120 Physics Spring 2008 Problem Set 3 due Monday, March 3
1. You are helping a friend who is a veterinarian to do some minor surgery on a cow. She has asked you to sterilize a scalpel and a hemostat (a kind of surgical clamp) by boiling them for 30 minutes. You boil them as ordered and then quickly transfer the instruments to a wellinsulated tray containing 200 grams of sterilized water at room temperature (22 C) which is just enough to cover the sterilized instruments. After a few minutes, the water and instruments will come to the same temperature, but will they be safe to hand to your friend without being burned? (Notes: You know that both the 50gram scalpel and 70gram hemostat are made of steel 1 1 which has a specific heat of 450 Jkg K . They were boiled in 2.0 kg of water with a 1 1 specific heat of 4190 Jkg K . Water boils at 100 C.)
2 2. A hollow sphere of radius 16.0 cm has a moment of inertia of 0.040 kgm about a line through its center of mass. Suppose the sphere rolls without slipping up a ramp inclined at 15 to the horizontal. At the bottom of the ramp, the sphere's total kinetic energy is 50.0 J. When the sphere has moved 2.0 m up the ramp, what is
(A) its total kinetic energy? (B) the speed of its center of mass?
3. You are driving your car uphill along a straight road. Suddenly, you see a squirrel enter the road just ahead of you. You slam on your brakes and skid in a straight line to a stop, leaving skid marks meters 25 long. Just your luck, a policeman observes the whole thing and gives you a ticket for exceeding the speed limit of 30 miles per hour. When you get home, you do some research on the Internet and find that you car weighs 8800 N and that the sliding friction force acting on your car during a skid is, for typical road surfaces on a dry day, about 5100 N. You also estimate that the hill you were traveling on makes an angle of 10 with the horizontal. Will you fight the speeding ticket in court?
4. George Ferris, Jr., a civil engineering graduate from Renselaar Polytechnic Institute, built the original Ferris wheel for the 1893 World's Columbian Exposition in Chicago (see photo at right). The wheel, an astounding engineering construction at the time, carried 36 wooden cars, each holding up to 60 passengers, around an enormous circle of radius 38 meters. The mass of each car was about 11,000 kg. The mass of the wheel's structure was about 60,000 kg, which was mostly in the circular grid from which the cars were suspended. When operating, the wheel made one complete rotation in about 2 minutes. Estimate the kinetic energy, in joules, of the wheel when turning and fully loaded. Assume an average passenger mass of 70 kg. (Note: For a fascinating account of the planning and construction of the Chicago World's Fair and the serial killer who roamed the streets of Chicago during this period, read The Devil in the White City by Erik Larson.)