Resistance of a fructum-shaped bar

  • Thread starter Thread starter Icheb
  • Start date Start date
  • Tags Tags
    Resistance
AI Thread Summary
To calculate the resistance of a frustum-shaped bar with only the radii of both ends provided, the resistance formula R = ρ * (l/A) can be used, where A is the cross-sectional area. The volume of the frustum can be calculated using V = (π * l / 3) * (r²_2 + r_2 * r_1 + r²_1), which depends on the unknown length l. One proposed method is to treat the frustum as a cube with the same volume, allowing for the calculation of area A as A = V/l. This approach enables the substitution of A into the resistance formula, although the exact length l remains a challenge. Understanding the frustum's geometry is essential for accurate calculations.
Icheb
Messages
42
Reaction score
0
I have to calculate the resistance of a bar that is shaped like a fructum and I'm only given the radius of both ends, not its length.

The formula to calculate the resistance in general is

R = \rho * \frac{l}{A}

And the formula for the volume of a fructum is

V = \frac{\pi * l}{3} (r^2_2 * r_2r_1 * r^2_1)

My problem is that I have difficulties incorporating the formula for the volume into the formula for the resistance.

Would it be possible to calculate the volume of the fructum (which would be dependant on l) and treat it like it's a cube with the same volume? That way, I could use A = \frac{V}{l}, then divide the volume by l and enter it into the formula for R.

Other than that, I have no idea what approach to take.
 
Last edited:
Physics news on Phys.org
Sorry, looked as best I can.

No idea what a fructum is.
 
Sorry, I misspelled it. I meant a frustum. It's like a cone, but with the "sharp" end cut off.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Resistance of three-dimensional objects
Replies
10
Views
890
Double pendulum Lagrangian using small angle approximation formula
Replies
5
Views
1K
Electric current and resistance question
Replies
2
Views
2K
Net force between two conducting strips
Replies
6
Views
845
Designing a speed bump given the maximum vertical wheel acceleration
Replies
18
Views
1K
Two concentric conducting spherical shells and resistor in between
Replies
44
Views
4K
Rod with Current on Rails in Magnetic Field
Replies
12
Views
2K
A particle's momentum in a magnetic field
Replies
3
Views
948
Calculating the Planck Length
Replies
3
Views
270
Identical Batteries in Parallel do not Draw Same Current, Non-Ideal?
Replies
7
Views
887

Hot Threads

Recent Insights

Back
Top