Formula of force

  • #1

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
iqbzhu9.jpg

Homework Equations




The Attempt at a Solution

 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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.
 
  • #3
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 ?
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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?
 
  • Like
Likes welovephysics
  • #5
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 ?
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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?
 
  • Like
Likes welovephysics
  • #7
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 ??
 
  • #8
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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?
 
  • #9
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) ?
 
  • #10
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
the box will move by L in time , t , am i right ?
It is moving at speed v, not L/t.
 
  • Like
Likes welovephysics
  • #11
It is moving at speed v, not L/t.
so , what are you trying to say , i didnt get you
 
  • #12
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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?
 
  • Like
Likes welovephysics
  • #13
If a car length L moves at speed v for time t, how far does it go?
car move by vt
 
  • #14
If a car length L moves at speed v for time t, how far does it go?
is it correct ??
 
  • #16
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
 
  • #17
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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.
 
  • Like
Likes welovephysics
  • #18
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
 

Attachments

  • #19
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 ?
 
  • #20
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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?
 
  • Like
Likes welovephysics
  • #21
No.
Think about this... if it went for twice as long, 2t, still at speed v, would it still be the same volume?
no
 
  • #22
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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?
 
  • #23
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
 
  • #24
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,514
6,423
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?
 
  • #25
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 ?
 

Related Threads on Formula of force

  • Last Post
Replies
8
Views
633
  • Last Post
Replies
7
Views
453
  • Last Post
Replies
3
Views
7K
Replies
3
Views
1K
  • Last Post
Replies
3
Views
891
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
6
Views
39K
  • Last Post
Replies
6
Views
71K
Top