1) Billy Bob "Bubba" Hickman is working in his barn one day. He has a 25 kg hay bale suspended from the barn's rafters on a 2.44 meter long rope. Bubba pulls on another rope horizontally until the rope holding the hay bale makes an angle of 20 degrees with respect to the vertical.
a) What force does Bubba have to exert on the rope to hold the hay bale in this position?
b) The rope slips out of Bubba's hands. The hay bale starts to swing. How long does it take for the hay bale to swing to the farthest distance from where it started (the farthest distance across the barn)?
c) Bubba runs to catch the hay bale. He tries to catch it at the bottom of the swing as it swings back towards him. How fast is the hay bale moving when it hits Bubba?
2) A narrow metal rod, of mass 1.22 kg and length 2.05 meters is free to rotate about one end of the rod.
a) What is the moment of inertia of the rod?
b) How much work is needed to make the rod go from rest to swinging at 10 revolutions per minute?
3) Bubba has a mass of 75.3 kilogram and stands in the center of a 4.12 meter long uniform board. The board has a mass of 16.2 kg. The board is supported on each end by cables, each of which can sustain a maximum tensile force of 564 Newtons before breaking. How far from the center of the board can Bubba walk before one of the cables breaks?
4) The elevator at a diamond mine is supported by a single steel cable of diameter 1.28cm. The total mass of the elevator and cable is 670kg. When the elevator is at surface level, it is 12m below the pulley holding the cable.
a) Determine the stress and strain on the cable when the elevator is at the surface level.
b) By how much does the cable stretch when the elevator has been lowered a distance of 350m below the surface of the ground.
c) What is the maximum mass that the elevator and its occupants may have before the cable breaks? (Neglect the mass of the cable.)
5) Ceres, the largest object in the asteroid belt, has a mass of 9.43x1020 kg and a radius of 487 km.
a) What is the acceleration due to gravity at the surface of Ceres?
b) What would be the orbital period of a satellite if it were to orbit Ceres at a distance of 925 km above its surface?
6) A 425 gram mass is attached to a horizontal spring. The spring is known to have a spring constant of 84.6 N/m. The mass is free to slide along a frictionless surface
a) The mass is then pulled to the side a distance of 5.67 cm and released. Determine the period and amplitude of the resulting oscillations.
b) Determine the magnitude of the maximum velocity of the mass, and state where it reaches that maximum velocity.
7) A harmonic oscillator moves according to the equation:
x=(13.8 cm)cos(11.7s-1t+ 0.77) .
a) What is the period of this oscillation?
b) What is the amplitude of this oscillation?
c) What is the maximum velocity of this oscillation?
d) What is the maximum acceleration of this oscillation?
8) Bubba sets a 1.25kg solid sphere of diameter 11.5cm at the top end of a 1.75m long board that is inclined an angle of 15 degrees relative to the horizontal. The sphere rolls down the incline without slipping.
a) Determine the linear speed of the sphere at the bottom of the incline.
b) Determine the rotational rate of the sphere at the bottom of the incline.
c) Determine how many times the sphere executed a complete rotation before it reached the bottom of the incline.
9) Consider a solid iron hollow cylinder (inner diameter 10.4 cm, outer diameter 18.8 cm, and length 45.0cm).
(The density of iron is 7.874 gm/cm3.)
a) Determine the mass of the cylinder.
b) Determine the moment of inertia of the cylinder if it spins about its long axis.
c) If the cylinder were spinning at 76.6 rpm, and brake pads were applied to the inner surface of the cylinder (like in drum brakes), how much force would be needed pressing the pads into the cylinder walls to stop the cylinder in 12.3 seconds? Assume that the coefficient of kinetic friction between the pads and the cylinder is 0.445.
10) A rotating metal plate of length 26cm and width 21cm is spinning about its center of mass at 22.3 radians per second. The metal plate has mass 22.4 kg. A solid cylinder of mass 34.3 kg and diameter 16cm is dropped onto the center of the rotating plate.
a) Determine the final speed of rotation of the system.
b) Determine the change in kinetic energy of the system.