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Fluids HW-2 (“Buoyancy”):
due______________
Read text section on Archimedes’ Principle & Buoyancy
Conceptual Questions
A block of wood has a steel ball glued to one surface. The block can be floated with the ball “high and dry” on
its top surface. When the block is inverted, and the ball immersed in water, does the volume of wood that is
submerged increase, decrease, or stay the same? Explain.
2. In the preceding problem, suppose the block of wood with the ball “high and dry” is floating in a tank of water.
When the block is inverted, does the water level in the tank increase, decrease, or stay the same? Explain.
3. A hydrometer, a device for measuring fluid density, is constructed as shown in Figure 1. If the hydrometer
samples fluid A, the small float inside the tube is submerged to the level A. When fluid B is sampled, the float is
submerged to level B. Which of these fluids is more dense?
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Figure 1
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Figure 2
Refer to Figure 2, in which a water-filled beaker contains a block of wood held submerged by a string fastened to
the bottom of the beaker. Suppose the beaker (with the wood tied to the bottom) is placed on a scale. At some
point the string breaks, and the wood rises to the surface where it floats. When the wood is floating, is the
reading on the scale the same, more than, or less than it was before? Explain.
An object’s density can be determined by first weighing it in air, then in water (provided the density of the
object is greater than the density of water, so that it is totally submerged when placed in water). Explain how
these two measurements can give the desired result.
In the movie Voyage to the Bottom of the Sea, the Earth is experiencing a rapid warming. In one scene, large
icebergs break up into small, car-sized chunks that drop downward through the water and bounce off the hull of
the submarine Seaview. Is this an example of good, bad, or ugly physics? Explain.
A person floats in a boat in a small swimming pool. Inside the boat with the person are some bricks. If the
person throws the bricks overboard into the pool, does the water level in the pool increase, decrease, or stay the
same?
A person floats in a boat in a small swimming pool. Inside the boat with the person are several blocks of wood.
Suppose the person now throws the blocks of wood into the pool. (a) Does the boat float higher, lower, or at the
same level relative to the water? Explain. (b) Does the water level in the pool increase, decrease, or stay the
same? Explain.
Why is it possible for people to float without effort in Utah’s Great Salt Lake?
One day, while snorkeling near the surface of a crystal-clear ocean, it occurs to you that you could go
considerably deeper by simply lengthening the snorkel tube. Unfortunately, this does not work well at all. Why?
Lead is more dense than aluminum. Is the buoyant force on a solid lead sphere more than, less than, or the same
as the buoyant force on a solid aluminum sphere of the same diameter? Does your answer depend on the fluid
that is causing the buoyant force? Explain.
A fish carrying a pebble in its mouth swims with a small, constant velocity in a small bowl. When the fish drops
the pebble to the bottom of the bowl, does the water level rise, fall, or stay the same? Explain.
On a planet in a different solar system, the acceleration of gravity is greater than it is on Earth. If you float in the
water on this planet, is it easier to float, harder, or the same as on Earth?
Since metal is more dense than water, how is it possible for a metal boat to float?
Problems on back…
Problems
A raft is 4.2 m wide and 6.5 m long. When a horse is loaded onto the raft, it sinks 2.7 cm deeper into the water.
What is the weight of the horse?
2. A 0.12-kg balloon is filled with helium (density  0179
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kg / m3 ). If the balloon is a sphere with a radius of 5.2
m, what is the maximum weight it can lift? (Don’t forget to include the weight of the helium.)
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3. A hot air balloon plus cargo has a mass of 327 kg and a volume of 687 m . The balloon is floating at a
constant height of 6.25 m above the ground. What is the density of the hot air in the balloon?
4. An air mattress is 2.2 m long, 0.65 m wide, and 13 cm deep. If the air mattress itself has a mass of 0.22 kg,
what is the maximum mass it can support in fresh water?
5. A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 20.0 N; when it is
completely immersed in water, the scale reads 17.7 N. What is (a) the volume and (b) the density of the block?
6. As in the previous problem, a solid block is suspended from a spring scale. If the reading on the scale when the
block is completely immersed in water is 25.0 N, and the reading when it is completely immersed in alcohol of
density 806 kg / m3 is 25.7 N, what is (a) the block’s volume and (b) its density?
7. A log floats in a river with one-fourth of its volume above the water. (a) What is the density of the log? (b) If
the river carries the log into the ocean, does the portion of the log above the water increase, decrease, or stay the
same? Explain.
8. A piece of lead has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.5 cm. If the puck is
placed in a mercury bath it floats. How deep below the surface of the mercury is the bottom of the lead puck?
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9. A wooden block with a density of 710 kg / m and a volume of 0.012 m is attached to the top of a vertical
spring whose force constant is k  540 N / m. Find the amount by which the spring is stretched or compressed
if it and the wooden block are (a) in air or (b) immersed in water. [The density of air may be neglected in part (a).]
10. A 1.25-kg wooden block has an iron ball of radius 1.22 cm glued to one side. (a) If the block floats in water
with the iron ball “high and dry,” what is the volume of wood that is submerged? (b) If the block is now
inverted, so that the iron ball is completely immersed, does the volume of wood that is submerged in water
increase, decrease, or remain the same? Explain. (c) Calculate the volume of wood that is submerged when the
block is in the inverted position.
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Answers
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Weight of horse = 7.22 kN
Weight of max’ load = 6,410 N
Density of hot air =  = 0.814 kg/m3
mmax = 185 kg
(a) V = 2.35 x 10–4 m3 (b)  = 8696 kg/m3
(a) V = 3.68 x 10–4 m3 (b)  = 7929 kg/m3
(a)  = 750 kg/m3 (b) It increases because the buoyant force is proportional to the density of the displaced
fluid and the density of salt water is greater than the density of fresh water.
8. hsubmerged = 2.08 cm
9. (a) The spring is compressed 0.155 m. (b) The spring is stretched 0.0632 m.
10. (a) V = 0.00131 m3
(b) The same total volume of water must be displaced in order to support the same total weight. Since the ball
now is submerged the volume of wood submerged will decrease.
(c) V = 0.00130 m3