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physics
mechanics

Questions and Answers of Mechanics

A 0.600-kg particle has a speed of 2.00 m/s at point A and kinetic energy of 7.50 J at point B. What is? (a) Its kinetic energy at A? (b) Its speed at B? (c) The total work done on the particle
A 0.300-kg ball has a speed of 15.0 m/s. (a) What is its kinetic energy? (b) What If its speed were doubled, what would be its kinetic energy?
A 3.00-kg object has a velocity (6.00i ─ 2.00j) m/s. (a) What is its kinetic energy at this time? (b) Find the total work done on the object if its velocity changes to (8.00i + 4.00j) m/s.
A 2 100-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 5.00 m before coming into contact with the top of the beam, and it drives the beam 12.0 cm farther into
A 4.00-kg particle is subject to a total force that varies with position as shown in Figure P7.13. The particle starts from rest at x = 0. What is its speed at? (a) x = 5.00 m, (b) x = 10.0
You can think of the work–kinetic energy theorem as a second theory of motion, parallel to Newton’s laws in describing how outside influences affect the motion of an object. In this problem,
In the neck of the picture tube of a certain black-and-white television set, an electron gun contains two charged metallic plates 2.80 cm apart. An electric force accelerates each electron in the
A 40.0-kg box initially at rest is pushed 5.00 m along a rough, horizontal floor with a constant applied horizontal force of 130 N. If the coefficient of friction between box and floor is 0.300, find
A 2.00-kg block is attached to a spring of force constant 500 N/m as in Figure 7.10. The block is pulled 5.00 cm to the right of equilibrium and released from rest. Find the speed of the block as it
A crate of mass 10.0 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The pulling force is 100 N parallel to the incline, which makes an angle of 20.0° with the horizontal. The
A 15.0-kg block is dragged over a rough, horizontal surface by a 70.0-N force acting at 20.0° above the horizontal. The block is displaced 5.00 m, and the coefficient of kinetic friction is 0.300.
A sled of mass m is given a kick on a frozen pond. The kick imparts to it an initial speed of 2.00 m/s. The coefficient of kinetic friction between sled and ice is 0.100. Use energy considerations to
The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during the
A 700-N Marine in basic training climbs a 10.0-m vertical rope at a constant speed in 8.00 s. What is his power output?
Make an order-of-magnitude estimate of the power a car engine contributes to speeding the car up to highway speed. For concreteness, consider your own car if you use one. In your solution state the
A skier of mass 70.0 kg is pulled up a slope by a motor driven cable. (a) How much work is required to pull him a distance of 60.0 m up a 30.0° slope (assumed frictionless) at a constant speed of
A 650-kg elevator starts from rest. It moves upward for 3.00 s with constant acceleration until it reaches its cruising speed of 1.75 m/s. (a) What is the average power of the elevator motor during
Calculate the mass of a solid iron sphere that has a diameter of 3.00 cm.
Find the order of magnitude of the density of the nucleus of an atom. What does this result suggest concerning the structure of matter? Model a nucleus as protons and neutrons closely packed
A 50.0-kg woman balances on one heel of a pair of high heeled shoes. If the heel is circular and has a radius of 0.500 cm, what pressure does she exert on the floor?
The four tires of an automobile are inflated to a gauge pressure of 200 kPa. Each tire has an area of 0.024 0 m2 in contact with the ground. Determine the weight of the automobile.
What is the total mass of the Earth’s atmosphere? (The radius of the Earth is 6.37 X 106 m, and atmospheric pressure at the surface is 1.013 X 105 N/m2.)
(a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 024 kg/m3 and that the air above exerts a pressure of 101.3 kPa. (b) At this depth, what force
The spring of the pressure gauge shown in Figure 14.2 has a force constant of 1 000 N/m, and the piston has a diameter of 2.00 cm. As the gauge is lowered into water, what change in depth causes the
The small piston of a hydraulic lift has a cross-sectional area of 3.00 cm2, and its large piston has a cross-sectional area of 200 cm2 (Figure 14.4). What force must be applied to the small piston
What must be the contact area between a suction cup (completely exhausted) and a ceiling if the cup is to support the weight of an 80.0-kg student?
(a) A very powerful vacuum cleaner has a hose 2.86 cm in diameter. With no nozzle on the hose, what is the weight of the heaviest brick that the cleaner can lift? (Fig P14.10a) (b) What If? A very
For the cellar of a new house, a hole is dug in the ground, with vertical sides going down 2.40 m. A concrete foundation wall is built all the way across the 9.60-m width of the excavation. This
A swimming pool has dimensions 30.0 m X 10.0 m and a flat bottom. When the pool is filled to a depth of 2.00 m with fresh water, what is the force caused by the water on the bottom? On each end? On
A sealed spherical shell of diameter d is rigidly attached to a cart, which is moving horizontally with an acceleration a as in Figure P14.13. The sphere is nearly filled with a luid having density p
The tank in Figure P14.14 is filled with water 2.00 m deep. At the bottom of one side wall is a rectangular hatch 1.00m high and 2.00 m wide, which is hinged at the top of the hatch. (a) Determine
The Abbott of Aberbrothock paid to have a bell moored to the Inchcape Rock to warn seamen of the hazard. Assume the bell was 3.00 m in diameter, cast from brass with a bulk modulus of 14.0 X 1010
Figure P14.16 shows Superman attempting to drink water through a very long straw. With his great strength he achieves maximum possible suction. The walls of the tubular straw do not collapse. (a)
Blaise Pascal duplicated Torricelli€™s barometer using a red Bordeaux wine, of density 984 kg/m3, as the working liquid (Fig. P14.17) What was the height h of the wine column for normal
Mercury is poured into a U-tube as in Figure P14.18a. The left arm of the tube has cross-sectional area A1 of 10.0 cm2, and the right arm has a cross-sectional area A2 of 5.00 cm2. One hundred grams
Normal atmospheric pressure is 1.013 X 105 Pa. The approach of a storm causes the height of a mercury barometer to drop by 20.0 mm from the normal height. What is the atmospheric pressure? (The
A U-tube of uniform cross-sectional area, open to the atmosphere, is partially filled with mercury. Water is then poured into both arms. If the equilibrium configuration of the tube is as shown in
The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities. It normally exerts a pressure of 100 to 200 mm of
(a) A light balloon is filled with 400 m3 of helium. At 0°C, the balloon can lift a payload of what mass? (b) What If? In Table 14.1, observe that the density of hydrogen is nearly half the
A Ping-Pong ball has a diameter of 3.80 cm and average density of 0.084 0 g/cm3. What force is required to hold it completely submerged under water?
A Styrofoam slab has thickness h and density ps. When a swimmer of mass m is resting on it, the slab floats in fresh water with its top at the same level as the water surface. Find the area of the
A piece of aluminum with mass 1.00 kg and density 2 700 kg/m3 is suspended from a string and then completely immersed in a container of water (Figure P14.25). Calculate the tension in the string (a)
The weight of a rectangular block of low-density material is 15.0 N. With a thin string, the center of the horizontal bottom face of the block is tied to the bottom of a beaker partly filled with
A 10.0-kg block of metal measuring 12.0 cm X 10.0 cm X 10.0 cm is suspended from a scale and immersed in water as in Figure P14.25b. The 12.0-cm dimension is vertical, and the top of the block is
To an order of magnitude, how many helium-filled toy balloons would be required to lift you? Because helium is an irreplaceable resource, develop a theoretical answer rather than an experimental
A cube of wood having an edge dimension of 20.0 cm and a density of 650 kg/m3 floats on water. (a) What is the distance from the horizontal top surface of the cube to the water level? (b) How
A spherical aluminum ball of mass 1.26 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water. Calculate (a) The outer radius of the ball and
Refer to Problem 31 and Figure P14.31. A hydrometer is to be constructed with a cylindrical floating rod. Nine fiduciary marks are to be placed along the rod to indicate densities of 0.98 g/cm3, 1.00
Determination of the density of a fluid has many important applications. A car battery contains sulfuric acid, for which density is a measure of concentration. For the battery to function properly,
How many cubic meters of helium are required to lift a balloon with a 400-kg payload to a height of 8 000 m? (Take PHe = 0.180 kg/m3.) Assume that the balloon maintains a constant volume and that the
A frog in a hemispherical pod (Fig P14.34) just floats without sinking into a sea of blue-green ooze with density 1.35 g/cm3. If the pod has radius 6.00 cm and negligible mass, what is the mass of
A plastic sphere floats in water with 50.0 percent of its volume submerged. This same sphere floats in glycerin with 40.0 percent of its volume submerged. Determine the densities of the glycerin and
A bathysphere used for deep-sea exploration has a radius of 1.50 m and a mass of 1.20 X 104 kg. To dive, this submarine takes on mass in the form of seawater. Determine the amount of mass the
The United States possesses the eight largest warships in the world—aircraft carriers of the Nimitz class—and are building two more. Suppose one of the ships bobs up to float 11.0 cm higher in
A horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 8.00 X 104 Pa and the pressure in the smaller pipe is
A large storage tank, open at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of flow from the leak is equal to 2.50 X
A village maintains a large tank with an open top, containing water for emergencies. The water can drain from the tank through a hose of diameter 6.60 cm. The hose ends with a nozzle of diameter 2.20
Water flows through a fire hose of diameter 6.35 cm at a rate of 0.0120 m3/s, the fire hose ends in a nozzle of inner diameter 2.20 cm. What is the speed with which the water exits the nozzle?
Water falls over a dam of height h with a mass flow rate of R, in units of kg/s. (a) Show that the power available from the water is P = Rgh where g is the free-fall acceleration. (b) Each
Figure P14.43 shows a stream of water in steady flow from a kitchen faucet. At the faucet the diameter of the stream is 0.960 cm. The stream fills a 125-cm3 container in 16.3 s. Find the diameter of
A legendary Dutch boy saved Holland by plugging a hole in a dike with his finger, which is 1.20 cm in diameter. If the hole was 2.00m below the surface of the North Sea (density 1 030 kg/m3), (a)
Through a pipe 15.0 cm in diameter, water is pumped from the Colorado River up to Grand Canyon Village, located on the rim of the canyon. The river is at an elevation of 564 m, and the village is at
Old Faithful Geyser in Yellowstone Park (Fig P14.46) erupts at approximately 1-h intervals, and the height of the water column reaches 40.0 m. (a) Model the rising stream as a series of separate
A Venturi tube may be used as a fluid flow meter (see Fig. 14.20). If the difference in pressure is P1 ─ P2 = 21.0 kPa, find the fluid flow rate in cubic meters per second, given that the
An airplane has a mass of 1.60 X 104 kg, and each wing has an area of 40.0 m2. During level flight, the pressure on the lower wing surface is 7.00 X 104 Pa. Determine the pressure on the upper wing
A Pitot tube can be used to determine the velocity of air flow by measuring the difference between the total pressure and the static pressure (Fig. P14.49). If the fluid in the tube is mercury,
An airplane is cruising at an altitude of 10 km. The pressure outside the craft is 0.287 atm; within the passenger compartment the pressure is 1.00 atm and the temperature is 20°C. A small leak
A siphon is used to drain water from a tank, as illustrated in Figure P14.51. The siphon has a uniform diameter. Assume steady flow without friction. (a) If the distance h = 1.00 m, find the speed
The Bernoulli effect can have important consequences for the design of buildings. For example, wind can blow around a skyscraper at remarkably high speed, creating low pressure. The higher
A hypodermic syringe contains a medicine with the density of water (Figure P14.53). The barrel of the syringe has a cross-sectional area A = 2.50 X 10─5 m2, and the needle has a cross-sectional
Figure P14.54 shows a water tank with a valve at the bottom. If this valve is opened, what is the maximum height attained by the water stream coming out of the right side of the tank? Assume that h =
A helium-filled balloon is tied to a 2.00-m-long, 0.050 0-kg uniform string. The balloon is spherical with a radius of 0.400 m. When released, it lifts a length h of string and then remains in
Water is forced out of a fire extinguisher by air pressure, as shown in Figure P14.56. How much gauge air pressure in the tank (above atmospheric) is required for the water jet to have a speed of
The true weight of an object can be measured in a vacuum, where buoyant forces are absent. An object of volume V is weighed in air on a balance with the use of weights of density P. If the density of
A wooden dowel has a diameter of 1.20 cm. It floats in water with 0.400 cm of its diameter above water (Fig. P14.58). Determine the density of the dowel.
A light spring of constant k = 90.0 N/m is attached vertically to a table (Fig. P14.59a). A 2.00-g balloon is filled with helium (density = 0.180 kg/m3) to a volume of 5.00 m3 and is then connected
Evangelista Torricelli was the first person to realize that we live at the bottom of an ocean of air. He correctly surmised that the pressure of our atmosphere is attributable to the weight of the
With reference to Figure 14.5, show that the total torque exerted by the water behind the dam about a horizontal axis through O is 1/6 pgwH3, show that the effective line of action of the total
In about 1657 Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres. Two teams of eight horses each could pull the hemispheres apart only on some trials, and
A 1.00-kg beaker containing 2.00 kg of oil (density = 916.0 kg/m3) rests on a scale. A 2.00-kg block of iron is suspended from a spring scale and completely submerged in the oil as in Figure P14.63.
A beaker of mass M beaker containing oil of mass moil (density = poil) rests on a scale. A block of iron of mass miron is suspended from a spring scale and completely submerged in the oil as in
In 1983, the United States began coining the cent piece out of copper-clad zinc rather than pure copper. The mass of the old copper penny is 3.083 g, while that of the new cent is 2.517 g. Calculate
A thin spherical shell of mass 4.00 kg and diameter 0.200 m is filled with helium (density = 0.180 kg/m3). It is then released from rest on the bottom of a pool of water that is 4.00 m deep. (a)
A uniform disk of mass 10.0 kg and radius 0.250 m spins at 300 rev/min on a low-friction axle. It must be brought to a stop in 1.00 min by a brake pad that makes contact with the disk at average
Show that the variation of atmospheric pressure with altitude is given by P = P0e─ay, where a = pog/P0, P0 is atmospheric pressure at some reference level y = 0, and p0 is the atmospheric
An incompressible, nonviscous fluid is initially at rest in the vertical portion of the pipe shown in Figure P14.69a, where L = 2.00 m. When the valve is opened, the fluid flows into the horizontal
The hull of an experimental boat is to be lifted above the water by a hydrofoil mounted below its keel, as shown in Figure P14.75. The hydrofoil has a shape like that of an airplane wing. Its area
A cube of ice whose edges measure 20.0 mm is floating in a glass of ice-cold water with one of its faces parallel to the water’s surface. (a) How far below the water surface is the bottom face of
A U-tube open at both ends is partially filled with water (Fig. P14.71a). Oil having a density of 750 kg/m3 is then poured into the right arm and forms a column L = 5.00 cm high (Fig. P14.71b) (a)
The water supply of a building is fed through a main pipe 6.00 cm in diameter. A 2.00-cm-diameter faucet tap, located 2.00 m above the main pipe, is observed to fill a 25.0-L container in 30.0 s.
The spirit-in-glass thermometer, invented in Florence, Italy, around 1654, consists of a tube of liquid (the spirit) containing a number of submerged glass spheres with slightly different masses
A woman is draining her fish tank by siphoning the water into an outdoor drain, as shown in Figure P14.74. The rectangular tank has footprint area A and depth h. The drain is located a distance d
A 1 000-kg roller coaster train is initially at the top of a rise, at point A. It then moves 135 ft, at an angle of 40.0° below the horizontal, to a lower point B. (a) Choose point B to be the
A 400-N child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy of the child–Earth system relative to the child’s lowest position when (a) The ropes
A person with a remote mountain cabin plans to install her own hydroelectric plant. A nearby stream is 3.00 m wide and 0.500 m deep. Water flows at 1.20 m/s over the brink of a waterfall 5.00 m high.
At 11:00 A.M. on September 7, 2001, more than 1 million British school children jumped up and down for one minute. The curriculum focus of the “Giant Jump” was on earthquakes, but it was
A bead slides without friction around a loop-the-loop (Fig. P8.5). The bead is released from a height h = 3.50R. (a) What is its speed at point A? (b) How large is the normal force on it if its
Dave Johnson, the bronze medalist at the 1992 Olympic decathlon in Barcelona, leaves the ground at the high jump with vertical velocity component 6.00 m/s. How far does his center of mass move up as
A glider of mass 0.150 kg moves on a horizontal frictionless air track. It is permanently attached to one end of a mass less horizontal spring, which has a force constant of 10.0 N/m both for
A loaded ore car has a mass of 950 kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0°

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