddy?

This is an interesting comparative scenarios exercise which I will be interested to see concluded to see if they turn out to be equivalent overall once the Two-way analysis is completed; or if they differ in some important aspect? Exciting. Thanks for your discussion so far, guys; it makes interesting cogitation fodder, even if just for the hell of it to keep one on one's toes!

 

[Pete]

We are measuring the time it takes for the toy boat to go from one side of the pool to the other. We are measuring a TIME, not a velocity or a distance.

We're measuring both time and distance, to calculate velocity.
Time is easy. Distance is harder, because the pool moves while the boat is in transit.

The distance is known, which is the diameter of the pool.

You're becoming a relativist, MD. The distance the boat goes relative to the ship is the length of the pool.
But, the ship is moving. But isn't the embankment your preferred standard?

How far does the ship move in the 22.5 seconds it takes the boat to go the length of the pool?

it still took 22.5 seconds for the toy boat to travel from one side of the pool to the other.

Correct. The motion of the pool-and-water does not affect the work of the motor.

 

[Pete]

In my naive reading so far, I think I see what Motor Daddy is getting at, Pete. In the pool on a ship, the toy boat as well as the pool water are already in equilibrium state even before the motor starts (ie the boat is floating and already being taken in the same direction as the pool water at the same rate). Whereas in the river-and-current example, the river water and the boat are not in equilibrium, but the motor must take the initial starting "drag backwards" into account just to remain stationary. And then must add more motor power to make headway against the current as well. So the setup starting and analysis of both scenarios may not be exactly the same?

In the river problem, the initial condition isn't defined, but is assumed to be with the boat already underway at constant speed.
Same for the pool problem. The initial acceleration is not considered, so we're effectively assuming it to be already underway at constant speed the instant it hits the water.

If you want to make the pool boat start as rest in the water, then the river boat can also start in the same way, which would be drifting with the current with the motor off.

This is an interesting comparative scenarios exercise which I will be interested to see concluded to see if they turn out to be equivalent overall once the Two-way analysis is completed; or if they differ in some important aspect? Exciting. Thanks for your discussion so far, guys; it makes interesting cogitation fodder, even if just for the hell of it to keep one on one's toes!

This is a great opportunity for an actual experiment.

You will need:

• A boat (eg http://www.toysrus.com/family/index.jsp?categoryId=2290619), with a full tank or fresh batteries
• Some still water with measurable landmarks or distance markers, such as a lake, a pond, or a swimming pool, for measuring the still-water speed.
• A straight section of smoothly flowing water with measurable landmarks or distance markers (Might be tricky. The creeks in my town are all only a couple of feet across, which means the flow won't be smooth enough. But there are larger creeks and rivers in driving distance, with nice parks by the banks which should be suitable.) A riverboat race course with distance buoys would be ideal.
• A stopwatch
• A still day (to reduce air resistance effects)
• Notepad and pen
• (Optional) A video camera, to show everyone what you did.

The stillwater speed should be averaged over a few trials in the pool.
The speed of the current can be measured by dropping in a stick and timing it over the distance.
A few trials each way should be recorded to get the average upstream and downstream speeds.

Who's in?

 

[Undefined]

In the river problem, the initial condition isn't defined, but is assumed to be with the boat already underway at constant speed.
Same for the pool problem. The initial acceleration is not considered, so we're assuming it to be already underway at constant speed.

If you want to make the pool boat start as rest in the water, then the river boat can also start in the same way, which would be drifting with the current with the motor off.


This is a great opportunity for an actual experiment.

You will need:

• A boat (eg http://www.toysrus.com/family/index.jsp?categoryId=2290619), with a full tank or fresh batteries
• Some still water with measurable landmarks or distance markers, such as a lake, a pond, or a swimming pool, for measuring the still-water speed.
• A straight section of smoothly flowing water with measurable landmarks or distance markers (Might be tricky. The creeks in my town are all only a couple of feet across, which means the flow won't be smooth enough. But there are larger creeks and rivers in driving distance, with nice parks by the banks which should be suitable.) A riverboat race course with distance buoys would be ideal.
• A stopwatch
• A still day (to reduce air resistance effects)
• Notepad and pen
• (Optional) A video camera, to show everyone what you did.

The stillwater speed should be averaged over a few trials in the pool.
The speed of the current can be measured by dropping in a stick and timing it over the distance.
A few trials each way should be recorded to get the average upstream and downstream speeds.

Who's in?

Oh yes! I see what you mean about the starting condition already in some form of equilibrium in both scenarios. But I naively don't get what you mean about the river current taking the boat with it? In the ship and pool, the boat is going along the same direction as the toy boat already? But in your river current, the boat is fighting against being taken downstream against the direction which the boat will move upstream from a starting position? They are two opposite direction starting conditions, aren't they? One with the current (shipboard direction of motion) and one against the current (upstream against the river flow)? Or do they end up equal when the two-way analysis is taken into account and completed?

Maybe RJBeery will do the experiment? He is good at it I hear!

 

[ash64449]

Simple algebra says 8km/hr for 90 minutes is 12km, not 10 km!

Who said i said 10 km? I said 12 km?

Boat doesn't have tendency to do squat! We measured the boat in order to find the still water speed. It traveled 10km in 1.25 hours! That is 8km/hr in still water.

Sorry,i actually meant 8km/h in still water.

The current has NOTHING to do with the time it takes for the boat to travel 10 km in still water!

Not a still water... Water has current!!! That's the whole point!!

Motor Daady: I�m sure james has it correct in post 12, but it is longer than need be proof.

Going up stream 5 miles against a current of S mph will take 5/(8-S) hours will it not? And the return trip going down stream will take 5/(8+S) will it not? We are told the total trip took 1.5 hours.
I.e. solve this equation: 1.5 = 5/(8-S) + 5/(8+S) for S.

Use trial and error if your not up to that algebraically. Here is a hint for the algebraic approach. Get rid of the fractions by multiplying both sides of equation by:
(8-S)(8+S). Then equation becomes: 1.5(8-S)(8+S) = 5(8+S) + 5(8-S).

The left side will produce a quadratic term (one with S^2) so after you have it reduced to standard form: aS^2 + bS + c = 0 apply the "quadratic formuale" to get S.

I�m just guessing but nearly sure your answer is the one with the + sign. (the solution with the negative sign is going to be a negative time (must arrive back at the start before you start the trip, if that were possible, I bet.)

Yeah.. this is correct.. Same way i solved the problem 2 years ago.

 

[Pete]

Oh yes! I see what you mean about the starting condition already in some form of equilibrium in both scenarios. But I naively don't get what you mean about the river current taking the boat with it? In the ship and pool, the boat is going along the same direction as the toy boat already? But in your river current, the boat is fighting against being taken downstream against the direction which the boat will move upstream from a starting position?
They are two opposite direction starting conditions, aren't they? One with the current (shipboard direction of motion) and one against the current (upstream against the river flow)? Or do they end up equal when the two-way analysis is taken into account and completed?

To make them the same, have the pool boat first travel in the opposite direction to the ship.

The river boat starting from unpowered drifting then motoring upstream is exactly the same as the pool boat starting from unpowered floating then motoring toward the back of the ship.

Maybe RJBeery will do the experiment? He is good at it I hear!

Maybe a few of us will do it and compare results. Are you interested?

 

[Motor Daddy]

You're becoming a relativist, MD.

Pete, That's hitting below the belt! NEVER!

 

[eram]

Pete, That's hitting below the belt! NEVER!

Hitting you below the belt has no effect, if you know what I mean.

Now stop trolling, your maths isn't that bad, you're just doing it on purpose.

 

[Motor Daddy]

Pete, I just got up to go to the bathroom (it's 4 am here) and figured I'd check the thread. I'll reply to the rest of your posts later, I'm going back to bed.

 

[Motor Daddy]

We're measuring both time and distance, to calculate velocity.
Time is easy. Distance is harder, because the pool moves while the boat is in transit.

The distance measured is in the pool frame. We use a ruler to measure the diameter of the pool and we know the distance. We just need to measure the time it takes for the toy boat to travel across the pool.

The distance the boat goes relative to the ship is the length of the pool.

Right.

But, the ship is moving. But isn't the embankment your preferred standard?

The embankment is the frame in which the boat was measured to travel 10km in 1.25 hours. The water also travels relative to the embankment, so you have a situation where the water is rushing past the embankment in one direction, and the boat is traveling UPSTREAM compared to the water, but also compared to the embankment. The water and the boat each have motion compared to the embankment, and also to each other. This is not the standard "embankment is at rest and the train is in motion." This is "the train is in motion and the embankment is in motion at the same time."

How far does the ship move in the 22.5 seconds it takes the boat to go the length of the pool?

It doesn't matter, the motion of the toy boat is a NET effect of the net forces.

 

[Pete]

The distance measured is in the pool frame. We use a ruler to measure the diameter of the pool and we know the distance. We just need to measure the time it takes for the toy boat to travel across the pool.

What is the distance in the embankment frame?

The embankment is the frame in which the boat was measured to travel 10km in 1.25 hours.

No, the water (or pool) frame is the frame in which the boat is measured to travel at 8km/hr.
In the embankment frame, the water/pool is moving.

So, please MD, answer these question and don't divert:
Compared to the embankment, how far does the ship, pool, and water move in the 22.5 seconds it takes the little boat to go the length of the pool?
How far does the little boat go on the trip to the back of the pool?
How far does it go on the trip to the front of the pool?

The water also travels relative to the embankment, so you have a situation where the water is rushing past the embankment in one direction, and the boat is traveling UPSTREAM compared to the water, but also compared to the embankment. The water and the boat each have motion compared to the embankment, and also to each other. This is not the standard "embankment is at rest and the train is in motion." This is "the train is in motion and the embankment is in motion at the same time."

Well, the whole point of relativity is that "the embankment is at rest" is just a convention, and we can equally say it is in motion.
But that doesn't have to be the case in this exercise. Let us just consider the embankment to be at rest, the water to be moving, and the boat to be moving.

It doesn't matter, the motion of the toy boat is a NET effect of the net forces.

So what is the net motion of the little boat?

 

[Motor Daddy]

So, please MD, answer these question and don't divert:
Compared to the embankment, how far does the ship, pool, and water move in the 22.5 seconds it takes the little boat to go the length of the pool?
How far does the little boat go on the trip to the back of the pool?
How far does it go on the trip to the front of the pool?

1. It's not magic. If not enough information is provided then you can't calculate anything. If the only information you give me is 22.5 seconds for a toy boat to travel across a pool I can't tell you squat. I need more information. 22.5 seconds is meaningless on its own.

2. You're confused. Look at what I did in posts 1452-1456. The embankment and the train are each in motion in the preferred frame. In the motorboat scenario the water is in motion and the boat is in motion. They each have indivdual motions in the preferred frame like 1452-1456 does. You can add 100 different objects all with different motions in the preferred frame and it always works, because light travel time never lies.

 

[Neddy Bate]

If not enough information is provided then you can't calculate anything. If the only information you give me is 22.5 seconds for a toy boat to travel across a pool I can't tell you squat. I need more information. 22.5 seconds is meaningless on its own.

Pete gave you all the information you need in post #90:

The swimming pool is 50m long, the little boat takes 22.5 seconds to go from one end to the other, and the pool is actually on a cruise ship which is currently being tugged through a harbour at 3.27 km/h.

Come on, Motor Daddy, is this really so difficult?

 

[Motor Daddy]

That's exactly how it works.

Let's put the motor boat in a 50m swimming pool (it's a little electric RC boat).
You time it to take 22.5 seconds to go from one end to the other.

So, the boat is moving at 8 km/h in still water, right?

Right.

But, there's a catch - the pool is actually on a cruise ship, which is currently being tugged through the harbor at 3.27 km/h.

What's your point?? The motion of the cruise ship doesn't equate to a current in the pool. The water is at rest in the pool. The water is not moving relative to the pool. In comparison, the water in a still body of water is not moving, it is still water. NO CURRENT.

So, in the 22.5 seconds it takes the boat to go the length of the pool, the whole pool moves 20.4 metres.
So, the little boat actually moves 70.4 metres if it's moving in the same direction as the ship (downstream), but only 4.6 metres if it's moving in the other direction (upstream).

Pete, you can't be serious?? The toy boat's motion is measured in the pool. The motion of the cruise ship at 3.27 km/hr doesn't mean the toy boat traveled that distance in the water in the harbour. Are you serious?

So how fast is the little boat actually moving? 8 ± 3.27 km/hr

Not!! The boat traveled at 8km/hr in the pool.

Does the little boat's motor RPM change depending on which way it goes? No, of course not.

Of course not, because the pool water is still, like glass! There is no current in the pool just because it is on a cruise ship. ???

Is a body of water carried in a swimming pool on a cruise ship equivalent to a body of water carried in a smooth current? Yes. The water in the middle of the pool doesn't 'know' whether it's in a pool or in a current - it's just carried along by the water around it in either case.

Right, so why would you try to add the motion of the cruise ship into the distance the toy boat traveled in the pool???

 

[Motor Daddy]

Pete gave you all the information you need in post #90:

The swimming pool is 50m long, the little boat takes 22.5 seconds to go from one end to the other, and the pool is actually on a cruise ship which is currently being tugged through a harbour at 3.27 km/h.

Come on, Motor Daddy, is this really so difficult?

Thanks, I somehow missed that info.

 

[Neddy Bate]

Motor Daddy, your own theory is all about absolute motion. Imagine the harbour is your preferred rest frame (where the speed of light is c in all directions). If you are on-board the cruise ship, and you do some of your light signal tests, you believe you can determine the speed of the cruise ship to be 3.27 km/hr. But if you are on-board the model boat, and you do some of your light signal tests, you don't believe you will determine the speed of the model boat to be 8 km/hr regardless of which direction the model boat is moving in the pool, do you? Your own theory tells you the model boat will have two different absolute speeds, depending on whether the model boat moves in the same direction as the cruise ship, or in the opposite direction as the cruise ship. Right?

 

[Motor Daddy]

Motor Daddy, your own theory is all about absolute motion. Imagine the harbour is your preferred rest frame (where the speed of light is c in all directions). If you are on-board the cruise ship, and you do some of your light signal test, you believe you can determine the speed of the cruise ship to be 3.27 km/hr.

Right.

But if you are on-board the model boat, and you do some of your light signal test, you don't believe you will determine the speed of the model boat to be 8 km/hr regardless of which direction the model boat is moving in the pool, do you?

You need to look a little closer at posts 1452-1456 that I just linked to because you OBVIOUSLY don't understand what is going on there. You obviously don't understand the preferred frame. I can measure the boat to be traveling 8km/hr in the pool while at the same time the pool is traveling along with the cruise ship at 3.27km/hr. It's no different than posts 1452-1456 except for the distances and times. Add as many as you want, put a few more boats traveling all different directions in the pool. Have one boat travel in the x direction, the other in the y direction, and heck, have one guy climb a set of stairs on the cruise ship in the x and z direction. Piece of cake for my theory, and the numbers all add up perfectly with no band-aids!

Your own theory tells you the model boat will have two different absolute speeds, depending on whether the model boat moves in the same direction as the cruise ship, or in the opposite direction as the cruise ship. Right?

The boat can have a preferred frame velocity at the same time it has a velocity in the pool and the numbers add up perfectly. So, if you ask me how fast the boat traveled in the pool I can answer that. If you ask me how far the boat traveled in the preferred frame I can answer that too. I can also tell you how far the cruise ship, the harbor, and the pool traveled in the preferred frame. Quite the powerful tool, eh?

 

[Neddy Bate]

If you ask me how far the boat traveled in the preferred frame I can answer that too.

Great. Assuming the harbor is a rest in the preferred frame, how far did the model boat travel in the preferred frame when it moved in the same direction as the cruise ship? And, still assuming the harbor is a rest in the preferred frame, how far did the model boat travel in the preferred frame when it moved in the opposite direction as the cruise ship?

 

[Motor Daddy]

Great. Assuming the harbor is a rest in the preferred frame, how far did the model boat travel in the preferred frame when it moved in the same direction as the cruise ship?

In 22.5 seconds the boat traveled 50 meters in the pool.
In 22.5 seconds the pool traveled 0 meters in the cruise ship.
In 22.5 seconds the cruise ship traveled 20.4375 meters in the harbor.
In 22.5 seconds the harbor traveled 0 meters in the preferred frame.
In 22.5 seconds the boat traveled 70.4375 meters in the preferred frame.
In 22.5 seconds the cruise ship traveled 20.4375 meters in the preferred frame.
In 22.5 seconds the pool traveled 20.4375 meters in the preferred frame.