Solving Formula of Forces Homework

In summary, the author discusses the formula for force, which is given as ρ(L^2)(v^2) and also = ρ(L^3). However, there may be an error in the second equation. The author also suggests that the formula can be written as ρ(L^4)(T^-2), but this does not follow as there are physical constants that impose relationships between the fundamental dimensions. The correct formula for force is still uncertain.
  • #1
foo9008
678
4

Homework Statement


from the notes , the author stated that force has the formula of ρ(L^2)(v^2) and also = ρ(L^3)
i think there's something wrong with the ρ(L^3)
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Homework Equations

The Attempt at a Solution


IMO , ρ(L^2)(v^2) can also be written as ρ(L^4)(T^2) , so Force is proportional to L^4 , am i right . ? IMO, the prototype force should be [ (100^4) ] x 0.12 N

correct me if i am wrong ...
 
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  • #2
I'm not sure, but in your picture, one is ##\rho## and the other is ##\rho_r.## Maybe there is detailed definitions in the problem?
 
  • #3
tommyxu3 said:
I'm not sure, but in your picture, one is ##\rho## and the other is ##\rho_r.## Maybe there is detailed definitions in the problem?
rho r is actually r , it's the pi buckingham theorem
 
  • #4
foo9008 said:
ρ(L^2)(v^2) can also be written as ρ(L^4)(T^2) , so Force is proportional to L^4
I guess you mean ρ(L^4)(T^-2), but either way it does not follow. The whole point of figuring out these dimensionless expressions is that you cannot change the scale of L and assume T fixed, etc. There are physical constants in the system, like viscosity, which impose a relationship between the fundamental dimensions. Changing L keeping T etc. fixed will therefore change the viscosity.
Similarly, density fixes a relationship between M and L.
 
  • #5
haruspex said:
I guess you mean ρ(L^4)(T^-2), but either way it does not follow. The whole point of figuring out these dimensionless expressions is that you cannot change the scale of L and assume T fixed, etc. There are physical constants in the system, like viscosity, which impose a relationship between the fundamental dimensions. Changing L keeping T etc. fixed will therefore change the viscosity.
Similarly, density fixes a relationship between M and L.
Then, what is the correct formula of force in this question?
 
  • #6
haruspex said:
I guess you mean ρ(L^4)(T^-2), but either way it does not follow. The whole point of figuring out these dimensionless expressions is that you cannot change the scale of L and assume T fixed, etc. There are physical constants in the system, like viscosity, which impose a relationship between the fundamental dimensions. Changing L keeping T etc. fixed will therefore change the viscosity.
Similarly, density fixes a relationship between M and L.
so , the author is correct ? it is (rho)(L^2)(L ) , where (v^2) = L ??
 
  • #7
foo9008 said:
so , the author is correct ? it is (rho)(L^2)(L ) , where (v^2) = L ??
I'm hampered by not knowing what Fr stands for in the first line.
I presume F=ρL2V2 comes from some earlier work.
If we accept both of those equations, the rest follows.
 
  • #8
haruspex said:
I'm hampered by not knowing what Fr stands for in the first line.
I presume F=ρL2V2 comes from some earlier work.
If we accept both of those equations, the rest follows.
So, the authors working is correct??
 
  • #9
foo9008 said:
So, the authors working is correct??
I'm not sure. I don't know where the first line of equations comes from, or what Fr represents. I'm surprised to see any reference to g here. How is gravity relevant? If gravity were to increase but the densities, masses, and lengths stay the same, those equations seem to say the velocity would increase. Why?
 

Related to Solving Formula of Forces Homework

What is the formula for calculating forces?

The formula for calculating forces is F = m x a, where F is force, m is mass, and a is acceleration.

How do I determine the direction of a force?

The direction of a force can be determined by its vector representation. A force can act in any direction, and its direction can be represented by an arrow pointing in the direction of the force.

What is the difference between net force and individual forces?

Net force is the sum of all individual forces acting on an object. Individual forces are specific forces acting on an object, while net force is the overall force acting on an object.

When do I use the formula F = ma versus F = mg?

The formula F = ma is used when an object is experiencing acceleration, while F = mg is used when an object is at rest or experiencing uniform motion.

How do I solve a formula of forces homework problem?

To solve a formula of forces homework problem, first identify the given values and the unknown value. Then, substitute the given values into the appropriate formula and solve for the unknown value. Be sure to pay attention to units and use the correct formula for the given scenario.

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