Name: ________________
Physics – Worksheet: Pressure and Buoyancy and Archimedes's Principle
𝐹
𝑃2 = 𝑃1 + 𝜌𝑔ℎ
𝑃=
𝑃𝑎𝑖𝑟 = 1.01 × 105 𝑃𝑎
𝜌𝑎𝑖𝑟 = 1.2 𝑘𝑔/𝑚3
𝐴
𝐹𝐵𝑜𝑢𝑦𝑎𝑛𝑡 = 𝑚𝑓𝑙 𝑔
𝜌=
𝑚
𝑉
𝜌𝑤𝑎𝑡𝑒𝑟 = 1000 𝑘𝑔/𝑚3
𝜌𝑔𝑜𝑙𝑑 = 1.93 × 103 𝑘𝑔/𝑚3
1.
A typical pool is 3.0 m deep. What is the water pressure at the bottom of the pool?
2.
Pressure is often measured in units of atmospheres (atm). To what depth must you swim to experience 3.0 atm
pressure?
3.
The small piston of a hydraulic lift has an area of 0.10 m2; the large piston has an area of 1.00 m2.
a. If a maximum force of 100 N may be applied to the small piston, what is the maximum weight of the vehicle
resting on the large piston that may be lifted?
4.
𝐹𝑜𝑢𝑡
b.
What is the total mechanical advantage gained? (𝑀𝐴 =
c.
In physics, it is always true that “you can’t get something for nothing.” In gaining this mechanical advantage,
what must be given up?
𝐹𝑖𝑛
)
King Hieron gave his artisans gold to make him a crown. After months of work, the artisans present the crown to the
king and the king pays them for their work. However, the king starts to suspect that he has been cheated by his artisans,
that they have stolen some of his gold and replaced it with silver. The king could cut his crown in two to see if the core
of the crown really is gold, but in so doing he would destroy the crown, which would be a shame if the artisans did not
cheat him. You, Archimedes, are given the task of determining whether the king has been cheated or not –and you are
not allowed to destroy the crown in the process.
a. As measured with a spring scale, the weight of the crown in air is 4.900 N. The weight of the crown when
submerged in water is 4.290 N. Draw pictures of the crown being weighed in air and in water and draw all
forces acting upon the crown.
b.
The buoyant force of the water is the weight of the displaced water. The difference between the two weights
will equal the buoyant force: Determine the volume of the crown.
c.
Determine the mass of the crown.
d.
Determine the density of the crown.
e.
Was the king cheated? Explain your answer.
f.
In most calculations, the buoyant force of air is neglected. Was it proper to neglect the buoyant force of air in
the calculation above? Explain your answer.