# Week 9 (Oct. 7 - 11)

Reading: PSE Chap 6, Circular motion and other applications of Newton's laws
Topics: circular motion and newtons' laws

Lab:

Homework Problems:

1. Pulley on a platform: Solution. A man stands on a platform that has a pulley rigidly attached to its top surface. A rope is threaded under the pulley. One end of the rope is attached securely to the ceiling; the other end is held firmly by the man standing on the platform. By pulling up on the pulley, the man can cause the platform to rise.
• Draw a free body diagram for the platform (mass M = 100 kg). Draw a separate free body diagram for the man (mass m=150 kg).
• What must be the tension in the rope so that the platform is suspended in the air without falling or rising.
• What must be the tension in the rope so that the platform rises at a constant velocity of 10 cm/second.
• What must be the tension in the rope so that the platform rises at a constant acceleration of 10 cm/second squared.
2. The effect of buoyancy on a falling body: Solution. 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 isuspended 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.
3. The effect of drag on a falling body: Solution. 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?

Midterm: Monday Oct. 17
General College Physics