Angular Momentum, Statics, & Fluids
1. Fluids At one point in a pipeline the water’s speed is 3.00 m/s and the gauge pressure is
5.00 × 104 Pa. Find the gauge pressure at a second point in the line, 11.0 m lower than the
first, if the pipe diameter at the second point is twice that at the first.
2. Fluids A narrow, U–shaped glass tube with open ends is filled with 25.0
cm of oil (of specific gravity 0.80) and 25.0 cm of water on opposite sides,
with a barrier separating the liquids.
(a) Assume that the two liquids do not mix, and find the final heights of
the columns of liquid in each side of the tube after the barrier is removed.
(b) For the following cases, arrive at your answer by simple physical
reasoning, not by calculations: (i) What would be the height on each side
if the oil and water had equal densities? (ii) What would the heights be if
the oil’s density were much less than that of water?
3. Fluids You drill a small hole in the side of a vertical cylindrical water tank that is standing
on the ground with its top open to the air.
(a) If the water level has a height H, at what height above the base should you drill the hole
for the water to reach its greatest distance from the base of the cylinder when it hits the
ground?
(b) What is the greatest distance the water will reach?
4. Fluids A cubical block of density ρB and with sides of length L floats in a liquid of greater
density ρL .
(a) What fraction of the block’s volume is above the surface of the liquid?
(b) The liquid is denser than water (density ρW ) and does not mix with it. If water is poured
on the surface of the liquid, how deep must the water layer be so that the water surface just
rises to the top of the block? Express your answer in terms of L, ρB , ρL , and ρW .
(c) Find the depth of the water layer in part (b) if the liquid is mercury, the block is made of
iron, and the side length is 10.0 cm.
5. Fluids A rock with mass m = 3.00 kg is suspended from the roof of an elevator by a light
cord. The rock is totally immersed in a bucket of water that sits on the floor of the elevator,
but the rock doesn’t touch the bottom or sides of the bucket.
(a) When the elevator is at rest, the tension in the cord is 21.0 N. Calculate the volume of the
rock.
(b) Derive an expression for the tension in the cord when the elevator is accelerating
upward with an acceleration of magnitude a. Calculate the tension when a = 2.50 m/s2
upward.
(c) Derive an expression for the tension in the cord when the elevator is accelerating
downward with an acceleration of magnitude a. Calculate the tension when a = 2.50 m/s2
downward.
(d) What is the tension when the elevator is in free fall with a downward acceleration equal
to g?
