A dike in Holland springs a leak through a hole of area $1 \mathrm{~cm}^2$ at a depth of $2 \mathrm{~m}$ below the water surface. How much force must a boy apply to the hole with his thumb to stop the leak? Could he do it?

A certain spring stretches 4 cm when a load of 20 N is suspended from it. How much will the spring stretch if $45 \mathrm{~N}$ is suspended from it (and it doesn't reach its elastic limit)?

A 12-kg piece of metal displaces 2 L of water when submerged. Show that its density is 6000 kg/m3. How does this compare with the density of water?

Calculate the average force per nail when Sarah. who weighs 120 pounds, lies on a bed of nails and is supported by 600 nails.

The weight of the atmosphere above 1 square meter of Earth’s surface is 100 000 newtons. If the density of the atmosphere were a constant

$$1.2 kg/m^3,$$

calculate where the top of the atmosphere would be.

Consider these three animals: A. dog, B. horse, and C. elephant. Rank them, from highest to lowest, for their a. surface areas. b. masses. c. weights. d. volumes. e. surface area per weight.

Consider an airplane with a total wing surface of $100$ square meters. At a certain speed the difference in the air pressure below and above the wings is $4 \%$ of atmospheric pressure. Show that the lift on the airplane is $400,000 \mathrm{~N}$.

A mountain-climber of mass 80 kg ponders the idea of attaching a helium-filled balloon to himself to effectively reduce his weight by 25% when he climbs. He wonders what the approximate size of such a balloon would be. Hearing of your physics skills, he asks you. Share with him your calculations that show the volume of the balloon should be about 17 m3 (slightly more than 3 m in diameter for a spherical balloon).

Estimate the buoyant force that air exerts on you. (Estimate your volume by knowing your weight and by assuming that your weight density is a bit less than that of water.)

Suppose you balance a 2-kg ball on the tip of your finger, which has an area of 1 cm2. Show that the pressure on your finger is 20 N/cm2, or is 200 kPa.

In a hydraulic system, why is the force exerted on a small piston multiplied when it acts on a larger piston?

In lab you submerge $100 {g}$ of $40^{\circ} {C}$ nails in $100 {g}$ of $20^{\circ} {C}$ water. (The specific heat of iron is $0.12 {cal} / {g} \cdot{ }^{\circ} {C}$.) Equate the heat gained by the water to the heat lost by the nails and show that the final temperature of the water becomes $22.1^{\circ} {C}$.

A power station with an efficiency of $0.4$ generates $10^8 \mathrm{~W}$ of electric power and dissipates $1.5 \times 10^8 \mathrm{~J}$ of heat energy each second to the cooling water that flows through it, which increases its temperature by 3 Celsius degrees. Knowing that the specific heat of water in SI units is $4184 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$, show that $12,000 \mathrm{~kg}$ of warmed water flows through the plant each second.

Wally Whacko claims to have invented a heat engine that will revolutionize industry. It runs between a hot source at