This document contains several buoyancy and density problems involving objects floating or sinking in fluids. The problems include: calculating the mass of a frog floating in a hemispherical pod; determining if shoveling gravel from a barge is a good decision; calculating the forces on a basketball submerged in water; ordering objects by density; and determining if blocks of materials will float or sink in various liquids. The document asks the reader to consider buoyancy scenarios involving a helium balloon of varying sizes and materials.

1. Buoyant force problems
High standard levels of thinking

2. Problem:
A Styrofoam slab has a thickness h
and a density ρobject. What is the
area of the slab, if it floats with its
top surface just awash in fresh water
when a swimmer of mass m is on
top?

3.  Problem:
 A frog in a hemispherical pod finds that he
just floats without sinking into a sea of
blue-green ooze with density 1.35
g/cm3. If the pod has radius 6 cm and
negligible mass, what is the mass of the
frog?

4.  Problem:
 A barge is carrying a load of gravel along
a river. It approaches a low bridge, and
the captain realizes that the top of the
pile of gravel is not going to make it
under the bridge. The captain orders the
crew to quickly shovel gravel from the pile
into the water. Is this a good decision?

5.  A standard basketball (mass = 624
grams; 24.3 cm in diameter) is held fully
under water. Calculate the buoyant force
and weight. When released, does the ball
sink to the bottom or float to the surface?
If it floats, what percentage of it is
sticking out of the water? If it sinks, what
is the normal force, FN with which it sits
on the bottom of the pool?

6.  Six objects (A-F) are in a liquid, as shown.
None of them are moving. Arrange them
in order of density, from lowest to
highest.

7.  A 10 cm3 block of paraffin (a type of wax)
weighs 0. 085 N. It is carefully submerged
in a container of gasoline. One cm3 of
gasoline weighs 0.0069 N.
 a. What is the weight of the gasoline
displaced by the paraffin?
 b. Will the block of paraffin sink or float in
the gasoline?

8.  A 15 cm3 block of gold weighs 2.8 N. It is
carefully submerged in a tank of mercury.
One cm3 of mercury weighs 0.13 N.
 a. Will the mercury be displaced by the
gold?
 b. Will the gold sink or float in the
mercury?

9. Based on density, explain whether the object
would float or sink in the following situations:
a. A block of solid paraffin (wax) in molasses.
b. A gold ring in molten platinum.
c. A piece of platinum in molten gold.
d. A drop of gasoline in mercury.
e. A drop of mercury in gasoline.

10. Imagine a spherical helium balloon with a radius of 2.0 meters.
(No seriously, imagine it…can you picture how large it would be?
What is the volume of the balloon?
1. Determine both the mass and the weight of the helium in
the balloon.
2. Determine both the mass and the weight of the air that
would be displaced by the balloon.
3. If the balloon was tethered to the ground by a string,
what would be the tension in the string? You can ignore the
weight of the balloon material (Draw a force diagram!)
4. If the person un-tethered the balloon and held onto the
string would he float away? Why or why not?
5. What radius would the helium balloon have to lift the
person off the ground?
6. In the previous question we ignored the material of a
balloon. If a helium balloon is made from Mylar which has an
AREA density of 0.01 g/cm2, what is the minimum radius a
helium balloon can have and still float (without supporting any
other weight). Remember, the surface area of a sphere is

11. Thanks…