Problem 1: A water tank standing on the floor has to small holes vertically above one another punched in one side. The holes are 2 cm and 8 cm above the floor.
1. Compute the distance x.
2. At what depth should a single hole be made to maximize x?
3. How high does the water stand in the tank (calculate H)
Problem 2: A horizontal block-spring system has a total mechanical energy of 10J, the amplitude of 0.2m, and a maximum speed of 1.5m/s. Find:
1. The spring content, k.
2. The mass of the block, m
3. The frequency of oscillation, f.
Problem 3: 1 kg piece of metal is heated to a high temperature T metal, and then dropped into a beaker containing 0.1kg of water at 20 degrees Celsius and 0.5 kg of ice at 0 degrees Celsius. Compute the initial temperature of the metal T metal, if the specific heat of the water is CH20 = 4186 J/kg degrees Celsius and the final equilibrium temperature of the mixture is 80 degrees Celsius. (Lf = 333,000 J/kg for water, c metal = 400 J/kg degrees Celsius)
Problem 4: An oscillator consists of a block attached to a spring (k = 40 N/m). At some time t, the position, velocity and acceleration of the block are: x = 5m, v = 10 m/s and a =-1.48m/s^2. Compute the frequency of oscillation, the mass of the block and the amplitude of the motion.
Problem 5: A horizontal spring oscillates by an amplitude A = 5cm. What is the magnitude of the displacement "x" when the kinetic energy KE is half the elastic potential energy U spring?