What is the mass of the water in the stirrer supported by surface tension?

In summary, a hollow stirrer with a diameter of 2.0 mm is inserted into a cup of water at 20∘C with a surface tension of 7.28×10−2 N/m. The task is to find the mass of water supported by the surface tension in the stirrer. Using the equations for surface tension, pressure, and force, the correct answer can be found by rearranging the equations to solve for mass. After a minor mistake, the correct answer was obtained.
  • #1
Galactium
12
0

Homework Statement


A hollow stirrer that has a diameter of 2.0 mm is inserted into a cup of water at 20∘C. The surface tension of water at that temperature is γ(surface tension) = 7.28×10−2 N/m.

What is the mass of the water supported by the surface tension in the stirrer?

Given:
d=2 mm
p(rho): 1000 kg/m^3
y(surface tension): 7.28E-2 N/m

Find: Mass

Conversions:
d=.002 m r=.001

Problem: I tried this equation, but I keep on getting the wrong answer, I am not sure if I am using the correct formula.

Homework Equations


Surface tension: deltaP=2y/r
Pressure: deltaP=F/A

The Attempt at a Solution


detlaP=2y/r
deltaP=F/A
F=mg
A=(pi)r^2
Plug them in:
mg/(pi)r^2=2y/r
Change the equation to equal mass (m):
m=2y(pi)r/g
 
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  • #2
Your work looks good. What numerical answer did you get for m?
 
  • #3
TSny said:
Your work looks good. What numerical answer did you get for m?
Nevermind, I got the right answer just a minor mistake. Sorry about that. Thanks for the help!
 

FAQ: What is the mass of the water in the stirrer supported by surface tension?

1. What is surface tension?

Surface tension is the force that holds the molecules of a liquid together at its surface. It is caused by the imbalance of intermolecular forces at the surface of the liquid, creating a "skin" or surface layer that resists external forces.

2. How does surface tension support the stirrer in the water?

The surface tension of water creates a cohesive force between the water molecules, allowing them to stick together and form a "skin" on the surface of the water. This cohesive force supports the weight of the stirrer, as long as the surface tension is not broken.

3. Why does the mass of the water in the stirrer matter?

The mass of the water in the stirrer is important because it affects the amount of force that is acting on the surface tension. A heavier mass will require a stronger surface tension to support it, while a lighter mass may not require as much surface tension.

4. What factors can affect the mass of the water in the stirrer?

The mass of the water in the stirrer can be affected by the size and weight of the stirrer itself, as well as the volume of water in the container. Other factors such as temperature, pressure, and the presence of other substances in the water can also impact the mass.

5. What units are used to measure the mass of water in the stirrer?

The mass of water in the stirrer is typically measured in grams (g) or kilograms (kg). In scientific experiments, it may also be measured in other units such as milligrams (mg) or pounds (lbs).

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