A square metal sheet 3.1 cm on a side and of negligible thickness is attached to a balance and inserted into a container of fluid. The contact angle is found to be zero, as shown in Figure (a), and the balance to which the metal sheet is attached reads 0.40 N. A thin veneer of oil is then spread over the sheet, and the contact angle becomes 180°, as shown in Figure (b). The balance now reads 0.39 N. What is the surface tension of the fluid?
Answer in N/m
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To find the surface tension of the fluid, we need to use the concept of surface tension and the change in force when the contact angle changes.
Surface tension is defined as the force acting per unit length along the boundary of a liquid surface. It is typically represented by the Greek letter "γ" (gamma).
The force acting along the boundary of the liquid-air interface can be calculated as the difference between the initial and final forces measured by the balance.
Let's denote:
- F_initial as the initial force measured by the balance (0.40 N)
- F_final as the final force measured by the balance with the oil spread (0.39 N)
- L as the length of the side of the square metal sheet (3.1 cm)
The change in force, ΔF, can be calculated as:
ΔF = F_initial - F_final
Now, we can calculate the surface tension γ using the formula:
γ = ΔF / L
Plugging in the values we have:
ΔF = 0.40 N - 0.39 N = 0.01 N
L = 3.1 cm = 0.031 m
Substituting these values into the formula, we get:
γ = 0.01 N / 0.031 m = 0.3226 N/m
Therefore, the surface tension of the fluid is approximately 0.3226 N/m.