The greatest ocean depths on Earth are found in the Marianas Trench near the Philippines. Calculate the pressure due to the ocean at the bottom of this trench, given its depth is 11.0 km and assuming the density of seawater is constant all the way down.

A glass tube contains mercury. What would be the height of the column of mercury which would create pressure equal to 1.00 atm?

A host pours the remnants of several bottles of wine into a jug after a party. The host then inserts a cork with a 2.00-cm diameter into the bottle, placing it in direct contact with the wine. The host is amazed when the host pounds the cork into place and the bottom of the jug (with a 14.0-cm diameter) breaks away. Calculate the extra force exerted against the bottom if he pounded the cork with a 120-N force.

A dam is used to hold back a river. The dam has a height $H=12 \mathrm{~m}$ and a width $W=10 \mathrm{~m}$. Assume that the density of the water is $\rho=1000 \mathrm{~kg} / \mathrm{m}^3$. (a) Determine the net force on the dam. (b) Why does the thickness of the dam increase with depth?

What led to the decline of the Mogul Empire?

What fraction of ice is submerged when it floats in freshwater, given the density of water at 0°C? is very close to 1000 kg/m³?

Assuming bicycle tires are perfectly flexible and support the weight of bicycle and rider by pressure alone, calculate the total area of the tires in contact with the ground if a bicycle and rider have a total mass of 80.0 kg, and the gauge pressure in the tires is

$$3.50 × 10^5 Pa.$$

What is the pressure drop due to the Bernoulli Effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)

Write an equation to represent each situation. Include a verbal model and define any variables you use. What number do you add to 17 to get 51?

A hollow cylinder is given a velocity of 5.0 m/s and rolls up an incline to a height of 1.0 m. If a hollow sphere of the same mass and radius is given the same initial velocity, how high does it roll up the incline?

Mercury is commonly supplied in flasks containing 34.5 kg (about 76 lb.). What is the volume in liters of this much mercury?

What is the average flow rate in cm³/s of gasoline to the engine of a car traveling at 100 km/h if it averages 10.0 km/L?

Consider the 12.0 kg motorcycle wheel. Assume it to be approximately an annular ring with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on its center stand, so that the wheel can spin freely. (a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? (b) What is the tangential acceleration of a point on the outer edge of the tire? (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?

The tip of a nail exerts tremendous pressure when hit by a hammer because it exerts a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00-mm diameter to create a pressure of

$$3.00 × 10^9 N/m^2?$$

(This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)