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1. In Figure 1, the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers. A light rope is wrapped around the cylinder, passes over the pulley, and has a box with mass mo suspended from its free Pulley end. There is no slipping between the rope and the pulley surface. The uniform cylinder has mass M and radius R. The pulley is a uniform disk with mass m and radius r. The box is released from rest and descends as the rope unwraps from Cylinder Box the cylinder. A) Use energy conservation to find the speed of the box when it has fallen a height H. Express your answers in Figure 1 terms of any or all of the variables mb, M, R, m, r, H and g (acceleration due to gravity). B) If mb = 3.00 kg, M = 5.00 kg, R = 40.0 cm, m = 2.00 kg, r = 20.0 cm and H = 1.50 m, what would be the answer in part A)? 2. An experimental bicycle wheel is placed on a test stand so that it is free to turn on its axle. If a constant net torque of 5.00 N.m is applied to the tire for 2.00 s, the angular speed of the tire increases from 0 to 100 rev/min. The external torque is then removed, and the wheel is brought to rest by friction in its bearings in 125 s. Assume the direction the wheel is rotating is the positive direction. A) Compute the moment of inertia of the wheel about the rotation axis. B) Compute the friction torque. C) Compute the total number of revolutions made by the wheel in the 125-s time Interval. 3. Two weights are connected by a very light flexible cord that passes over a Wpulley = 40.0-N frictionless pulley of radius R = 0.400 m. The pulley is a solid uniform disk and is supported by a hook connected to the ceiling (Figure 2). What force does the ceiling exert on the hook? Express first your answers in terms of any or all of the variables Wpulley, WA WB, R and g (acceleration due to gravity), and then their 125 N = WB numerical values. WA = 75.0 N Figure 2 4. A large wooden turntable in the shape of a flat uniform disk has a radius of 2.00 m . and a total mass of 120 kg. The turntable is initially rotating at 3.00 rad/s about a vertical axis through its center. Suddenly, a 70.0-kg parachutist makes a soft landing on the turntable at a point near the outer edge. A) Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.) B) Compute the kinetic energy of the system before and after the parachutist lands. Why are these kinetic energies not equal? 2.20 m 5. A worker wants to turn over a uniform, 1250-N, rectangular crate by pulling at 53.0 on one of its vertical sides (Fig. P11.69). The floor is rough enough to prevent the crate from Pull 53.0 1.50 m slipping. A) What pull is needed to just start the crate to tip? B) How hard does the floor push upward on the crate? C) Find the friction force on the crate. D) What is the minimum Figure 3 coefficient of static friction needed to prevent the crate from slipping on the floor? 6. A 10.0-kg mass is traveling to the right with a speed of 2.00 m/s on a frictionless horizontal surface when it collides with and sticks to a second 10.0-kg mass that is initially at rest but is attached to a light spring that is neither stretched nor compressed with a force constant 80.0 N/m. The system undergoes SHM. A) Find the frequency, amplitude, the period of the subsequent oscillations and the phase angle. B) Find the maximum and minimum velocities and acceleration attained by the oscillating system C) How long does it take the system to return the first time to the position it had immediately after the collision? D) Write the equations for the displacement, velocity, and acceleration of the system as function of time. 7. In March 2006, two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km and the other at 64,000 km. Pluto already was known to have a large satellite Charon, orbiting at 19,600 km with an orbital period of 6.39 days. Assuming that the satellites do not affect each other, find the orbital periods of the two small satellites without the mass of Pluto