Solved Examples of Surface Tension Problems: AP Physics 2

📚 Quick Study Guide

• 💧 Surface Tension: Arises from cohesive forces between liquid molecules, creating a 'skin' at the surface.
• 📏 Definition: Force per unit length acting along the surface.
• 🧮 Formula: $\gamma = \frac{F}{L}$, where $\gamma$ is surface tension, $F$ is force, and $L$ is the length over which the force acts.
• 🌡️ Temperature Dependence: Surface tension generally decreases with increasing temperature.
• 🧼 Surfactants: Substances that reduce surface tension (e.g., soaps and detergents).
• 🌐 Units: Commonly measured in N/m (Newtons per meter) or dynes/cm (dynes per centimeter).
• 🧪 Applications: Explains phenomena like capillary action, droplet formation, and insect walking on water.

🧪 Practice Quiz

1. Question 1: A needle of length 5 cm is floating on the surface of water. If the surface tension of water is 0.073 N/m, what is the force due to surface tension supporting the needle?
   1. 0.00365 N
   2. 0.0073 N
   3. 0.0146 N
   4. 0.0365 N
2. Question 2: What happens to the surface tension of water when the temperature increases?
   1. Increases
   2. Decreases
   3. Remains the same
   4. Becomes zero
3. Question 3: A rectangular frame with one movable side of length 10 cm is dipped in a soap solution. If a force of $2 \times 10^{-3}$ N is required to move the side, what is the surface tension of the soap solution?
   1. 0.01 N/m
   2. 0.02 N/m
   3. 0.03 N/m
   4. 0.04 N/m
4. Question 4: Which of the following is NOT a direct application of surface tension?
   1. Capillary action
   2. Formation of rain droplets
   3. Buoyancy of a ship
   4. Insects walking on water
5. Question 5: A liquid has a surface tension of 0.05 N/m. How much force is required to lift a thin wire of length 2 cm from the surface of the liquid?
   1. 0.0005 N
   2. 0.001 N
   3. 0.002 N
   4. 0.004 N
6. Question 6: What is the effect of adding a surfactant to water?
   1. Increases surface tension
   2. Decreases surface tension
   3. No effect on surface tension
   4. Increases the viscosity
7. Question 7: The surface tension of a liquid is measured to be 0.06 N/m. What is this value in dynes/cm? (1 N = $10^5$ dynes, 1 m = 100 cm)
   1. 0.06 dynes/cm
   2. 6 dynes/cm
   3. 60 dynes/cm
   4. 600 dynes/cm