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physics
mechanics

Questions and Answers of Mechanics

(a) What is the average density of the sun? (b) What is the average density of a neutron star that has the same mass as the sun but a radius of only 20.0 km?
A hollow cylindrical copper pipe is 1.50 m long and has an outside diameter of 3.50 cm and an inside diameter of 2.50 cm. How much does it weigh?
Black Smokers black smokers are hot volcanic vents that emit smoke deep in the ocean floor. Many of them teem with exotic creatures, and some biologists think that life on earth may have begun around
Oceans on Mars scientists have found evidence that Mars may once have had an ocean 0.500 km deep. The acceleration due to gravity on Mars is 3.71 mls'. (a) What would be the gauge pressure at the
(a) Calculate the difference in blood pressure between the feet and top of the head for a person who is 1.65 m tall. (b) Consider a cylindrical segment of a blood vessel 2.00 cm long and 1.50 nun in
In intravenous feeding, a needle is inserted in a vein in the patient's arm and a tube leads from the needle to a reservoir of fluid (density 1050 kg/m') located at height h above the arm. The top of
A barrel contains a 0.120-m layer of oil floating on water that is 0.250 m deep. The density of the oil is 600 kg/m. (a) What is the gauge pressure at the oil-water interface? (b) What is the gauge
A 975-kg car has its tires each inflated to "32.0 pounds (a) What are the absolute and gauge pressures in these tires in lb/in.', Pa, and atm? (b) If the tires were perfectly round, could the tire
You are designing a diving bell to withstand the pressure of seawater at a depth of 250 m.(a) What is the gauge pressure at this depth? (You can ignore changes in the density of the water with
What gauge pressure must a pump produce to pump water from the bottom of the Grand Canyon (elevation 730 m) to Indian Gardens (elevation 1370 m)? Express your results in Pascal’s and in atmospheres.
The liquid in the open-tube manometer in Fig. 14.9a is mercury, y, = 3.00 cm, and y, = 7.00 cm. Atmospheric pressure is 980 millibars. (a) What is the absolute pressure at the bottom of the V-shaped
There is a maximum depth at which Figure 14.33 a diver can breathe through a snorkel tube Exercise 14.17. (Fig. 14.33) because as the depth increases, so does the pressure difference, which tends to
A tall cylinder with a cross-sectional area 12.0 cm3 is partially filled with mercury; the surface of the mercury is 5.00 cm above the bottom of the cylinder. Water is slowly poured in on top of the
A lake in the far north of the Yukon is covered with a 1.75-m-thick layer of ice. Find the absolute pressure and the gauge pressure at a depth of 2.50 m in the lake.
A closed container is partially filled with water. Initially, the air above the water is at atmospheric pressure (1.01 x 1(1' Pa) and the gauge pressure at the bottom of the water is 2500 Pa. Then
An electrical short cut off all power to a submersible diving vehicle when it is 30 m below the surface of the ocean the crew must push out a hatch of area 0.75 m2 and weight 300 N on the bottom to
Exploring Venus the surface pressure on Venus is 92 am, and the acceleration due to gravity there is 0.894g. In a future exploratory mission, an upright cylindrical tank of benzene is sealed at the
A cylindrical disk of wood Figure 14.34 Exercise 14.23 weighing 45.0 N and having a diameter of 30.0 cm floats on a cylinder of oil of density 0.850 g/cm3 (Fig. 14.34). The cylinder of oil is 75.0 cm
Hydraulic Lift L the hydraulic lift shown in Fig. 14.8, what must be the ratio of the diameter of the vessel at the car to the diameter of the vessel where the force F, is applied so that a 1520-kg
Hydraulic Lift II The piston of a hydraulic automobile lift is 0.30 m in diameter. What gauge pressure, in Pascal’s, is required to lift a car with a mass of 1200 kg? Also express this pressure in
A slab of ice floats on a freshwater lake. What minimum volume must the slab have for a 45.0-kg woman to be able to stand on it without getting her feet wet?
An ore sample weighs 17.50 N in air. When the sample is suspended by a light cord and totally innerved in water, the tension in the cord is 11.20 N. Find the total volume and the density of the
You are preparing some apparatus for a visit to a newly discovered planet Caasi having oceans of glycerin and a surface acceleration due to gravity of 4.15 rn/s2. If your apparatus floats in the
An object of average density P floats at the surface of a fluid of density Pf/Wd. (a) How must the two densities be related? (b) In view of the answer to part (a), how can steel ships float in water?
A hollow plastic sphere is held below the surface of a freshwater lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.650 m3 and the tension in the cord is 900 N. (a)
A cubical block of wood, 10.0cmon aside floats at the interface between oil and water with its lower surface 1.50 cm below the interface (Fig. 14.35). The density of the oil is 790 kg/m3.(a) What is
A solid aluminum ingot weighs 89 N in air. (a) What is its volume? (b) The ingot is suspended from a rope and totally inunersed in water. What is the tension in the rope (the apparent weight of the
A rock is suspended by a light string. When the rock is in air, the tension in the string is 39.2 N. When the rock is totally inunersed in water, the tension is 28.4 N. When the rock is totally
Water runs into a fountain, filling all the pipes, at a steady rate of 0.750 rn/S3. (a) How fast will it shoot out of a hole 4.50 cm in diameter? (b) At what speed will it shoot out if the diameter
A shower head has 20 circular openings, each with radius 1.0 mm. The shower head is connected to a pipe with radius 0.80 cm. If the speed of water in the pipe is 3.0 m/s, what is its speed as it
Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.070 m2, and the magnitude
Water is flowing in a pipe with a circular cross section but with varying cross-sectional area, and at all points the water completely fills the pipe. (a) At one point in the pipe the radius is 0.150
(a) Derive Eq. (14.12). (b) If the density increases why 1.50% from point 1 to point 2, what happens to the volume flow rate?
A sealed tank containing seawater to a height of 11.0 m also contains air above the water at a gauge pressure of 3.00 atm. Water flows out from the bottom through a small hole. How fast is this water
A small circular hole 6.00 nun in diameter is cut in the side of a large water tank, 14.0 m below the water level in the tank. The top of the tank is open to the air. Find (a) The speed of efflux of
What gauge pressure is required in the city water mains for a stream from a fire hose connected to the mains to reach a vertical height of 15.0 m? (Assume that the mains have a much larger diameter
At one point in a pipeline the water's speed is 3.00 mls and the gauge pressure is 5.00 X 104 Pa. Find the gauge pressure at a second point in the line, no m lower than the first, if the pipe
Lift on an Airplane Air streams horizontally past a small airplane's wings such that the speed is 70.0 m/s over the top surface and 60.0 m/s past the bottom surface. If the plane has a wing area of
A soft drink (mostly water) flows in a pipe at a beverage plant with a mass flow rate that would fill 220 0.355-L cans per minute. At point 2 in the pipe, the gauge pressure is 152 kPa and the
At a certain point in a horizontal pipeline, the water's speed is 2.50 m/s and the gauge pressure is 1.80 X 104 Pa. Find the gauge pressure at a second point in the line if the cross-sectional area
A golf course sprinkler system discharges water from a horizontal pipe at the rate of 7200 cm'/s. At one point in the pipe, where the radius is 4.00 cm, the water's absolute pressure is 240 X 10' Pa.
In a lecture demonstration, a professor pulls apart two hemispherical steel shells (diameter D) with ease using their attached handles. She then places them together, pumps out the air to an absolute
The deepest point known in any of the earth's oceans is in the Marianas Trench, 10.92 k/D deep. (a) Assuming water is incompressible, what is the pressure at this depth? Use the density of seawater.
A swimming pool is 5.0 m long, 4.0 m wide and 3.0 m deep. Compute the force exerted by the water against (a) The bottom; and (b) Either end. (Hint: Calculate the force on a thin, horizontal strip at
The upper edge of a gate in a dam runs along the water surface. The gate is 2.00 m high and 4.00 m wide and is hinged along a horizontal line through its center (Fig. 14.36). Calculate the torque
Force and Torque on a Dam. A dam has the shape of a rectangular solid. The side facing the lake has area A and height H. The surface of the freshwater lake behind the dam is at the top of the dam.
Submarines on Europa some scientists are eager to send a remote-
An astronaut is standing at the north pole of a newly discovered, spherically symmetric planet of radius R. In his hands be holds a container full of a liquid with mass m and volume V. At the surface
Ballooning on Mars it has been proposed that we could explore Mars using inflated balloons to hover just above the surface. "The buoyancy of the atmosphere would keep the balloon aloft. The density
The earth does not have a uniform density; it is most dense at its center and least dense at its surface. An approximation of its density is p(r) = A - Br, where A = 12,700kg/rri' and B = 1.50 X 10
In Example 12.10 (Section 12.6) we saw that inside a planet of uniform density (not a realistic assumption for the earth) the acceleration due to gravity increases uniformly with distance from the
A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height of the water column is
The Great Molasses Flood on the afternoon of January 15, 1919, an unusually warm day in Boston, a 27.4-m-high, 27.4-m-diameter cylindrical metal tank used for storing molasses ruptured. Molasses
An open barge has the dimensions shown in Fig. 14.38. If the barge is made out of 4.0-cm-thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in
A hot-air balloon has a volume of 2200 m3. The balloon fabric (the envelope) weighs 900 N. The basket with gear and full propane tanks weighs 1700 N. If the balloon can barely lift an additional 3200
Advertisements for a certain small car claim that it floats in water. (a) If the car's mass is 900 kg and its interior volume is 3.0 m, what fraction of the car is immersed when it floats? You can
A single ice cube with mass 9.70 g floats in a glass completely full of 420 cm3 of water. You can ignore the water's surface tension and its variation in density with temperature (as long as it
A piece of wood is 0.600 m long, 0.250 m wide and 0.080 m thick. Its density is 600 kg/m3. What volume of lead must be fastened underneath it to sink the wood in calm water so that its top is just
A hydrometer consists of a spherical bulb and a cylindrical stem with a Cross-sectional area of 0.400 cm' (see Fig. 14.13a). The total volume of bulb and stem is 13.2 cm'. When immersed in water, the
The densities of air, helium, and hydrogen (at p = 1.0 atm and T = 20°C) are 1.20 kg/m', 0.166 kg/m, and 0.0899 kg/m, respectively. (a) What is the volume in cubic meters displaced by a
SHM of a Floating Object An object with height h, mass M, and a uniform cross-sectional area A floats upright in a liquid with density p. (a) Calculate the vertical distance from the surface of the
A 950-kg cylindrical can buoy float vertically in salt water. The diameter of the buoy is 0.900 m. (a) Calculate the additional distance the buoy will sink when a 70.O-kg man stands on top. (Use the
A firehouse must be able to shoot water to the top of a building 35.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m'/s and shoots out of a round nozzle. (a) What
You drill a small hole in the side of a vertical cylindrical water tank that is standing on the ground with its top open to the air. (a) If the water level has a height H, at what height above the
A vertical cylindrical tank of cross-sectional area AI is open to the air at the top and contains water to a depth ho. A worker accidentally pokes a hole of area A2 in the bottom of the tank.(a)
A block of balsa wood placed in one scale pan of an equal-arm balance is exactly balanced by a 0.0950-kg brass mass in the other scale pan. Find the true mass of the balsa wood if its density is 150
Block A in Fig. 14.39 hangs by a cord from spring balance D and is submerged in a liquid C contained in beaker B. The mass of the beaker is 1.00 kg; the mass of the liquid is 1.80 kg. Balance D reads
A hunk of aluminum is completely covered with a gold shell to form an ingot of weight45.0 N. When you suspend the ingot from a spring balance and submerge the ingot in water, the balance reads 39.0
A plastic ball has radius 12.0 cm and floats in water with 16.0% of its volume submerged.(a) What force must you apply to the ball to hold it at rest totally below the surface of the water?(b) If you
The weight of a king's solid crown is w. When the crown is suspended by a light rope and completely immersed in water, the tension in the rope (the crown’s apparent weight) is fw. (a) Prove that
A piece of steel has a weight w, an apparent weight (see Problem 14.75) w water when completely immersed in water, and an apparent weight would when completely immersed in an unknown fluid. (a)
You cast some metal of density Pm in a mold, but you are worried that there might be cavities wit13in the casting. You measure the weight of the casting to be w, and the buoyant force when it is
A cubical block of wood 0.100 m on a side and with a density of 550 kg/m' floats in a jar of water. Oil with a density of 750 kg/cm3 is poured on the water until the top of the oil layer is 0.035 m
Dropping Anchor an iron ancl30r with mass 35.0 kg and density 7860 kg/m' lies on the deck of a small barge that has vertical sides and floats in a freshwater river. 1be area of the bottom of the
Assume that crude oil from a supertanker has density 750 kg/m'. The tanker runs aground on a sandbar. To reflect the tanker, its oil cargo is pumped out into steel barrels, each of which has a mass
A cubical block of density PB and with sides of length L floats in a liquid of greater density PL (a) What fraction of the block's volume is above the surface of the liquid? (b) The liquid is denser
A barge is in a rectangular lock on a freshwater river. 1be lock is 60.0 m long and 20.0 m wide, and the steel doors on each end are closed. With the burgee floating in the lock, a 2.50 X 10 N load
A U-shaped tube with a horizontal portion of length I (Fig. 14.40) contains a liquid. What is the reference in height between the liquid clowns in the vertical arms?(a) If the tube bas an
A cylindrical container of an incompressible liquid with density p rotates with constant angular speed w about its axis of symmetry, which we take to be the y-axis (Fig. 14.41). (a) Show that the
An incompressible fluid with density p is in a horizontal test rube of inner cross-sectional area. The test tube spins in a horizontal circle in an ultracentrifuge at an angular speed w.
Un-tethered helium balloons, floating in a car that has all the windows rolled up and outside air vents closed, move in the direction of the car's acceleration, but loose balloons filled with air
Water stands at a depth H in a large, open tank whose side walls are vertical (Fig. 14.42). A hole is made in one of the walls at a depth h below the water surface.(a) At what distance R from the
A cylindrical bucket, open at the top, is 25.0 cm high and 10.0 cm in diameter. A circular hole with a cross-sectional area 1.50 cm2 is cut in the center of the bottom of the bucket. Water flows into
Water flows steadily from an open tank as in Fig. 14.43. The elevation of point 1 is 10.0 m, and the elevation of points 2 and 3 is 2.00 m. 1be cross-sectional area at point 2 is 0.0480 m2; at point
In 1993 the radius of Hurricane Emily was about 350 km. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km. reached about 200 km/h. As air swirled in from the rim
Two very large open tanks A and F (Fig. 14.44) certain the same liquid. A horizontal pipe BCD, having a constriction at C and open to the air at D, leads out of the bottom of tank A, and a vertical
The horizontal pipe shown in Fig. 14.45 has a cross-sectional area of 40.0 cm3 at the wider portions and 10.0 cm2 at the constriction. Water is Hawing in the pipe, and the discharge from the pipe is
A liquid flowing from a vertical pipe has a definite shape as it flows from the pipe. To get the equation for this shape, assume that the liquid is in free fall once it leaves the pipe lust as it
A rock with mass m = 3.00 kg is suspended from the roof of an elevator by a light cord. The rock is totally immersed in a bucket of water that sits on the floor of the elevator, but the rock doesn't
Suppose a piece of Styrofoam, p = 180 kg/m3, is held completely submerged in water (Fig. 14.46).(a) What is the tension in the cord? Find this using Archimedes's principle.(b) Use P = Po + pgh to
A large tank with diameter D, open to the air contains water to a height H. A small hole with diameter d (d« D) is made at the base of the tank. Ignoring any effects of viscosity, calculate the time
A siphon, as shown in Fig. 14.47, is a convenient device for removing liquids from containers. To establish the How, the tube must be initially filled with fluid. Let the fluid have density p, and
The following passage is quoted from a letter. It is the practice of carpenters hereabouts, when laying out and leveling up the foundations of relatively long buildings, to use a garden hose filled
What types of natural phenomena could serve as time standards?
Suppose that the three fundamental standards of the metric system were length, density, and time rather than length, mass, and time. The standard of density in this system is to be defined as that of
The height of a horse is sometimes given in units of “hands.” Why is this poor standard of length?
Express the following quantities using the prefixes given in Table 1.4: (a) 3 X 10–4 m (b) 5 X 10–5 s (c) 72 X 102 g
Suppose that two quantities A and B have different dimensions. Determine which of the following arithmetic operations could be physically meaningful: (a) A + B (b) A/B(c) B – A (d) AB.
If an equation is dimensionally correct, does this mean that the equation must be true? If an equation is not dimensionally correct, does this mean that the equation cannot be true?
Do an order-of-magnitude calculation for an everyday situation you encounter. For example, how far do you walk or drive each day?

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