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Question: Tarzan has foolishly gotten himself into another


Tarzan has foolishly gotten himself into another scrape with the animals and must be rescued once again by Jane. The 60.0-kg Jane starts from rest at a height of 5.00 m in the trees and swings down to the ground using a thin, but very rigid, 30.0-kg vine 8.00 m long. She arrives just in time to snatch the 72.0-kg Tarzan from the jaws of an angry hippopotamus. What is Jane’s (and the vine’s) angular speed
(a) just before she grabs Tarzan and
(b) just after she grabs him?
(c) How high will Tarzan and Jane go on their first swing after this daring rescue?


> 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.

> The deepest point known in any of the earth’s oceans is in the Marianas Trench, 10.92 km deep. (a) Assuming water is incompressible, what is the pressure at this depth? Use the density of seawater. (b) The actual pressure is 1.16 × 108 Pa; your calculate

> A cube of oak wood with very smooth faces normally floats in water. Suppose you submerge it completely and press one face flat against the bottom of a tank so that no water is under that face. Will the block float to the surface? Is there a buoyant force

> 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 pressure of p, and hands them to a bodybuilder in the

> You are a construction engineer working on the interior design of a retail store in a mall. A 2.00-m-long uniform bar of mass 8.50 kg is to be attached at one end to a wall, by means of a hinge that allows the bar to rotate freely with very little fricti

> You need to measure the mass M of a 4.00-mlong bar. The bar has a square cross section but has some holes drilled along its length, so you suspect that its center of gravity isn’t in the middle of the bar. The bar is too long for you to

> You are to use a long, thin wire to build a pendulum in a science museum. The wire has an un stretched length of 22.0 m and a circular cross section of diameter 0.860 mm; it is made of an alloy that has a large breaking stress. One end of the wire will b

> The compressive strength of our bones is important in everyday life. Young’s modulus for bone is about 1.4 × 1010 Pa. Bone can take only about a 1.0% change in its length before fracturing. (a) What is the maximum force that can be applied to a bone whos

> An amusement park ride consists of airplane-shaped cars attached to steel rods (Fig. P11.84). Each rod has a length of 15.0 m and a cross-sectional area of 8.00 cm2. (a) How much is each rod stretched when it is vertical and the ride is at rest? (Assume

> A 1.05-m-long rod of negligible weight is supported at its ends by wires A and B of equal length (Fig. P11.83). The cross-sectional area of A is 2.00 mm2 and that of B is 4.00 mm2. Young’s modulus for wire A is 1.80 × 1011

> A wire of length l0 and cross-sectional area A supports a hanging weight W. (a) Show that if the wire obeys Eq. (11.7), it behaves like a spring of force constant AY/l0, where Y is Young’s modulus for the wire material. (b) What would the force constant

> A 12.0-kg mass, fastened to the end of an aluminum wire with an un stretched length of 0.70 m, is whirled in a vertical circle with a constant angular speed of 120 rev/min. The cross-sectional area of the wire is 0.014 cm2. Calculate the elongation of th

> Ancient pyramid builders are balancing a uniform rectangular slab of stone tipped at an angle u above the horizontal using a rope (Fig. P11.80). The rope is held by five workers who share the force equally. (a) If u = 20.0°, what force does ea

> A garage door is mounted on an overhead rail (Fig. P11.79). The wheels at A and B have rusted so that they do not roll, but rather slide along the track. The coefficient of kinetic friction is 0.52. The distance between the wheels is 2.00 m, and each is

> A weight W is supported by attaching it to a vertical uniform metal pole by a thin cord passing over a pulley having negligible mass and friction. The cord is attached to the pole 40.0 cm below the top and pulls horizontally on it (Fig. P11.78). The pole

> An engineer is designing a conveyor system for loading hay bales into a wagon (Fig. P11.77). Each bale is 0.25 m wide, 0.50 m high, and 0.80 m long (the dimension perpendicular to the plane of the figure), with mass 30.0 kg. The center of gravity of each

> Two identical, uniform beams weighing 260 N each are connected at one end by a frictionless hinge. A light horizontal crossbar attached at the midpoints of the beams maintains an angle of 53.0° between the beams. The beams are suspended from t

> Two uniform, 75.0-g marbles 2.00 cm in diameter are stacked as shown in Fig. P11.75 in a container that is 3.00 cm wide. (a) Find the force that the container exerts on the marbles at the points of contact A, B, and C. (b) What force does each marble exe

> If you put a uniform block at the edge of a table, the center of the block must be over the table for the block not to fall off. (a) If you stack two identical blocks at the table edge, the center of the top block must be over the bottom block, and the c

> A gate 4.00 m wide and 2.00 m high weighs 700 N. Its center of gravity is at its center, and it is hinged at A and B. To relieve the strain on the top hinge, a wire CD is connected as shown in Fig. P11.73. The tension in CD is increased until the horizon

> You are trying to raise a bicycle wheel of mass m and radius R up over a curb of height h. To do this, you apply a horizontal force

> In the human arm, the forearm and hand pivot about the elbow joint. Consider a simplified model in which the biceps muscle is attached to the forearm 3.80 cm from the elbow joint. Assume that the person’s hand and forearm together weigh 15.0 N and that t

> Two friends are carrying a 200-kg crate up a flight of stairs. The crate is 1.25 m long and 0.500 m high, and its center of gravity is at its center. The stairs make a 45.0° angle with respect to the floor. The crate also is carried at a 45.0&

> One end of a uniform meter stick is placed against a vertical wall (Fig. P11.66). The other end is held by a lightweight cord that makes an angle u with the stick. The coefficient of static friction between the end of the meter stick and the wall is 0.40

> A worker wants to turn over a uniform, 1250-N, rectangular crate by pulling at 53.0° on one of its vertical sides (Fig. P11.65). The floor is rough enough to prevent the crate from slipping. (a) What pull is needed to just start the crate to t

> A uniform metal bar that is 8.00 m long and has mass 30.0 kg is attached at one end to the side of a building by a frictionless hinge. The bar is held at an angle of 64.0o above the horizontal by a thin, light cable that runs from the end of the bar oppo

> The yoga exercise “Downward-Facing Dog” requires stretching your hands straight out above your head and bending down to lean against the floor. This exercise is performed by a 750-N person as shown in Fig. P11.63. When

> A holiday decoration consists of two shiny glass spheres with masses 0.0240 kg and 0.0360 kg suspended from a uniform rod with mass 0.120 kg and length 1.00 m (Fig. P11.62). The rod is suspended from the ceiling by a vertical cord at each end, so that it

> A uniform, horizontal flagpole 5.00 m long with a weight of 200 N is hinged to a vertical wall at one end. A 600-N stuntwoman hangs from its other end. The flagpole is supported by a guy wire running from its outer end to a point on the wall directly abo

> (a) In Fig. P11.60 a 6.00-m-long, uniform beam is hanging from a point 1.00 m to the right of its center. The beam weighs 140 N and makes an angle of 30.0° with the vertical. At the right-hand end of the beam a 100.0-N weight is hung; an unkno

> A helicopter has a large main rotor that rotates in a horizontal plane and provides lift. There is also a small rotor on the tail that rotates in a vertical plane. What is the purpose of the tail rotor? (Hint: If there were no tail rotor, what would happ

> As part of an exercise program, a 75-kg person does toe raises in which he raises his entire body weight on the ball of one foot (Fig. P11.59). The Achilles tendon pulls straight upward on the heel bone of his foot. This tendon is 25 cm long and has a cr

> A uniform drawbridge must be held at a 37° angle above the horizontal to allow ships to pass underneath. The drawbridge weighs 45,000 N and is 14.0 m long. A cable is connected 3.5 m from the hinge where the bridge pivots (measured along the bridge) and

> A uniform, 7.5-m-long beam weighing 6490 N is hinged to a wall and supported by a thin cable attached 1.5 m from the free end of the beam. The cable runs between the beam and the wall and makes a 40° angle with the beam. What is the tension in the cable

> You are asked to design the decorative mobile shown in Fig. P11.56. The strings and rods have negligible weight, and the rods are to hang horizontally. (a) Draw a free-body diagram for each rod. (b) Find the weights of the balls A, B, and C. Find the ten

> Women often suffer from back pains during pregnancy. Model a woman (not including her fetus) as a uniform cylinder of diameter 30 cm and mass 60 kg. Model the fetus as a 10-kg sphere that is 25 cm in diameter and centered about 5 cm outside the front of

> A 72.0-kg weightlifter doing arm raises holds a 7.50-kg weight. Her arm pivots around the elbow joint, starting 40.0° below the horizontal (Fig. P11.54). Biometric measurements have shown that, together, the forearms and the hands account for

> You are testing a small flywheel (radius 0.166 m) that will be used to store a small amount of energy. The flywheel is pivoted with low-friction bearings about a horizontal shaft through the flywheel’s center. A thin, light cord is wrapped multiple times

> You have one object of each of these shapes, all with mass 0.840 kg: a uniform solid cylinder, a thin-walled hollow cylinder, a uniform solid sphere, and a thin-walled hollow sphere. You release each object from rest at the same vertical height h above t

> The V6 engine in a 2014 Chevrolet Silverado 1500 pickup truck is reported to produce a maximum power of 285 hp at 5300 rpm and a maximum torque of 305 ft.lb at 3900 rpm. (a) Calculate the torque, in both ft.lb and N.m, at 5300 rpm. Is your answer in ft.l

> A small block with mass 0.130 kg is attached to a string passing through a hole in a frictionless, horizontal surface .The block is originally revolving in a circle with a radius of 0.800 m about the hole with a tangential speed of 4.00 m/s. The string i

> A 500.0-g bird is flying horizontally at 2.25 m/s, not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0 cm below the top (Fig. P10.85). The bar is uniform, 0.750 m long, has a mass of 1.50 kg, and is hinged at

> Occasionally, a rotating neutron star (see Exercise 10.41) undergoes a sudden and unexpected speedup called a glitch. One explanation is that a glitch occurs when the crust of the neutron star settles slightly, decreasing the moment of inertia about the

> You are designing a slide for a water park. In a sitting position, park guests slide a vertical distance h down the waterslide, which has negligible friction. When they reach the bottom of the slide, they grab a handle at the bottom end of a 6.00-m-long

> A local ice hockey team has asked you to design an apparatus for measuring the speed of the hockey puck after a slap shot. Your design is a 2.00-m-long, uniform rod pivoted about one end so that it is free to rotate horizontally on the ice without fricti

> In your job as a mechanical engineer you are designing a flywheel and clutch-plate system like the one in Example 10.11. Disk A is made of a lighter material than disk B, and the moment of inertia of disk A about the shaft is one-third that of disk B. Th

> A large turntable with radius 6.00 m rotates about a fixed vertical axis, making one revolution in 8.00 s. The moment of inertia of the turntable about this axis is 1200 kg.m2. You stand, barefooted, at the rim of the turntable and very slowly walk towar

> A uniform rod of length L rests on a frictionless horizontal surface. The rod pivots about a fixed frictionless axis at one end. The rod is initially at rest. A bullet traveling parallel to the horizontal surface and perpendicular to the rod with speed v

> The solid wood door of a gymnasium is 1.00 m wide and 2.00 m high, has total mass 35.0 kg, and is hinged along one side. The door is open and at rest when a stray basketball hits the center of the door head-on, applying an average force of 1500 N to the

> A uniform solid cylinder with mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped

> A uniform, 0.0300-kg rod of length 0.400 m rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.0200 kg, are mounted so that they can slide along the rod. They are initially h

> A 42.0-cm-diameter wheel, consisting of a rim and six spokes, is constructed from a thin, rigid plastic material having a linear mass density of 25.0 g/cm. This wheel is released from rest at the top of a hill 58.0 m high. (a) How fast is it rolling when

> You are designing a system for moving aluminum cylinders from the ground to a loading dock. You use a sturdy wooden ramp that is 6.00 m long and inclined at 37.0o above the horizontal. Each cylinder is fitted with a light, frictionless yoke through its c

> A solid, uniform, spherical boulder starts from rest and rolls down a 50.0-m-high hill, as shown in Fig. P10.71. The top half of the hill is rough enough to cause the boulder to roll without slipping, but the lower half is covered with ice and there is n

> A solid uniform ball rolls without slipping up a hill (Fig. P10.70). At the top of the hill, it is moving horizontally, and then it goes over the vertical cliff. (a) How far from the foot of the cliff does the ball land, and how fast is it moving just be

> A basketball (which can be closely modeled as a hollow spherical shell) rolls down a mountainside into a valley and then up the opposite side, starting from rest at a height H0 above the bottom. In Fig. P10.69, the rough part of the terrain prevents slip

> A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down a track (Fig. P10.68). Points A and B are on a circular part of the track having radius R. The diameter of the shell is very small compared to h

> A yo-yo is made from two uniform disks, each with mass m and radius R, connected by a light axle of radius b. A light, thin string is wound several times around the axle and then held stationary while the yo-yo is released from rest, dropping as the stri

> When a tall, heavy refrigerator is pushed across a rough floor, what factors determine whether it slides or tips?

> You complain about fire safety to the landlord of your high-rise apartment building. He is willing to install an evacuation device if it is cheap and reliable, and he asks you to design it. Your proposal is to mount a large wheel (radius 0.400 m) on an a

> Two weights are connected by a very light, flexible cord that passes over an 80.0-N frictionless pulley of radius 0.300 m. The pulley is a solid uniform disk and is supported by a hook connected to the ceiling (Fig. P10.65). What force does the ceiling e

> A lawn roller in the form of a thin-walled, hollow cylinder with mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle. If it rolls without slipping, find the acceleration and the friction force.

> Two metal disks, one with radius R1 = 2.50 cm and mass M1 = 0.80 kg and the other with radius R2 = 5.00 cm and mass M2 = 1.60 kg, are welded together and mounted on a frictionless axis through their common center, as in Problem 9.77. (a) A light string i

> A block with mass m = 5.00 kg slides down a surface inclined 36.9° to the horizontal (Fig. P10.62). The coefficient of kinetic friction is 0.25. A string attached to the block is wrapped around a flywheel on a fixed axis at O. The flywheel has

> A large 16.0-kg roll of paper with radius R = 18.0 cm rests against the wall and is held in place by a bracket attached to a rod through the center of the roll (Fig. P10.61). The rod turns without friction in the bracket, and the moment of inertia of the

> The mechanism shown in Fig. P10.60 is used to raise a crate of supplies from a ship’s hold. The crate has total mass 50 kg. A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.25 m and moment of inertia I = 2.

> Figure P10.59 illustrates an Atwood’s machine. Find the linear accelerations of blocks A and B, the angular acceleration of the wheel C, and the tension in each side of the cord if there is no slipping between the cord and the surface o

> You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22,500-N elevator is to be accelerated upward by connecting it to a counterweight by means of a light (but strong!) cable passing over a solid u

> A thin, uniform, 3.80-kg bar, 80.0 cm long, has very small 2.50-kg balls glued on at either end (Fig. P10.57). It is supported horizontally by a thin, horizontal, frictionless axle passing through its center and perpendicular to the bar. Suddenly the rig

> In Example 10.10 (Section 10.6) the angular speed v changes, and this must mean that there is nonzero angular acceleration. But there is no torque about the rotation axis if the forces the professor applies to the weights are directly, radially inward. T

> A uniform, 8.40-kg, spherical shell 50.0 cm in diameter has four small 2.00-kg masses attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the center of the sphere and two of the small mas

> A grindstone in the shape of a solid disk with diameter 0.520 m and a mass of 50.0 kg is rotating at 850 rev/min. You press an ax against the rim with a normal force of 160 N (Fig. P10.54), and the grindstone comes to rest in 7.50 s. Find the coefficient

> A 50.0-kg grindstone is a solid disk 0.520 m in diameter. You press an ax down on the rim with a normal force of 160 N (Fig. P10.54). The coefficient of kinetic friction between the blade and the stone is 0.60, and there is a constant friction torque of

> In a simplified version of the musculature action in leg raises, the abdominal muscles pull on the femur (thigh bone) to raise the leg by pivoting it about one end (Fig. P11.53). When you are lying horizontally, these muscles make an angle of approximate

> A loaded cement mixer drives onto an old drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help, sets the handbrake, and waits. Meanwhile, a boat approaches, so the drawbridge is

> A therapist tells a 74-kg patient with a broken leg that he must have his leg in a cast suspended horizontally. For minimum discomfort, the leg should be supported by a vertical strap attached at the center of mass of the leg–cast syste

> End A of the bar AB in Fig. P11.50 rests on a frictionless horizontal surface, and end B is hinged. A horizontal force

> You open a restaurant and hope to entice customers by hanging out a sign (Fig. P11.49). The uniform horizontal beam supporting the sign is 1.50 m long, has a mass of 16.0 kg, and is hinged to the wall. The sign itself is uniform with a mass of 28.0 kg an

> A claw hammer is used to pull a nail out of a board (Fig. P11.48). The nail is at an angle of 60° to the board, and a force F S 1 of magnitude 400 N applied to the nail is required to pull it from the board. The hammer head contacts the board at point A,

> A uniform, 255-N rod that is 2.00 m long carries a 225-N weight at its right end and an unknown weight W toward the left end (Fig. P11.47). When W is placed 50.0 cm from the left end of the rod, the system just balances horizontally when the fulcrum is l

> Why is a tapered water glass with a narrow base easier to tip over than a glass with straight sides? Does it matter whether the glass is full or empty?

> Suppose you could use wheels of any type in the design of a soapbox-derby racer (an unpowered, four-wheel vehicle that coasts from rest down a hill). To conform to the rules on the total weight of the vehicle and rider, should you design with large massi

> A uniform, 8.0-m, 1150-kg beam is hinged to a wall and supported by a thin cable attached 2.0 m from the free end of the beam (Fig. P11.46). The beam is supported at an angle of 30.0° above the horizontal. (a) Draw a free-body diagram of the b

> Mountaineers often use a rope to lower themselves down the face of a cliff (this is called rappelling). They do this with their body nearly horizontal and their feet pushing against the cliff (Fig. P11.45). Suppose that an 82.0-kg climber, who is 1.90 m

> Sir Lancelot rides slowly out of the castle at Camelot and onto the 12.0-m-long drawbridge that passes over the moat (Fig. P11.44). Unbeknownst to him, his enemies have partially severed the vertical cable holding up the front end of the bridge so that i

> A box of negligible mass rests at the left end of a 2.00-m, 25.0-kg plank (Fig. P11.43). The width of the box is 75.0 cm, and sand is to be distributed uniformly throughout it. The center of gravity of the non-uniform plank is 50.0 cm from the right end.

> A door 1.00 m wide and 2.00 m high weighs 330 N and is supported by two hinges, one 0.50 m from the top and the other 0.50 m from the bottom. Each hinge supports half the total weight of the door. Assuming that the door’s center of gravity is at its cent

> A 350-N, uniform, 1.50-m bar is suspended horizontally by two vertical cables at each end. Cable A can support a maximum tension of 500.0 N without breaking, and cable B can support up to 400.0 N. You want to place a small weight on this bar. (a) What is

> A 60.0-cm, uniform, 50.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (Fig. E11.8). A very small 25.0-N tool is placed on the shelf midway between the points where the wires are attached to it. Find the tension

> Two people carry a heavy electric motor by placing it on a light board 2.00 m long. One person lifts at one end with a force of 400 N, and the other lifts the opposite end with a force of 600 N. (a) What is the weight of the motor, and where along the bo

> Two people are carrying a uniform wooden board that is 3.00 m long and weighs 160 N. If one person applies an upward force equal to 60 N at one end, at what point does the other person lift? Begin with a free-body diagram of the board.

> A ladder carried by a fire truck is 20.0 m long. The ladder weighs 3400 N and its center of gravity is at its center. The ladder is pivoted at one end (A) about a pin (Fig. E11.5); ignore the friction torque at the pin. The ladder is raised into position

> A student is sitting on a frictionless rotating stool with her arms outstretched as she holds equal heavy weights in each hand. If she suddenly lets go of the weights, will her angular speed increase, stay the same, or decrease? Explain.

> A steel cable with cross-sectional area 3.00 cm2 has an elastic limit of 2.40 × 108 Pa. Find the maximum upward acceleration that can be given a 1200-kg elevator supported by the cable if the stress is not to exceed one-third of the elastic limit.

> A 4.0-m-long steel wire has a cross-sectional area of 0.050 cm2. Its proportional limit has a value of 0.0016 times its Young’s modulus. Its breaking stress has a value of 0.0065 times its Young’s modulus. The wire is fastened at its upper end and hangs

> A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 40.0 kg. Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.500 kg, traveling perpendicular to the door at 12.

> The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center (Fig. E10.43). When the skater’s hands and arms are brought in and wrapped around his body

> A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 18 kg.m2. She then tucks into a small ball, decreasing this moment of inertia to 3.6 kg.m2. While tucked, she makes two comp

> Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 1014 times as great as that of ordinary solid matter. Suppose we represent the star a

> A small block on a frictionless, horizontal surface has a mass of 0.0250 kg. It is attached to a massless cord passing through a hole in the surface (Fig. E10.40). The block is originally revolving at a distance of 0.300 m from the hole with an angular s

2.99

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