Problem 1 - Fluids & Solids For full credit, you must demonstrate the algebraic steps used to solve for the desired unknown, and you must show the correct units in your work and solution. The inside diameters of the larger portions of the horizontal pipe depicted in the figure are 12 cm. The tops of the vertical columns are open to the atmosphere. The fluid depicted in the figure has a specific gravity of 0.95, and the flow rate of fluid into the larger portion of the horizontal pipe is 1.5 m/s. (a) What is the absolute pressure at the base of the taller column of fluid, i.e. where the taller vertical column meets the horizontal pipe? Use the equation for variation of pressure with depth to show that the answer is 102,231 Pa. (b) What is the gauge pressure at the base of the shorter column of fluid, i.e. where the shorter vertical column meets the horizontal pipe. Combine the definition of gauge pressure with the equation of variation of pressure with depth to show that the answer is 465.5 Pa. (c) If the flow speed of the fluid entering the large horizontal pipe on the left is 2.5 m/s, what is the flow speed through the constricted section of the pipe? Apply the Venturi effect to show that the answer is 2.69 m/s.

Problem 2 - Heat & Temperature For full credit, you must demonstrate the algebraic steps used to solve for the desired unknown, and you must show the correct units in your work and solution. A solid cube of copper and a solid cube of aluminum have equal masses and initially have the same internal energy. The two cubes have equal masses of m = 2.4 kg, and the cubes have equal amounts of internal energy, 650,000 Joules each. (a) What is the temperature of the copper cube in Celsius? Show that the answer is 427C (b) What is the temperature of the aluminum cube in Fahrenheit? Show that the answer is 82F Next the two cubes are put in thermal contact with each other and isolated from the environment until they reach thermal equilibrium. (c) What is the final temperature in Kelvin reached by the two cubes? Show that the answer is 421 K

Problem 3 - Simple Harmonic Motion & Waves For full credit, you must demonstrate the algebraic steps used to solve for the desired unknown, and you must show the correct units in your work and solution. When five people get in a car, their weight compresses the springs in the suspension of the car by 0.85 cm. (a) If the combined mass of the people in the car is 380 kg, what is the effective spring constant of the car's suspension? Show that the answer is 438,118 N/m. (b) If the mass of the car without the people is 2500 kg, what frequency will the car bounce at if the people get out and bounce it up and down? Show that the answer is 2.1 Hz