PHY 113, Summer 2007
Langenbrunner
HW 10 – due Tuesday, June 26
1. A uniform spherical shell of mass M and radius R rotates about a vertical axis on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it falls a distance h from rest? (There are two ways to do this problem!)
(ignore the “roblem 66”on the bottom of that figure)
2. A yo-yo with inner radius r (that's the one the string is wrapped around), outer radius R, mass M, and moment of inertia I, “rolls” down its string while you hold the end of the string stationary.
a) What is the acceleration of the center of mass of the yo-yo in terms of r, R, M, and I?
b) What is the tension in the string?
3. A man stands on a platform that is rotating (without friction) with an angular speed of 1.2 rev/s; his arms are outstretched and he holds a brick in each hand. The rotational inertia of the system consisting of the man, bricks, and platform about the central axis is 6.0 kg*m2. If by moving the bricks the man decreased the rotational inertia of the system to 2.0 kg*m2,
a) What is the resulting angular speed of the platform and
b) What is the ratio of the new kinetic energy of the system to the original kinetic energy?
4. Two skaters, each of mass 50 kg, approach each other along parallel paths separated by 3.0 m. they have opposite velocities of 1.4 m/s each. One skater carries one end of a long pole with negligible mass, and the other skater grabs the other end of it as she passes. Assume frictionless ice.
a) What is their angular velocity after the other skater grabs the end of the pole?
b) What is the kinetic energy of the system?
Next the skaters each pull along the pole so as to reduce their separation to 10 m. What are
c) their angular speed and
d) the kinetic energy of the system?
e) Explain the source of the increased kinetic energy.
5. A nonuniform bar is suspended at rest in a horizontal position by two massless cords as shown. One cord makes and angle θ=36.9 degrees with the vertical; the other makes the angle φ=53.1 degrees with the vertical. If the length L of the bar is 6.10 m, compute the distance x from the left-hand end of the bar to its center of mass.
(that’s a θ on the left and a φ on the right)
6. An office window has dimensions 3.4 m by 2.1 m. As a result of the passage of a storm, the outside air pressure drops to 0.96 atm, but inside the pressure is held at 1.0 atm. What net force pushes out on the window?
7. Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person of height 1.83 m. The density of blood is 1.06 x 103 kg/m3.
8. An iron anchor of density 7870 kg/m3appears 200 N lighter in water than in air.
a) What is the volume of the anchor?
b) How much does it weight in air?
9. A garden hose with an internal diameter of 1.9 cm is connected to a (stationary) lawn sprinkler that consists merely of an enclosure with 24 holes, each 0.13 in diameter. If the water in the hose has a speed of 0.91 m/s, at what speed does it leave the sprinkler holes?
10. Water is moving with a speed of 5.0 m/s through a pipe with a cross sectional area of 5.0 cm2. The water gradually descends 10 m as the pipe increased in area to 8.0 cm2.
a) What is the speed at the lower level?
b) If the pressure at the upper level is 1.5 x 105 Pa, what is the pressure at the lower level?
11. If the density of ice is 0.917 x 103 kg/m3 and the density of salt water is 1.024 x 103 kg/m3, calculate the fraction of icebergs that are actually submerged. (That is, find Vsubmerged divided by Vtotal.)