Supplemental Problems
SUP1. A block of wood has a mass of 12 kg and dimensions 0.5 m by 0.2 m by 0.2 m.
(a) Find the density ρo, of the wooden block.with the square sides parallel to the water surface, how far
beneath the surface of the water is the bottom of the block?
(b) If the block is placed in water (ρ = 1000 kg/m3)
(c) A weight is placed on the top of the block. The block sinks to a point that the top of the block is exactly even with the water surface. Find the mass of the added weight.
SUP2. A tapered horizontal pipe carries water from one building to another on the same level. The wider end has a cross-sectional area of 4 m2. The narrower end has a cross-sectional area of 2 m2. Water enters the wider end at a velocity of 10 m/sec.
(a) What is the speed of the water at the narrow end of the pipe?
(b) The gauge pressure of the water at the wide end of the pipe is 2 x 105pascals. Using Bernoulli’s equation, find the gauge pressure at the narrow end of the pipe.
SUP3. A small airplane has wings with surface area 9 m2 each. The speed of the air across the top of the wing is 50 m/sec, and across the bottom of the wing, 40 m/sec. Take the density of air to be 1.2 kg/m3
(a) Find the difference in the pressure between the top and the bottom of the wing.
(b) i) Find the net lift upward on the plane.
ii) If there is no other lift on the plane, what would be the mass of the plane? Assume the plane is not
accelerating up or down.
SUP4. A block of wood floats in water, with 2/3 of it submerged. The wood is then placed in oil, and 9/10 of it is submerged. Find the density of the wood, and of the oil.