Instructor: K.W.Nicholson
1. A woman whose mass is 80 kg stands at the rim of a horizontal turntable having a moment of inertia of 500 kg m2 and a radius of 2m. Beside her is her faithful but very obese dog Fido, who's mass is 100 kg. The system is initially at rest, and the turntable is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim in a clockwise direction (looking downward) at a constant speed of 2 m/s relative to the earth. Fido, who's trying to lose weight, begins galloping at 3 m/s in the same direction the woman is walking, only at a distance of 1 m from the rim. In what direction and with what angular speed does the turntable rotate?
2. You are asked to design an alternative adult relaxation device. A person sits in a chair that hangs from the middle of a 2.0-m long, 10-kg uniform beam, as shown below. The seat bounces soothingly up and down with a little effort. Determine the mass of the object hanging from the rope that will keep the beam oriented as shown when a 60-kg person (including the mass of the chair) hangs from the rope attached to the beam. Assume that g = 10 m/s .
3. If a solid disk begins rolling down an incline that is 3 m high with initial speed v0 = 20 m/s, how fast is it going when it reaches the bottom?
4. If the density of ice is rice = 0.917 x 103 kg/m3 and the density of seawater is rsw = 1.03x103 kg/m3, what fractional part of the iceberg is submerged ?
5. If 30 g of ice at 0° C is dropped into a styrofoam cup containing 100 g of water at 80° C, what is the final temperature of the water ? (Assume all heat goes into heating the water.)
6. One mole of ideal gas does 4000 J work on the surroundings as it expands isothermally to a final pressure of 1 atm and a final volume of 40 liters. Determine the:
a. Final temperature of the gas.
b. The initial volume of the gas.
7. What is the thermal energy of 200g of He gas at 77° C ?
8. A particular engine has a power out of 5000 W and an efficiency of 25 %. If the engine expels 8000 J of thermal energy in each cycle, find :
a. the heat absorbed in each cycle
b. the time for each cycle.
9. A 7 kg mass is hung from the bottom of a vertical spring fastened to an overhead beam. The mass is set into vertical oscillations having a period of 3 s. Find the force constant of the spring.
10. The motion of an object with mass 4 kg is described by the equation x = (4 cos (št/6)) m.
a) Find the position at t = 2 s
b) Find the amplitude of motion.
c) The frequency of the motion
d) The total energy of the system.