# Week 2

Read: Archimedes' Principle and Falling Bodies (ASGv2 Chap. 3) and Falling Bodies and Pendular Motion (ASGv2 Chap. 4).

Key topics: Archimedes' principle, the effect of buoyancy and drag on bodies falling in fluids, pendular and periodic motion.
Homework:
1. Floating iceberg (Ex. 3.1),
2. The effect of buoyancy on a falling body: A pure indium ball having a diameter d = 1 cm is suspended from a tiny thread in a vacuum chamber.
• What is the tension in the string? Hint: look up the density of indium (a soft metal).
• If the ball is suspended in a vat of liquid gallium (instead of a vacuum), what is the tension in the string? Hint: look up the density of gallium.
• If the thread is now snipped, what is the acceleration of the indium ball as it falls through the liquid gallium? Ignore drag (but not buoyancy) for now.
1. PHY 201 problem: The effect of drag on a falling body: In reality, drag reduces the acceleration of a falling body because it exerts a force opposite the direction of motion of the falling body. In the previous problem, as the indium ball accelerates, the drag force exerted by the liquid gallium increases until the sum of the drag and buoyancy balance the ball's weight. At this time, the ball achieves so-called "terminal velocity."
• What is the terminal velocity of the ball? Hint: at terminal velocity, the acceleration is zero. Let's assume that the flow around the ball is turbulent, so that the drag force is given by D = 1/2 * (fluid density) * (cross sectional area of sphere) * (drag coefficient of sphere) * v^2. The drag coefficient of a sphere is approximately 1.
• Now: repeat this problem for indium ball if it is submerged in liquid mercury (instead of liquid gallium). In particular: what is its terminal velocity? Does the indium ball ascend or descend?
Lab: Archimedes' principle (Ex. 3.4) and Falling bodies (Ex. 3.5)

Chapter 3 (8 videos):

Chapter 4 (4 videos):

Physics 1