- #1

arhzz

- 266

- 52

- Homework Statement
- Determine the surface tension γ of a liquid with the help of the capillary effect. The capillary has an inner diameter of 0.5 mm and the liquid with a density of 875 kg / m3 rises 3.4 cm. To do this, derive the formula for γ from the equilibrium of forces

- Relevant Equations
- F = mg

Hello! To this I did what was recommended and this is what it looks like

$$ F = mg $$

$$ F = \rho * V * g $$

$$ F = \ rho * \pi^2 * h * g $$

Than for the surface tension I did the same thing to get an expression for F.

$$ y = \frac {F} {2 \pi r}$$

Than tried to get F out and than equate both of the equations, than F and pi would be on both sides so it would cancel out leaving me with this.

$$ \rho * r^2 *h * g = 2 * y * r $$

Than I tried to get the tension out so I moved everything accordingly and got this $$ y = \frac {h* \rho*g*r} {2}$$

The result should be 0,0365 N/m

Now the reason why I am posting this question is why is it recommened to use the equilibrium of forces? I tried to calculate the tension, with an equation that was given to us in class, it doenst include any forces and I got a whole diffrent result. I'd assume this is the right way to do it given the suggestion in the task itself but why? And in a situation where this "hint" wasnt given to me I'd never come to use this variant, id just do with the formula provided in class. Any insights?

Thank you!

$$ F = mg $$

$$ F = \rho * V * g $$

$$ F = \ rho * \pi^2 * h * g $$

Than for the surface tension I did the same thing to get an expression for F.

$$ y = \frac {F} {2 \pi r}$$

Than tried to get F out and than equate both of the equations, than F and pi would be on both sides so it would cancel out leaving me with this.

$$ \rho * r^2 *h * g = 2 * y * r $$

Than I tried to get the tension out so I moved everything accordingly and got this $$ y = \frac {h* \rho*g*r} {2}$$

The result should be 0,0365 N/m

Now the reason why I am posting this question is why is it recommened to use the equilibrium of forces? I tried to calculate the tension, with an equation that was given to us in class, it doenst include any forces and I got a whole diffrent result. I'd assume this is the right way to do it given the suggestion in the task itself but why? And in a situation where this "hint" wasnt given to me I'd never come to use this variant, id just do with the formula provided in class. Any insights?

Thank you!