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physics
mechanics
Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions
Figure represents an insect caught at the midpoint of a spider-web thread. The thread breaks under a stress of 8.20 x 108 N/m2 and a strain of 2.00. Initially, it was horizontal and had a length of 2.00 cm and a cross sectional area of 8.00 x 10-12 m2. As the thread was stretched under the weight
Figure is an overhead view of a rigid rod that turns about a vertical axle until the identical rubber stoppers A and B arc forced against rigid walls at distances rA = 7.0 cm and rB = 4.0 cm from the axle. Initially the stoppers touch the walls without being compressed. Then force F of magnitude
Figure shows a uniform ramp between two buildings that allows for motion between the buildings due to strong winds. At its left end, it is hinged to the building wall; at its right end, it has a roller that can roll along the building wall. There is no vertical force on the roller from the
In Figure a 10 kg sphere is supported on a frictionless plane inclined at angle θ = 45? from the horizontal. Angle Φ is 25. Calculate the tension in the cable.
In Figure a uniform 40.0 kg beam is centered over two rollers. Vertical lines across the beam mark off equal lengths. Two of the lines are centered over the rollers; a 10.0 kg package of tamales is centered over roller B. What are the magnitudes of the forces on the beam from? (a) Roller A and (b)
In Figure, an 817 kg construction bucket is suspended by a cable A that is attached at O to two other cables B and C, making angles θ1 = 51.0? and θ2 = 66.0? with the horizontal. Find the tensions in (a) Cable A, (b) Cable B, and (c) Cable C.
In Figure a package of mass m hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at angle θ = 40? with the horizontal; cord to is at angle θ. (a) For what value of θ is the tension in cord 2 minimized? (b) In terms of mg, what is the minimum
The force F in Figure keeps the 6.40 kg block and the pulleys in equilibrium. The pulleys have negligible mass and friction. Calculate the tension T in the uppercable.
In Figure two identical, form, and frictionless spheres, each of mass m, rest in a rigid rectangular container. A line connecting their centers is at 45? to the horizontal. Find the magnitudes of the forces on the spheres from (a) The bottom of the container, (b) The left side of the container, (c)
Four bricks of length L, identical and uniform, are stacked on top of one another (Figure) in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of (a) a1 (b) a2 (c) a3 (d) a4, and (e) h, such that the stack is in-equilibrium.
After a fall, a 95 kg rock climber finds himself dangling from the end of a rope that had been 15 m long and 9.6 mm in diameter but has stretched by 2.8 cm. For the rope, calculate(a) The strain,(b) The stress, and(c) The Young's modulus.
In Figure a rectangular slab of slate rests on a bedrock surface inclined at angle θ = 26. The slab has length L = 43 m, thickness Z = 2.5 m, and width 17 = 12 m, and 1.0 cm3 of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.39. (a) Calculate the component
A uniform ladder whose length is 5.0 m and whose weight is 400 N leans against a frictionless vertical wall. The coefficient of static friction between the level ground and the foot of the ladder is 0.46. What is the greatest distance the foot of the ladder can be placed from the base of the wall
In Figure block A (mass 10 kg) is in equilibrium, but it would slip if block B (mass 5.0 kg) were any heavier. For angle θ = 30?, what is the coefficient of static friction between block A and the surface below it?
A mine elevator is supported by a single steel cable 2.5 cm in diameter. The total mass of the elevator cage and occupants is 670 kg. By how much does the cable stretch when the elevator hangs by?(a) 12 m of cable and(b) 362 m of cable (Neglect the mass of the cable.)
In Figure a uniform rod of mass m is hinged to a building at its lower end, while its upper end is held in place by a rope attached to the wall. If angle θ1 = 60°, what value must angle θ2 have so that the tension in the rope is equal to mg/2?
A73 kg man stands on a level bridge of length L. He is at distance L/4 from one end. The bridge is uniform and weighs 2.7kN what are the magnitudes of the vertical forces on the bridge from its supports at?(a) The end farther from him and(b) The nearer end?
A makeshift swing is constructed by making a loop in one end of a rope and tying the other end to a tree limb. A child is sitting in the loop with the rope hanging vertically when the child's father pulls on the child with a horizontal force and displaces the child to one side. Just before the
The system in Figure is in equilibrium. The angles are θ1 = 60? and 02 = 20?, and the ball has mass M = 2.0 kg. What is the tension in? (a) String ab and (b) String bc?
Figure shows a stationary arrangement of two crayon boxes and three cords. Box A has a mass of 11.0 kg and is on a ramp at angle θ = 30.0?; box B has a mass of 7.00 kg and hangs on a cord. The cord connected to box A is parallel to the ramp, which is frictionless. (a) What is the tension in the
A construction worker attempts to lift a uniform beam off the floor and raise it to a vertical position. The beam is 2.50 m long and weighs 500 N. At a certain instant the worker holds the beam momentarily at rest with one end at distance d = 1.50 m above the floor, as shown in Figure by exerting a
A solid copper cube has an edge length of 85.5 cm. How much stress must be applied to the cube to reduce the edge length to 85.0 cm? The bulk modulus of copper is 1.4 x 1011 N/m2.
A uniform beam is 5.0 m long and has a mass of 53 kg. In Figure the beam is supported in a horizontal position by a hinge and a cable, with angle θ = 60?. In unit-vector notation, what is the force on the beam from the hinge?
In Figure a uniform beam with a weight of 60 N and a length of 3.2m is hinged at its lower end, and a horizontal force F of magnitude 50 N acts at its upper end. The beam is held vertical by a cable that makes angle θ = 25? with the ground and is attached to the beam at height h = 2.0 m. What
In Figure a uniform beam of length 12.0 m is supported by a horizontal cable and a hinge at angle θ = 50.0?. The tension in the cable is 400 N. In unit-vector notation, what are?. (a) The gravitational force on the beam and. (b) The force on the beam from the hinge?.
Four bricks of length L, identical and uniform, are stacked on a table in two ways, as shown in Figure. We seek to maximize the overhang distance h in both arrangements. Find the optimum distances a1, a2, b1 and b2, and calculate h for the twoarrangements.
A pan balance is made up of a rigid, massless rod with a hanging pan attached at each end. The rod is supported at and frees to rotate about a point not at its center. It is balanced by unequal masses placed in the two pans. When an unknown mass m is placed in the left pan, it is balanced by a mass
The rigid square frame in Figure consists of the four side bars AB, BC, CD, and DA plus two diagonal bars AC and BD, which pass each other freely at E. By means of the turnbuckle G, bar AB is put under tension, as if its ends were subject to horizontal, outward forces T of magnitude 535 N. (a)
A gymnast with mass 46.0 kg stands on the end of a uniform balance beam as shown in Figure. The beam is 5.00 m long and has a mass of 250 kg (excluding the mass of the two supports). Each support is 0.540 m from its end of the beam. In unit-vector notation, what are the forces on the beam due
Figure shows a 300 kg cylinder that is horizontal. Three steel wires support the cylinder from a ceiling. Wires 1 and 3 are attached at the ends of the cylinder, and wire 2 is attached at the center. The wires each have a cross-sectional area of 2.00 x 10-6 m2. Initially (before the cylinder was
Figure shows details of a finger in the crimp hold of the climber in Figure. A tendon that runs from muscles in the forearm is attached to the far bone in the finger. Along the way, the tendon runs through several guiding sheaths called pulleys. The A2 pulley is attached to the first finger bone;
A uniform cube of side length 8.0 cm rests on a horizontal floor. The coefficient of static friction between cube and floor is μ. A horizontal pull P is applied perpendicular to one of the vertical faces of the cube, at a distance 1.0 cm above the floor on the vertical midline of the cube face.
A cylindrical aluminum rod, with an initial length of 0.8000 m and radius 1000.0 cm, is clamped in place at one end and then stretched by a machine pulling parallel to its length at its other end. Assuming that the rod's density (mass per unit volume) does not charge, find the force magnitude that
A beam of length L is carried by three men, one man at one end and the other two supporting the beam between them on a crosspiece placed so that the load of the beam is equally divided among the three men. How far from the beam's free end is the crosspiece placed? (Neglect the mass of the
A trap door in a ceiling is 0.91 m square, has a mass of 11 kg, and is hinged along one side, with a catch at the opposite side. If the center of gravity of the door is 1.0 cm toward the hinged side from the door's center, what are the magnitudes of the forces exerted by the door on?(a) The catch
A uniform ladder is 10 m long and weighs 200 N. In Figure the ladder leans against a vertical, frictionless wall at height h = 8.0 m above the ground. A horizontal force F is applied to the ladder at distance d = 2.0 m from its base (measured along the ladder). (a) If force magnitude F = 50 N, what
If the (square) beam in Figure is of Douglas fir, what must be its thickness to keep the compressive stress on it to of its ultimate strength?
Find the pressure increase in the fluid in a syringe when a nurse applies a force of 42 N to the syringe's circular piston, which has a radius of 1.1 cm.
Three liquids that will not mix are poured into a cylindrical container. The volumes and densities of the liquids are 0.50 L, 2.6 g/cm3; 0.25 L, 1.0 g/cm3; and 0.40 L, 0.80 g/cm3.What are the force on the bottom of the container due to these liquids? One liter = 1L = 1000 cm3. (Ignore the
An office window has dimensions 3.4 m by 2.1 m. As a result of the passage of a storm, the outside air pressure drops to 0.96 atm, but inside the pressure is held at 1.0 atm. What net force pushes out on the window?
You inflate the front tires on your cat to 28 psi. Later, you measure your blood pressure, obtaining a reading of 120/80, the readings being in mm Hg. In metric countries (which is to say, most of the world), these pressures are customarily reported in kilopascals (kPa). In kilopascals, what
A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed, a fish has a density of 1.08 g/cm3. To what fraction of its expanded body volume must the fish
A partially evacuated airtight container has a tight fitting lid of surface area 77 m2 and negligible mass. If the force required to remove the lid is 480 N and the atmospheric pressure is 1.0 x 105 Pa, what is the internal air pressure?
In 1654 Otto von Guericke, inventor of the air pump gave a demonstration before the noblemen of the Holy Roman Empire in which two teams of eight horses could not pull apart two evacuated brass hemispheres. (a) Assuming the hemispheres have (strong) thin walls, so that R in Figure may be considered
Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person of height 1.83 m. The density of blood is 1.06 x 103 kg/m3.
At a depth of 10.9 km, the Challenger Deep in the Marianas Trench of the Pacific Ocean is the deepest site in any ocean. Yet, in 1960, Donald Walsh and Jacques Piccard reached the Challenger Deep in the bathyscaph Trieste. Assuming that seawater has a uniform density of 1024 kg/m3, approximate the
The maximum depth dmax that a diver can snorkel is set by the density of the water and the fact that human lungs can function against a maximum pressure difference (between inside and outside the chest cavity) of 0.050 atm. what is the difference in dmax for fresh water and the water of the Dead
Crew members attempt to escape from a damaged submarine 100 m below the surface. What force must be applied to a pop-out hatch, which is 1.2m by 0.60 m, to push it out at that depth? Assume that the density of the ocean water is 1024 kg/m3 and the internal air pressure is at 1.00 atm.
The plastic tube in Figure has a cross-sectional area of 5.00 cm2 .The tube is filled with water until the short arm (of length d = 0.800 m) is full. Then the short arm is sealed and more water is gradually poured into the long arm. If the seal will pop off when the force on it exceeds 9.80 N, what
What gauge pressure must a machine produce in order to suck mud of density 1800 kg/m3 up a tube by a height of 1.5 m?
The bends during flight anyone who scuba dives is advised not to fly within the next 24 h because the air mixture for diving can introduce nitrogen to the bloodstream. Without allowing the nitrogen to come out of solution slowly, any sudden air-pressure reduction (such as during airplane ascent)
Giraffe bending to drink in a giraffe with its head 2.0 m above its heart, and its heart 2.0 m above its feet, the (hydrostatic) gauge pressure in the blood at its heart is 250 torr. Assume that the giraffe stands upright and the blood density is 1.06 x 103 kg/m3. In torr (or mm Hg), find the
In Figure an open tube of length L = 1.8 m and cross-sectional area A = 4.6 cm2 is fixed to the top of a cylindrical barrel of diameter D = 1.2 m and height H = 1.8 m. The barrel and tube are filled with water (to the top of the tube). Calculate the ratio of the hydrostatic force on the bottom of
Blood pressure in Argentinosaurus.(a) If this long-necked, gigantic sauropod had a head height of 21 m and a heart height of 9.0 m, what (hydrostatic) gauge pressure in its blood was required at the heart such that the blood pressure at the brain was 80 torr (just enough to perfuse the brain with
Snorkeling by humans and elephants when a person snorkels, the lungs are connected directly to the atmosphere through the snorkel tube and thus are at atmospheric pressure. In atmospheres, what is the difference Δp between this internal air pressure and the water pressure against the body if the
Two identical cylindrical vessels with their bases at the same level each contain a liquid of density 1.30 x 103 kg/m3. The area of each base is 4.00 cm2, but in one vessel the liquid height is 0.854m and in the other it is 1.560m. Find the work done by the gravitational force in equalizing the
When a pilot takes a tight turn at high speed in a modern fighter airplane, the blood pressure at the brain level decreases blood no longer perfuse the brain, and the blood in the brain drains. If the heart maintains the (hydrostatic) gauge pressure in the aorta at 120 torr (or mm Hg) when the
In analyzing certain geological features, it is often appropriate to assume that the pressure at some horizontal level of compensation, deep inside Earth, is the same over a large region and is equal to the pressure due to the gravitational force on the overlying material. Thus, the pressure on the
The L-shaped tank shown in Figure is filled with water and is open at the top. If d = 5.0 m, what is the force due to the water (a) On face A and (b) On faceB?
A large aquarium of height 5.00 m is filled with fresh water to a depth of 2.00 m. One wall of the aquarium consists of thick plastic 8.00 m wide. By how much does the total force on that wall increase if the aquarium is next filled to a depth of 4.00 m?
In Figure water stands at depth D = 35.0 m behind the vertical upstream face of a dam of width W = 314m. Find (a) The net horizontal force on the dam from the gauge pressure of the water and (b) The net torque due that force about a line through O parallel to the width of the dam. (c) Find the
In one observation, the column in a mercury barometer (as is shown in Figure) has a measured height h of 740.35 mm. The temperature is -5.0°C, at which temperature the density of mercury p is 1.3608 x 104 kg/m3. The free-fall acceleration g at the site of the barometer is 9.7835 m/s2. What is the
To suck lemonade of density 1000 kg/m3 up a straw to a maximum height of 4.0 cm, what minimum gauge pressure (in atmospheres) must you produce in your lungs?
What would be the height of the atmosphere if the air density(a) Were uniform and(b) Decreased linearly to zero with height? Assume that at sea level the air pressure is 1.0 atm and the air density is 1.3 kg/m3 kg.
A piston of cross-sectional area a is used in a hydraulic press to exert a small force of magnitude f on the enclosed liquid. A connecting pipe leads to a larger piston of cross sectional area A (Figure). (a) What force magnitude F will the larger piston sustain without moving? (b) If the piston
In Figure a spring of spring constant 3.00 x 104 N/m is between a rigid beam and the output piston of a hydraulic lever. An empty container with negligible mass sits on the input piston. The input piston has area Ai and the output piston has area 18.0Ai. Initially the spring is at its rest length.
In Figure a cube of edge length L = 0.600m and mass 450 kg is suspended by a rope in an open tank of liquid of density 1030 kg/m3. Find (a) The magnitude of the total downward force on the top of the cube from the liquid and the atmosphere, assuming atmospheric pressure is 1.00 atm, (b) The
An iron anchor of density 7870 kg/m3 appears 200 N lighter in water than in air.(a) What is the volume of the anchor?(b) How much does it weigh in air?
A boat floating in fresh water displaces water weighing 35.6kN.(a) What is the weight of the water this boat displaces when floating in salt water of density 1.10 x 103 kg/m3?(b) What is the difference between the volume of fresh water displaced and the volume of salt water displaced?
Three children, each of weight 356 N make a log raft by lashing together logs of diameter 0.30 m and length 1.80 m. How many logs will be needed to keep them afloat in fresh water? Take the density of the logs to be 800 kg/m3.
A 5.00 kg object is released from rest while fully submerged in a liquid. The liquid displaced by the submerged object has a mass of 3.00 kg. How far and in what direction does the object move in 0.200s, assuming that it moves freely and that the drag force on it from the liquid is negligible?
A block of wood floats in fresh water with two-thirds of its volume V submerged and in oil with 0.90V submerged. Find the density of(a) The wood and(b) The oil.
A flotation device is in the shape of a right cylinder, with a height of 0.500 m and a face area of 4.00 m2 on top and bottom, and its density is 0.400 times that of fresh water. It is initially held fully submerged in fresh water, with its top face at the water surface. Then it is allowed to
A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half-submerged in a liquid of density 800 kg/m3.(a) What is the mass of the sphere?(b) Calculate the density of the material of which the sphere is made.
Lurking alligators an alligator waits for prey by floating with only the top of its head exposed, so that the prey cannot easily see it. One way it can adjust the extent of sinking is by controlling the size of its lungs. Another way may be by swallowing stones (gastrulates) that then reside in the
What fraction of the volume of an iceberg (density 917 kg/m3) would be visible if the iceberg floats?(a) In the ocean (salt water, density 1024 kg/m3) and(b) In a river (fresh water, density 1000 kg/m3)? (When salt water freezes to form ice, the salt is excluded. So, an iceberg could provide fresh
A small solid ball is released from rest while fully submerged in a liquid and then its kinetic energy is measured when it has moved 4.0 cm in the liquid. Figure gives the results after many liquids are used: The kinetic energy K is plotted versus the liquid density Pliq, and Ks = 1.60 J sets the
A hollow spherical iron shell floats almost completely submerged in water. The outer diameter is 60.0 cm, and the density of iron is 7.87 g/cm3. Find the inner diameter.
In Figure a rectangular block is gradually pushed face-down into a liquid. The block has height d; on the bottom and top the face area is A = 5.67 cm2. Figure gives the apparent weight W app of the block as a function of the depth h of its lower face. The scale on the vertical axis is set by Ws =
An iron casting containing a number of cavities weighs 6000 N in air and 4000 N in water. What is the total volume of all the cavities in the casting? The density of iron (that is, a sample with no cavities) is 7.87 g/cm3.
Suppose that you release a small ball from rest at a depth of 0.600 m below the surface in a pool of water. If the density of the ball is 0.300 that of water and if the drag force on the ball from the water is negligible, how high above the water surface will the ball shoot as it emerges from the
The volume of air space in the passenger compartment of an 1800 kg car is 5.00 m3. The volume of the motor and front wheels is 0.750 m3, and the volume of the rear wheels, gas tank, and trunk is 0.800 m3; water cannot enter these two regions. The car rolls into a lake. (a) At first, no water enters
A block of wood has a mass of 3.67 kg and a density of 600 kg/m3. It is to be loaded with lead (1.14 x 104 kg/m3) so that it will float in water with 0.900 of its volume submerged. What mass of lead is needed if the lead is attached to?(a) The top of the wood and(b) The bottom of the wood?
When researchers find a reasonably complete fossil of a dinosaur, they can determine the mass and weight of the living dinosaur with a scale model sculpted from plastic and based on the dimensions of the fossil bones. The scale of the model is 1/20; that is, lengths are l/20 actual length, areas
Figure shows an iron ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has a height of 6.00 cm, a face area of 12.0 cm2 on the top and bottom, and a density of 0.30 g/cm3, and 2.00cm of its height is above the water surface.
A garden hose with an internal diameter of 1.9 cm is connected to a (stationary) lawn sprinkler that consists merely of a container with 24 holes, each 0.13 cm in diameter. If the water in the hose has a speed of 0.91 m/s, at what speed does it leave the sprinkler holes?
Two streams merge to form a river. One stream has a width of 8.2 m, depth of 3.4m, and current speed of 2.3 m/s. The other stream is 6.8 m wide and 3.2m deep, and flows at 2.6 m/s. If the river has width 10.5 m and speed 2.9 m/s, what is its depth?
Canal effect figure shows an anchored barge that extends across a canal by distance d = 30m and into the water by distance b = 12m. The canal has a width D = 55m, & water depth H = 14m, and a uniform water-flow speed vi = 1.5m/s. Assume that the flow around the barge is uniform. As the water
Figure shows two sections of an old pipe system that runs through a hill, with distances dA = dB = 30 m and D = 110 m. On each side of the hill, the pipe radius is 2.00 cm. However, the radius of the pipe inside the hill is no longer known. To determine it, hydraulic engineers first establish that
Water is pumped steadily out of a flooded basement at a speed of 5.0 m/s through a uniform hose of radius l.0 cm. The hose passes out through a window 3.0 m above the waterline. What is the power of the pump?
The water flowing through a 1.9 cm (inside diameter) pipe flows out through three 1.3 cm pipes. (a) If the flow rates in the three smaller pipes are 26, 19, and 11 L/min, what is the flow rate in the 1.9 cm pipe?(b) What is the ratio of the speed in the l.9 cm pipe to that in the pipe carrying
Water is moving with a speed of 5.0 m/s through a pipe with a cross-sectional area of 4.0 cm2. The water gradually descends 10 m as the pipe cross-sectional area increases to 8.0 cm2.(a) What is the speed at the lower level?(b) If the pressure at the upper level is 1.5 x 105 Pa, what is the
The intake in Figure has cross-sectional area of 0.74 m2 and water flow at 0.40 m/s. At the outlet, distance D = 180 m below the intake, the cross-sectional area is smaller than at the intake and the water flows out at 9.5 m/s. What is the pressure difference between inlet and outlet?
A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.90 m/s and a pressure of 170kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m above the input point, what are the(a) Speed and(b) Water pressure at the second floor?
Models of torpedoes are sometimes tested in a horizontal pipe of flowing water, much as a wind tunnel is used to test model airplanes. Consider a circular pipe of internal diameter 25.0 cm and a torpedo model aligned along the long axis of the pipe. The model has a 5.00 cm diameter and is to be
A cylindrical tank with a large diameter is filled with water to a depth D = 0.30 m. A hole of cross-sectional area A = 6.5 cm2 in the bottom of the tank allows water to drain out.(a) What is the rate at which water flows out, in cubic meters per second?(b) At what distance below the bottom of the
Suppose that two tanks, 1, and 2, each with a large opening at the top, contain different liquids. A small hole is made in the side of each tank at the same depth h below the liquid surface, but the hole in tank 1 has half the cross-sectional area of the hole in tank 2.(a) What is the ratio p1/p2
How much work is done by pressure in forcing 1.4 m3 of water through a pipe having an internal diameter of 13 mm if the difference in pressure at the two ends of the pipe is 1.0 atm?
In Figure water flows through a horizontal pipe and then out into the atmosphere at a speed v1 = 15 m/s. The diameters of the left and right sections of the pipe are 5.0 cm and 3.0 cm. (a) What volume of water flows into the atmosphere during a 10 min period? In the left section of the pipe, what
In Figure the fresh water behind a reservoir dam has depth D = 15 m. A horizontal pipe 4.0 cm in diameter passes through the dam at depth d = 6.0 m. A plug secures the pipe opening. (a) Find the magnitude of the frictional force between plug and pipe wall. (b) The plug is removed. What water volume
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