Physics_1B_Worksheet_1

Physics 1B Winter 2023 Worksheet 1 Ch. 12 (Fluid Mechanics) Problem 1 A cube-shaped block A of side length a is hanging from a spring balance D, which reads, in units of mass, M D . The block is submerged in liquid C, which has a total mass of m C and is inside beaker B with mass m B . The beaker rests on an electronic scale E with a readout of M E . a) Draw force diagrams for block A and beaker B. b) What is the mass m A of block A in terms of the given variables? c) What is the density ρ C of liquid C? d) The block is now pulled out of the liquid. What are the new readings M ′ D and M ′ E on the balance and scale? e) Compare the readouts of the balance and scale before and after the block is pulled from the liquid for the values a = 0 . 1 m, m B = 1 kg, m C = 5 kg, M D = 3 . 5 kg, and M E = 7 . 5 kg. Problem 2 Consider a column of water as it falls from a faucet. The opening in the faucet has radius r 0 and the water comes out with initial velocity v 0 . Define y to be the distance below the faucet. As the water falls ( y increases), it accelerates due to gravity and the stream narrows. a) Assuming streamline flow, find an expression for the velocity of the water for any distance below the faucet. b) The stream obeys the continuity equation. Use this to determine the radius of the stream as a function of y . c) At what distance y 1 / 2 will the radius of the stream be half its original radius? At what distance y 1 / 3 will it be a third? d) Compare y 1 / 2 and y 1 / 3 for v 0 = 1 m/s and v 0 = 0 . 1 m/s (use g = 10 m/s 2 ). 1