Final answer:
To calculate the force with which surface tension resists stretching the longer side of the water container, we need to calculate the increase in area and then use the formula F = E / d. After calculation, we get that the surface tension of the water resists the change with a force of approximately 0.01095 J.
Step-by-step explanation:
Surface tension is the energy required to increase the surface area of a liquid. It is measured in units of energy per area, such as joules per square meter (J/m²). The surface tension of water is due to its strong intermolecular hydrogen bonding, which leads to a high surface tension compared to other liquids.
Now, let's calculate the force with which surface tension resists the stretching of the longer side of the water container. The longer side of the container is initially 42 cm, and it is stretched by an additional 8 cm. Therefore, the increase in length is 8 cm (or 0.08 m) and the width remains unchanged at 15 cm (or 0.15 m). The increase in area can be calculated by multiplying the increase in length with the initial width, which gives us
0.08 m * 0.15 m = 0.012 m².
The energy required to increase the surface area can be found by multiplying the increase in area with the energy cost per unit area, which is given as 73 mJ/m². Therefore, the energy required to stretch the longer side of the water container is
0.012 m² * (73 * 10^-3 J/m²) = 0.000876 J.
The force with which surface tension resists the change can be calculated using the formula
F = E / d,
where F is the force, E is the energy, and d is the displacement. In this case, the displacement is the increase in length, which is 0.08 m. Using the calculated energy value, the force is
0.000876 J / 0.08 m = 0.01095 J.
Therefore, the surface tension of the water resists the change with a force of approximately 0.01095 J.