"(I) If the force F needed to move the wire in Fig. 13–37 is 3.1 x 10⁻³ N, calculate the surface tension γ of the enclosed fluid. Assume ℓ = 0.070 m.
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Verified step by step guidance

1. Identify the relationship between the force required to move the wire, the length of the wire, and the surface tension. The formula to use is F = 2\gamma \ell, where F is the force, \gamma is the surface tension, and \ell is the length of the wire.
2. Substitute the given values into the formula. Here, F = 3.1 \times 10^{-3} \text{ N} and \ell = 0.070 \text{ m}.
3. Rearrange the formula to solve for \gamma. The rearranged formula will be \gamma = \frac{F}{2\ell}.
4. Plug the values of F and \ell into the rearranged formula to find the value of \gamma.
5. Ensure the units are consistent and calculate the value of \gamma to find the surface tension of the fluid.

Key Concepts

Surface Tension

Surface tension is a physical property of liquids that describes the elastic-like force existing at the surface of a liquid. It arises from the cohesive forces between liquid molecules, which are stronger at the surface due to the lack of neighboring molecules above. This phenomenon causes the surface to behave like a stretched elastic membrane, influencing how liquids interact with solids and gases.

Force and Surface Area Relationship

In the context of surface tension, the force exerted by the liquid on a wire or object is directly related to the surface area in contact with the liquid. The formula for surface tension (γ) can be expressed as γ = F/ℓ, where F is the force applied and ℓ is the length of the contact line. Understanding this relationship is crucial for calculating surface tension from the given force and dimensions.

Units of Measurement

Surface tension is typically measured in newtons per meter (N/m), which quantifies the force acting along a line of unit length at the surface of the liquid. This unit reflects how much force is needed to increase the surface area of the liquid by one meter. Familiarity with units is essential for correctly interpreting and converting measurements in physics problems.