# Formula of force

## Homework Statement

A model boat 1/100 size of its prototype has 0.12N of resistance when stimulating a speed of 5m/s of the prototype , what is the corresponding resistance in the prototype ? water is the fluid in both cases and frictional forces can be neglected.
Why the author need to transform the force into ρ(L^2)(v^2) ?
I know the unit of force is kg(m)(s^-2) , so , IMO , F is directly proportional to L only , right . but , not (L^3)
Fr = Fp / Fm

## The Attempt at a Solution

haruspex
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Why the author need to transform the force into ρ(L^2)(v^2) ?
I know the unit of force is kg(m)(s^-2) ,
That's for an accelerating mass, the mass being constant. Here, it's the water that is being moved, and the mass of that is related to the cross-sectional area (L2) and the velocity.

That's for an accelerating mass, the mass being constant. Here, it's the water that is being moved, and the mass of that is related to the cross-sectional area (L2) and the velocity.
since we do not know the mass of water ( we only know the density of water) , so we use (rho)(L^3 ) to find the mass of water ?

haruspex
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since we do not know the mass of water ( we only know the density of water) , so we use (rho)(L^3 ) to find the mass of water ?
That would be true if we were considering a cube of water of side L, but L is the characteristic dimension of the model/prototype. How does the mass of water displaced in time t relate to L, t, ρ and v?

welovephysics
That would be true if we were considering a cube of water of side L, but L is the characteristic dimension of the model/prototype. How does the mass of water displaced in time t relate to L, t, ρ and v?
ρ(L^3) [(L) / (T^-2) ] , which is ρ(L^3)v what are you trying to say ?

haruspex
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ρ(L^3) [(L) / (T^-2) ] , which is ρ(L^3)v what are you trying to say ?
No, that's not it. The object moves at speed v. Think of it as a box of side L. What volume of water has to move aside to make way for it in time t?

welovephysics
No, that's not it. The object moves at speed v. Think of it as a box of side L. What volume of water has to move aside to make way for it in time t?
L^3 ???
i dont really understand what you are trying to say , can you explain further ??

haruspex
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L^3 ???
i dont really understand what you are trying to say , can you explain further ??
How far does the box move in time t? What volume does the leading face of the box sweep through as the box advances that distance?

How far does the box move in time t? What volume does the leading face of the box sweep through as the box advances that distance?
the box will move by L in time , t , am i right ? the volume that the leading face of the box sweep through as the box advances that distance is (L^3) ?

haruspex
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the box will move by L in time , t , am i right ?
It is moving at speed v, not L/t.

welovephysics
It is moving at speed v, not L/t.
so , what are you trying to say , i didnt get you

haruspex
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so , what are you trying to say , i didnt get you
If a car length L moves at speed v for time t, how far does it go?

welovephysics
If a car length L moves at speed v for time t, how far does it go?
car move by vt

If a car length L moves at speed v for time t, how far does it go?
is it correct ??

haruspex
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car move by vt
Yes, so try answering my post #8 again.

welovephysics
How far does the box move in time t? What volume does the leading face of the box sweep through as the box advances that distance?
distance moved = vt , volume of the leading face of the box sweep through as the box advances that distance is vt + L

haruspex
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distance moved = vt , volume of the leading face of the box sweep through as the box advances that distance is vt + L
How do you get vt+L? Maybe it would help you to think about a more solid analogy. You are digging a tunnel. The excavator is a cube LxLxL. If it advances a distance vt, how much soil does it have to excavate? Draw a picture.

welovephysics
How do you get vt+L? Maybe it would help you to think about a more solid analogy. You are digging a tunnel. The excavator is a cube LxLxL. If it advances a distance vt, how much soil does it have to excavate? Draw a picture.

Still vt + L

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How do you get vt+L? Maybe it would help you to think about a more solid analogy. You are digging a tunnel. The excavator is a cube LxLxL. If it advances a distance vt, how much soil does it have to excavate? Draw a picture.
sorry , the volume of the leading face of the box sweep through as the box advances that distance is (L^3) , what are you trying to say ?

haruspex
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sorry , the volume of the leading face of the box sweep through as the box advances that distance is (L^3) , what are you trying to say ?
No.
Think about this... if it went for twice as long, 2t, still at speed v, would it still be the same volume?

welovephysics
No.
Think about this... if it went for twice as long, 2t, still at speed v, would it still be the same volume?
no

haruspex
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no
So it can't be L3, right?
If the leading face is LxL and advances distance vt, what shape does it 'carve out'? What are the dimensions of that shape?

So it can't be L3, right?
If the leading face is LxL and advances distance vt, what shape does it 'carve out'? What are the dimensions of that shape?
what shape ? i am getting more confused now

haruspex
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what shape ? i am getting more confused now
Lay a light box, LxLxL, on soft snow. Press down on it, pushing it down a distance vt. Remove the box. What shape hole have you made in the snow? What is its volume?

Lay a light box, LxLxL, on soft snow. Press down on it, pushing it down a distance vt. Remove the box. What shape hole have you made in the snow? What is its volume?
volume = (L)(L)( L +vt) , shape = rectangular , is it correct ?

haruspex
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volume = (L)(L)( L +vt) , shape = rectangular , is it correct ?
Nearly right. But we are only interested in the volume swept out by the leading face. That moves a distance vt, not L+vt.

Nearly right. But we are only interested in the volume swept out by the leading face. That moves a distance vt, not L+vt.
so the volume = (L)(L)(vt) ???

haruspex