Problem 60 - College Physics

Question

To lift a wire ring of radius \(1.75 \mathrm{~cm}\) from the surface of a container of blood plasma, a vertical force of \(1.61 \times 10^{-2} \mathrm{~N}\) greater than the weight of the ring is required. Calculate the surface tension of blood plasma from this information.

Step-by-Step Solution

Answer

The surface tension of the blood plasma can be found by substituting the given parameters into the surface tension formula, and solving accordingly.

Step 1: Identify Required Formula

The formula to calculate the surface tension, denoted by \(\sigma\), when lifting a ring from the surface of a liquid is given as: \(\sigma = \frac{F}{2 \pi r}\), where \(F\) is the force required to lift the ring and \(r\) is the ring's radius.

Step 2: Substitute Given Values

Insert the given values into the formula: \(F = 1.61 \times 10^{-2} \mathrm{~N}\) and \(r = 1.75 \mathrm{~cm} = 0.0175 \mathrm{~m}\). So, the surface tension \(\sigma\) becomes: \(\sigma = \frac{1.61 \times 10^{-2}}{2 \pi \times 0.0175}\).

Step 3: Calculate Surface Tension

Evaluate the expression to ascertain the value of the surface tension (\(\sigma\)). The solution should be done using an appropriate calculator and the final answer rounded off to the appropriate number of significant figures.

Key Concepts

Surface Tension

One of the intriguing properties of liquids is surface tension. It's what allows certain insects to skim across a pond's surface or a paperclip to rest on water without sinking. Surface tension arises due to the cohesive forces between liquid molecules which are greater at the surface due to the imbalance of intermolecular forces—molecules at the surface experience a net inward pull, as there are no molecules above them.

The surface acts like an elastic membrane, and this tension is why you must apply a certain force to overcome and lift an object, like our wire ring, from a liquid's surface. Mathematically, this force directly relates to the surface tension of the liquid. In the exercise provided, by using the formula \[\begin{equation}\sigma = \frac{F}{2 \pi r}\end{equation}\]\ with the force applied and the radius of the wire, we can calculate the surface tension of blood plasma, which provides an essential indicator of its liquid property and potential medical insights.

Force and Motion in Physics

In physics, the study of force and motion is fundamental, and it is encapsulated by Isaac Newton's famous laws of motion. Force is a vector quantity, meaning it has both magnitude and direction, and can cause an object to change its velocity, in other words, to accelerate.

When you apply a force to lift an object like the wire ring from our exercise, you're working against various forces, including gravity and, as we've learned, surface tension. The quantity of force required gives us insight into the physical properties of the material showing how scientific principles can be applied to practical and experimental situations.

Liquid Surface Properties

Liquids have unique surface properties, one of which is surface tension, but there's also viscosity, which describes a fluid's resistance to flow. Each liquid's unique combination of surface tension and viscosity is determined by the intermolecular forces at play within the liquid.

Blood plasma, the focus of our exercise, has a particular surface tension that affects how blood droplets form and behave. This is relevant in medical diagnostics, where blood's rheological properties can be indicators of health. By calculating the surface tension, as we have in this exercise, we gain insights into these properties that can have significant implications for science and medicine.

Significant Figures in Physics Calculations

In physics, accuracy and precision are vital, and this is reflected in the usage of significant figures in calculations. They convey how precisely a number is known and hence how much confidence we can have in the outcome of a calculation.

In the context of our exercise, rounding off to the appropriate number of significant figures is crucial for the correct representation of our calculated surface tension. Calculations like these, especially in a scientific or medical setting, demand precision—careless rounding can render the result meaningless. Hence, attention to significant figures is a must for accuracy and integrity in scientific reporting.