1. Astronauts and cosmonauts have used pressurized spacesuits to explore

the low-pressure regions of space. The pressure inside one of these suits

must be close to that of Earth’s atmosphere at sea level so that the space

explorer may be safe and comfortable. The pressure on the outside of the

suit is a fraction of 1.0 Pa. Clearly, pressurized suits are made of extremely

sturdy material that can tolerate the stress from these pressure

differences. If the average interior surface area of a pressurized spacesuit

is 3.3 m² , what is the force exerted on the suit’s material? Assume that the

pressure outside the suit is zero and that the pressure inside the suit is

1.01 x10⁵ Pa.

2. A strange idea to control volcanic eruptions is developed by a daydreaming

 engineer. The engineer imagines a giant piston that fits into the

volcano’s shaft, which leads from Earth’s surface down to the magma

chamber. The piston controls an eruption by exerting pressure that is

equal to or greater than the pressure of the hot gases, ash, and magma

that rise from the magma chamber through the shaft. The engineer assumes

that the pressure of the volcanic material is 4.0 x10¹¹ Pa, which is

the pressure in Earth’s interior. If the material rises into a cylindrical

shaft with a radius of 50.0 m, what force is needed on the other side of

the piston to balance the pressure of the volcanic material?

3. The largest goat ever grown on a farm had a mass of 181 kg; on the other

hand, the smallest “pygmy” goats have a mass of only about 16 kg. Imagine

an agricultural show in which a large goat with a mass of 181 kg

exerts a pressure on a hydraulic-lift piston that is equal to the pressure

exerted by three pygmy goats, each of which has a mass of 16.0 kg. The

area of the piston on which the large goat stands is 1.8 m² . What is the

area of the piston on which the pygmy goats stand?

4. The greatest load ever raised was the offshore Ekofisk complex in the

North Sea. The complex, which had a mass of 4.0 x10 7 kg, was raised

6.5 m by more than 100 hydraulic jacks. Imagine that his load could have

been raised using a single huge hydraulic lift. If the load had been placed

on the large piston and a force of 1.2 x10⁴ N had been applied to the

small piston, which had an area of 5.0 m² , what must the large piston’s

area have been?

5. The pressure that can exist in the interior of a star due to the weight of

the outer layers of hot gas is typically several hundred billion times

greater than the pressure exerted on Earth’s surface by Earth’s atmosphere.

Suppose a pressure equal to that estimated for the sun’s interior

(2.0 x10¹⁶ Pa) acts on a spherical surface within a star. If a force of

1.02 N x10³¹ N produces this pressure, what is the area of the surface?

What is the sphere’s radius r? (Recall that a sphere’s surface area equals

4 p ² .)

6. The eye of a giant squid can be more than 35 cm in diameter—the

largest eye of any animal. Giant squid also live at depths greater than a

mile below the ocean’s surface. At a depth of 2 km, the outer half of a

giant squid’s eye is acted on by an external force of 4.6 x10⁶ N. Assuming

the squid’s eye has a diameter of 38 cm, what is the pressure on the

eye? (Hint: Treat the eye as a sphere.)

7. The largest tires in the world, which are used for certain huge dump

trucks, have diameters of about 3.50 m. Suppose one of these tires has a

volume of 5.25 m³ and a surface area of 26.3 m² . If a force of 1.58 x10⁷ N

acts on the inner area of the tire, what is the absolute pressure inside the

tire? What is the gauge pressure on the tire’s surface?

Answers