91Ó°ÊÓ

Hot air is less dense than cold air. Could a hot-air balloon be flown on the Moon, where there is no atmosphere?

(a) No, there is no cold air to displace, so no buoyancy force would exist.

(b) Yes, warm air always rises, especially in a weak gravitational field like that of the Moon.

(c) Yes, but the balloon would have to be filled with helium instead of hot air.

(III) The Earth is not a uniform sphere, but has regions of varying density. Consider a simple model of the Earth divided into three regions—inner core, outer core, and mantle. Each region is taken to have a unique constant density (the average density of that region in the real Earth):

(a) Use this model to predict the average density of the entire Earth. (b) If the radius of the Earth is 6380 km and its mass is 5.98 × 10²⁴Kg, determine the actual average density of the Earth and compare it (as a percent difference) with the one you determined in (a).

Why don’t ships made of the iron sink?

How high should the pressure head be if water is to come from a faucet at a speed of \({\bf{9}}{\bf{.2\;m/}}{{\bf{s}}^{\bf{2}}}\) Ignore viscosity.

A bicycle pump is used to inflate a tire. The initial tire (gauge) pressure is 210 kPa (30 psi). At the end of the pumping process, the final pressure is 310 kPa (45 psi). If the diameter of the plunger in the cylinder of the pump is 2.5 cm, what is the range of the force that needs to be applied to the pump handle from beginning to end?

Question: A simple model (Fig. 10–56) considers a continent as a block (density\( \approx {\bf{2800}}\;{\bf{kg/}}{{\bf{m}}^{\bf{3}}}\)) floating in the mantle rock around it (density\( \approx {\bf{3300}}\;{\bf{kg/}}{{\bf{m}}^{\bf{3}}}\)). Assuming the continent is 35 km thick (the average thickness of the Earth’s continental crust), estimate the height of the continent above the surrounding mantle rock.

Figure 10-56

A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.5 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of 35° above the horizontal and covers a radius of 6.0 m. (a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.) (b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second? (c) How fast is the water flowing inside the 1.9-cm-diameter pipe?

An object that can float in both water and in oil (whose density is less than that ofwater) experiences a buoyant force that is

(a) Greater when it is floating in oil than when floating in water.

(b) Greater when it is floating in water than when floating in oil.

(c) The same when it is floating in water or in oil.

(I) Estimate the pressure needed to raise a column of water to the same height as a 46-m-tall pine tree.