A 1-m-tall barrel is closed on top except for a thin pipe extending $5 \mathrm{~m}$ up from the top. When the barrel is filled with water up to the base of the pipe (1 meter deep), the water pressure on the bottom of the barrel is $10 \mathrm{kPa}$. What is the pressure on the bottom when water is added to fill the pipe to its top?

Calculate the water pressure at the base of a dam when the depth of water behind the dam is $100 \mathrm{~m}$.

On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is $20,000 \mathrm{~N}$. (b) What is the volume of the displaced air?

In lab you find that a 1 -kg rock suspended above water weighs $10 \mathrm{~N}$. When the rock is suspended beneath the surface of the water, the scale reads $8 \mathrm{~N}$.

The top floor of a building is 50 m above the basement. Calculate how much greater the water pressure is in the basement compared with the pressure on the top floor.

Calculate the water pressure at the base of Hoover Dam. The depth of water behind the dam is 220 m. (Neglect the pressure due to the atmosphere.)

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

Construct a table of all the possible combinations of numbers that can come up when you throw two dice. Your friend says, "Yes, I know that 7 is the most likely total number when two dice are thrown. But why 7?" Based on your table, answer your friend, and explain that, in thermodynamics, the situations that are likely to be observed are those that can be formed in the greatest number of ways.

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.

What will be the final temperature of 100 g of

$$20^\circ C$$

water when 100 g of

$$40^\circ$$

iron nails are submerged in it? (The specific heat of iron is

$$0.12 cal/gC^\circ.)$$

A hot-air balloon is accelerating upward under the influence of two forces, its weight and the buoyant force. For simplicity, consider the weight to be only that of the hot air within the balloon, thus ignoring the balloon fabric and the basket. The hot air inside the balloon has a density of $\rho_{\mathrm { hot air }}=0.93 \mathrm{kg} / \mathrm{m}^{3}$, and the density of the cool air outside is $\rho_{\mathrm { cool air }}=1.29 \mathrm{kg} / \mathrm{m}^{3}$. What is the acceleration of the rising 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.)

A penny on its side moving at speed v slides off the horizontal surface of a table a vertical distance y from the floor. (a) Show that the penny lands a distance $v \sqrt{2 y / g}$ from the base of the coffee table. (b) If the speed is 3.5 m/s and the coffee table is 0.4 m tall, show that the distance the coin lands from the base of the table is 1.0 m. (Use g=9.8 m/s2.)

A ball is thrown horizontally from a cliff at a speed of 10 m/s. Show that its speed one second later is about 14 m/s.