# Week 9

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

Lab:

Homework Problems: Problems will be due on Tuesday, October 19 at noon.

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?
4. David's sling: Solution. King David, facing Goliath, swings a stone in the pouch of a sling above his head. The trajectory of the stone is in a circle whose plane is parallel to the ground. The sling is of length L = 1 meter; the stone is of mass m = 200 grams. The rotation rate is twice per second. Ignore gravity and drag (let's focus on the circular motion).
• Draw a free body diagram for the stone at a particular instant.
• What is the speed of the stone? Is it accelerating? If so, in which direction?
• What is the tension in the string? What would happen if the string snapped?
5. Race track: Solution. A 2000 kg race car rounds a curve at 150 mph. The radius of curvature of the track is 100 meters. What is the minimum coefficient of friction between the tires and the road so that the car does not slide?

Quiz: Monday, Oct. 17.
AP Physics