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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

What is the rotational inertia of a solid iron disk of mass 49 kg, with a thickness of 5.00 cm and radius of 20.0 cm, about an axis through its center and perpendicular to it?
A weightless rod, 10.0 m long, supports three weights as shown. Where is its center of gravity?
A door weighing 300.0 N measures 2.00 m × 3.00 m and is of uniform density; that is, the mass is uniformly distributed throughout the volume. A doorknob is attached to the door as shown. Where is the center of gravity if the doorknob weighs 5.0 N and is located 0.25 m from the edge?
A plate of uniform thickness is shaped as shown. Where is the center of gravity? Assume the origin (0, 0) is located at the lower left corner of the plate; the upper left corner is at (0, s) and upper right corner is at (s, s).
A stone used to grind wheat into flour is turned through 12 revolutions by a constant force of 20.0 N applied to the rim of a 10.0-cm-radius shaft connected to the wheel. How much work is done on the stone during the 12 revolutions?
A flywheel of mass 182 kg has an effective radius of 0.62 m (assume the mass is concentrated along a circumference located at the effective radius of the flywheel). (a) How much work is done to bring this wheel from rest to a speed of 120 rpm in a time interval of 30.0 s? (b) What is the applied
A Ferris wheel rotates because a motor exerts a torque on the wheel. The radius of the London Eye, a huge observation wheel on the banks of the Thames, is 67.5 m and its mass is 1.90 × 10 6 kg. The cruising angular speed of the wheel is 3.50 × 10−3 rad/s. (a) How much work does the motor need
A rod is being used as a lever as shown. The fulcrum is 1.2 m from the load and 2.4 m from the applied force. If the load has a mass of 20.0 kg, what force must be applied to lift the load?
A weight of 1200 N rests on a lever at a point 0.50 m from a support. On the same side of the support, at a distance of 3.0 m from it, an upward force with magnitude F is applied. Ignore the weight of the board itself. If the system is in equilibrium, what is F?
A sculpture is 4.00 m tall and has its center of gravity located 1.80 m above the center of its base. The base is a square with a side of 1.10 m. To what angle ( can the sculpture be tipped before it falls over?
A bowling ball made for a child has half the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume). By what factor is the (a) mass and (b) rotational inertia of the child's ball reduced compared with the adult ball?
A house painter is standing on a uniform, horizontal platform that is held in equilibrium by two cables attached to supports on the roof. The painter has a mass of 75 kg and the mass of the platform is 20.0 kg. The distance from the left end of the platform to where the painter is standing is d =
Four identical uniform meter sticks are stacked on a table as shown. Where is the x -coordinate of the cm of the meter sticks if the origin is chosen at the left end of the lowest stick? Why does the system balance?
A uniform diving board, of length 5.0 m and mass 55 kg, is supported at two points; one support is located 3.4 m from the end of the board and the second is at 4.6 m from the end. What are the forces acting on the board due to the two supports when a diver of mass 65 kg stands at the end of the
A house painter stands 3.0 m above the ground on a 5.0-m-long ladder that leans against the wall at a point 4.7 m above the ground. The painter weighs 680 N and the ladder weighs 120 N. Assuming no friction between the house and the upper end of the ladder, find the force of friction that the
A mountain climber is rappelling down a vertical wall. The rope attaches to a buckle strapped to the climber's waist 15 cm to the right of his center of gravity. If the climber weighs 770 N, find(a) The tension in the rope and(b) The magnitude and direction of the contact force exerted by the wall
A sign is supported by a uniform horizontal boom of length 3.00 m and weight 80.0 N. A cable, inclined at an angle of 35° with the boom, is attached at a distance of 2.38 m from the hinge at the wall. The weight of the sign is 120.0 N. What is the tension in the cable and what are the
A boom of mass m supports a steel girder of weight W hanging from its end. One end of the boom is hinged at the floor; a cable attaches to the other end of the boom and pulls horizontally on it. The boom makes an angle q with the horizontal. Find the tension in the cable as a function of m, W, q,
You are asked to hang a uniform beam and sign using a cable that has a breaking strength of 417 N. The store owner desires that it hang out over the sidewalk as shown. The sign has a weight of 200.0 N and the beam's weight is 50.0 N. The beam's length is 1.50 m and the sign's dimensions are 1.00 m
Refer to Problem 37. You chose an angle q of 33.8°. An 8.7-kg cat has climbed onto the beam and is walking from the wall toward the point where the cable meets the beam. How far can the cat walk before the cable breaks?
A man is doing push-ups. He has a mass of 68 kg and his center of gravity is located at a horizontal distance of 0.70 m from his palms and 1.00 m from his feet. Find the forces exerted by the floor on his palms and feet.
Find the rotational inertia of the system of point particles shown in the figure assuming the system rotates about the(a) x -axis,(b) y -axis,(c) z -axis.The z -axis is perpendicular to the xy -plane and points out of the page. Point particle A has a mass of 200 g and is located at ( x, y, z ) = (
Your friend balances a package with mass m = 10 kg on top of his head while standing. The mass of his upper body is M = 55 kg (about 65% of his total mass). Because the spine is vertical rather than horizontal, the force exerted by the sacrum on the spine ( in Fig 8.32) is directed approximately
Find the tension in the Achilles tendon and the force that the tibia exerts on the ankle joint when a person who weighs 750 N supports himself on the ball of one foot. The normal force N = 750 N pushes up on the ball of the foot on one side of the ankle joint, while the Achilles tendon pulls up on
In the movie Terminator, Arnold Schwarzenegger lifts someone up by the neck and, with both arms fully extended and horizontal, holds the person off the ground. If the person being held weighs 700 N, is 60 cm from the shoulder joint, and Arnold has an anatomy analogous to that in Fig. 8.30, what
Find the force exerted by the biceps muscle in holding a 1-L milk carton (weight 9.9 N) with the forearm parallel to the floor. Assume that the hand is 35.0 cm from the elbow and that the upper arm is 30.0 cm long. The elbow is bent at a right angle and one tendon of the biceps is attached to the
A person is doing leg lifts with 3.0-kg ankle weights. She is sitting in a chair with her legs bent at a right angle initially. The quadriceps muscles are attached to the patella via a tendon; the patella is connected to the tibia by the patellar tendon, which attaches to bone 10.0 cm below the
One day when your friend from Problem 40 is picking up a package, you notice that he bends at the waist to pick it up rather than keeping his back straight and bending his knees. You suspect that the lower back pain he complains about is caused by the large force on his lower vertebrae ( in Fig.
A man is trying to lift 60.0 kg off the floor by bending at the waist (see Fig. 8.32). Assume that the man's upper body weighs 455 N and the upper body's center of gravity is 38 cm from the sacrum (tailbone).(a) If, when bent over, the hands are a horizontal distance of 76 cm from the sacrum, what
Verify that the units of the rotational form of Newton's second law [Eq. (8-9)] are consistent. In other words, show that the product of a rotational inertia expressed in kg·m2 and an angular acceleration expressed in rad/s2 is a torque expressed in N·m?
A spinning flywheel has rotational inertia I = 400.0 kg·m2. Its angular velocity decreases from 20.0 rad/s to zero in 300.0 s due to friction. What is the frictional torque acting?
A turntable must spin at 33.3 rpm (3.49 rad/s) to play an old-fashioned vinyl record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 2.0 revolutions, starting from rest? The turntable is a uniform disk of diameter 30.5 cm and mass 0.22 kg?
Four point masses of 3.0 kg each are arranged in a square on massless rods. The length of a side of the square is 0.50 m. What is the rotational inertia for rotation about an axis(a) Passing through masses B and C?(b) Passing through masses A and C?(c) Passing through the center of the square and
A lawn sprinkler has three spouts that spray water, each 15.0 cm long. As the water is sprayed, the sprinkler turns around in a circle. The sprinkler has a total rotational inertia of9.20 Ã— 10ˆ’2 kg·m2. If the sprinkler starts from rest and takes 3.20 s to reach its
A chain pulls tangentially on a 40.6-kg uniform cylindrical gear with a tension of 72.5 N. The chain is attached along the outside radius of the gear at 0.650 m from the axis of rotation. Starting from rest, the gear takes 1.70 s to reach its rotational speed of 1.35 rev/s. What is the total
Four masses are arranged as shown. They are connected by rigid, mass less rods of lengths 0.75 m and 0.50 m. What torque must be applied to cause an angular acceleration of 0.75 rad/s 2 about the axis shown?
A bicycle wheel, of radius 0.30 m and mass 2 kg (concentrated on the rim), is rotating at 4.00 rev/s. After 50 s the wheel comes to a stop because of friction. What is the magnitude of the average torque due to frictional forces?
A playground merry-go-round (see Fig. 8.5), made in the shape of a solid disk, has a diameter of 2.50 m and a mass of 350.0 kg. Two children, each of mass 30.0 kg, sit on opposite sides at the edge of the platform. Approximate the children as point masses. (a) What torque is required to bring the
Two children standing on opposite sides of a merry-ground (see Fig. 8.5) are trying to rotate it. They each push in opposite directions with forces of magnitude 10.0 N. (a) If the merry-go-round has a mass of 180 kg and a radius of 2.0 m, what is the angular acceleration of the merry-go-round?
Refer to Atwood's machine (Example 8.2).(a) Assuming that the cord does not slip as it passes around the pulley, what is the relationship between the angular acceleration of the pulley (a) and the magnitude of the linear acceleration of the blocks (a)?(b) What is the net torque on the pulley about
Derive the rotational form of Newton's second law as follows. Consider a rigid object that consists of a large number N of particles. Let Fi, mi, and ri represent the tangential component of the net force acting on the i th particle, the mass of that particle, and the particle's distance from the
A solid sphere is rolling without slipping or sliding down a board that is tilted at an angle of 35° with respect to the horizontal. What is its acceleration?
A solid sphere is released from rest and allowed to roll down a board that has one end resting on the floor and is tilted at 30° with respect to the horizontal. If the sphere is released from a height of 60 cm above the floor, what is the sphere's speed when it reaches the lowest end of the board?
How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.0 cm and a mass of 15.8 g. The laser scans at a constant tangential velocity of 1.20 m/s. Assume that the music is first detected at a radius of 20.0 mm from the center of the disk.
A hollow cylinder, a uniform solid sphere, and a uniform solid cylinder all have the same mass m. The three objects are rolling on a horizontal surface with identical translational speeds v. Find their total kinetic energies in terms of m and v and order them from smallest to largest?
A solid sphere of mass 0.600 kg rolls without slipping along a horizontal surface with a translational speed of 5.00 m/s. It comes to an incline that makes an angle of 30° with the horizontal surface. Ignoring energy losses due to friction, to what vertical height above the horizontal surface does
A bucket of water with a mass of 2.0 kg is attached to a rope that is wound around a cylinder. The cylinder has a mass of 3.0 kg and is mounted horizontally on frictionless bearings. The bucket is released from rest. (a) Find its speed after it has fallen through a distance of 0.80 m. What are (b)
A 1.10-kg bucket is tied to a rope that is wrapped around a pole mounted horizontally on frictionless bearings. The cylindrical pole has a diameter of 0.340 m and a mass of 2.60 kg. When the bucket is released from rest, how long will it take to fall to the bottom of the well, a distance of 17.0 m?
A uniform solid cylinder rolls without slipping down an incline. A hole is drilled through the cylinder along its axis. The radius of the hole is 0.50 times the (outer) radius of the cylinder.(a) Does the cylinder take more or less time to roll down the incline now that the hole has been drilled?
A solid sphere of radius R and mass M slides without friction down a loop-the-loop track. The sphere starts from rest at a height of h above the horizontal. Assume that the radius of the sphere is small compared to the radius r of the loop.(a) Find the minimum value of h in terms of r so that the
A hollow cylinder, of radius R and mass M, rolls without slipping down a loop-the-loop track of radius r. The cylinder starts from rest at a height h above the horizontal section of track. What is the minimum value of h so that the cylinder remains on the track all the way around the loop?
If the hollow cylinder of Problem 66 is replaced with a solid sphere, will the minimum value of h increase, decrease, or remain the same? Once you think you know the answer and can explain why, redo the calculation to find h.
The string in a yo-yo is wound around an axle of radius 0.500 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.200 kg and outer radius 2.00 cm. Starting from rest, it rotates and falls a distance of 1.00 m (the length of the string). Assume for
A turntable of mass 5.00 kg has a radius of 0.100 m and spins with a frequency of 0.550 rev/s. What is its angular momentum? Assume the turntable is a uniform disk?
Find the ratio of the rotational inertia of the Earth for rotation about its own axis to its rotational inertia for rotation about the Sun?
Assume the Earth is a uniform solid sphere with radius of 6.37 × 106 m and mass of 5.97 × 1024 kg. Find the magnitude of the angular momentum of the Earth due to rotation about its axis>
The mass of a flywheel is 5.6 × 104 kg. This particular flywheel has its mass concentrated at the rim of the wheel. If the radius of the wheel is 2.6 m and it is rotating at 350 rpm, what is the magnitude of its angular momentum?
The angular momentum of a spinning wheel is 240 kg·m2 /s. After application of a constant braking torque for 2.5 s, it slows and has a new angular momentum of 115 kg·m2 /s. What is the torque applied?
How long would a braking torque of 4.00 N·m have to act to just stop a spinning wheel that has an initial angular momentum of 6.40 kg·m2 /s?
A figure skater is spinning at a rate of 1.0 rev/s with her arms outstretched. She then draws her arms in to her chest, reducing her rotational inertia to 67% of its original value. What is her new rate of rotation?
A skater is initially spinning at a rate of 10.0 rad/s with a rotational inertia of 2.50 kg·m2 when her arms are extended. What is her angular velocity after she pulls her arms in and reduces her rotational inertia to 1.60 kg·m2?
A uniform disk with a mass of 800 g and radius 17.0 cm is rotating on frictionless bearings with an angular speed of 18.0 Hz when Jill drops a 120-g clod of clay on a point 8.00 cm from the center of the disk, where it sticks. What is the new angular speed of the disk?
A spoked wheel with a radius of 40.0 cm and a mass of 2.00 kg is mounted horizontally on frictionless bearings. JiaJun puts his 0.500-kg guinea pig on the outer edge of the wheel. The guinea pig begins to run along the edge of the wheel with a speed of 20.0 cm/s with respect to the ground. What is
A diver can change his rotational inertia by drawing his arms and legs close to his body in the tuck position. After he leaves the diving board (with some unknown angular velocity), he pulls himself into a ball as closely as possible and makes 2.00 complete rotations in 1.33 s. If his rotational
The rotational inertia for a diver in a pike position is about 15.5 kg·m2; it is only 8.0 kg·m2 in a tuck position.(a) If the diver gives himself an initial angular momentum of 106 kg·m2 /s as he jumps off the board, how many turns can he make when jumping off a 10.0-m
A bicycle has wheels of radius 0.32 m. Each wheel has a rotational inertia of 0.080 kg·m2 about its axle. The total mass of the bicycle including the wheels and the rider is 79 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle (including rider) is the
Consider the merry-go-round of Practice Problem 8.1. The child is initially standing on the ground when the merry-go-round is rotating at 0.75 rev/s. The child then steps on the merry-go-round. How fast is the merry-ground rotating now? By how much did the rotational kinetic energy of the
If the cylinder rotates at 300.0 rpm, what is the magnitude of the average torque required to tilt its axis by 60.0° in a time of 3.00 s? [Draw a vector diagram of the initial and final angular momentum.]
How should the disk be oriented to prevent rocking from side to side and from bow to stern? Does this orientation make it difficult to steer the ship? Explain.
The Moon's distance from Earth varies between 3.56 × 105 km at perigee and 4.07 × 105 km at apogee. What is the ratio of its orbital speed around Earth at perigee to that at apogee?
A ceiling fan has four blades, each with a mass of 0.35 kg and a length of 60 cm. Model each blade as a rod connected to the fan axle at one end. When the fan is turned on, it takes 4.35 s for the fan to reach its final angular speed of 1.8 rev/s. What torque was applied to the fan by the motor?
The distance from the center of the breastbone to a man's hand, with the arm outstretched and horizontal to the floor, is 1.0 m. The man is holding a 10.0-kg dumbbell, oriented vertically, in his hand, with the arm horizontal. What is the torque due to this weight about a horizontal axis through
A uniform rod of length L is free to pivot around an axis through its upper end. If it is released from rest when horizontal, at what speed is the lower end moving at its lowest point? [The gravitational potential energy change is determined by the change in height of the center of gravity.]
A gymnast is performing a giant swing on the high bar. In a simplified model of the giant swing, assume that the gymnast keeps his arms and body straight as he swings all the way around the upper bar. Assume also that the gymnast does no work during the swing. With what angular speed should he be
The 12.2-m crane weighs 18 kN and is lifting a 67-kN load. The hoisting cable (tension T 1) passes over a pulley at the top of the crane and attaches to an electric winch in the cab. The pendant cable (tension T2), which supports the crane, is fixed to the top of the crane. Find the tensions in the
A collection of objects is set to rolling, without slipping, down a slope inclined at 30°. The objects are a solid sphere, a hollow sphere, a solid cylinder, and a hollow cylinder. A frictionless cube is also allowed to slide down the same incline. Which one gets to the bottom first? List the
In many problems in previous chapters, cars and other objects that roll on wheels were considered to act as if they were sliding without friction. (a) Can the same assumption be made for a wheel rolling by itself? Explain your answer. (b) If a moving car of total mass 1300 kg has four wheels, each
A uniform cylinder with a radius of 15 cm has been attached to two cords and the cords are wound around it and hung from the ceiling. The cylinder is released from rest and the cords unwind as the cylinder descends.(a) What is the acceleration of the cylinder?(b) If the mass of the cylinder is 2.6
A modern sculpture has a large horizontal spring, with a spring constant of 275 N/m, that is attached to a 53.0-kg piece of uniform metal at its end and holds the metal at an angle of 50.0° above the horizontal direction. The other end of the metal is wedged into a corner as shown. By how much has
A painter (mass 61 kg) is walking along a trestle, consisting of a uniform plank (mass 20.0 kg, length 6.00 m) balanced on two sawhorses. Each sawhorse is placed 1.40 m from an end of the plank. A paint bucket (mass 4.0 kg, diameter 28 cm) is placed as close as possible to the right-hand edge of
An experimental flywheel, used to store energy and replace an automobile engine, is a solid disk of mass 200.0 kg and radius 0.40 m? (a) What is its rotational inertia? (b) When driving at 22.4 m/s (50 mph), the fully energized flywheel is rotating at an angular speed of 3160 rad/s. What is the
(a) Assume the Earth is a uniform solid sphere. Find the kinetic energy of the Earth due to its rotation about its axis? (b) Suppose we could somehow extract 1.0% of the Earth's rotational kinetic energy to use for other purposes. By how much would that change the length of the day? (c) For how
A flat object in the xy -plane is free to rotate about the z -axis. The gravitational field is uniform in the ˆ’ y -direction. Think of the object as a large number of particles with masses mi located at coordinates (xi, yi), as in the figure?(a) Show that the torques on the particles about the
The operation of the Princeton Tokomak Fusion Test Reactor requires large bursts of energy. The power needed exceeds the amount that can be supplied by the utility company. Prior to pulsing the reactor, energy is stored in a giant flywheel of mass 7.27 × 105 kg and rotational inertia 4.55 × 106
A box of mass 42 kg sits on top of a ladder. Ignoring the weight of the ladder, find the tension in the rope. Assume that the rope exerts horizontal forces on the ladder at each end. [Use a symmetry argument; then analyze the forces and torques on one side of the ladder.]
A person is trying to lift a ladder of mass 15 kg and length 8.0 m. The person is exerting a vertical force on the ladder at a point of contact 2.0 m from the center of gravity. The opposite end of the ladder rests on the floor. (a) When the ladder makes an angle of 60.0° with the floor, what is
A crustacean (Hemisquilla ensigera) rotates its anterior limb to strike a mollusk, intending to break it open. The limb reaches an angular velocity of 175 rad/s in 1.50 ms. We can approximate the limb as a thin rod rotating about an axis perpendicular to one end (the joint where the limb attaches
Part (a) of the figure shows a simplified model of how the triceps muscle connects to the forearm. As the angle q is changed, the tendon wraps around a nearly circular arc. Explain how this is much more effective than if the tendon is connected as in part (b) of the figure?
Part (a) of the figure shows a simplified model of how the biceps muscle enables the forearm to support a load. What are the advantages of this arrangement as opposed to the alternative shown in part (b), where the flexor muscle is in the forearm instead of in the upper arm? Are the two equally
In Section 8.6, it was asserted that the sum of all the internal torques (that is, the torques due to internal forces) acting on a rigid object is zero. The figure shows two particles in a rigid object. The particles exert forces and on each other. These forces are directed along a line that
A playground merry-go-round (Fig. 8.5) spins with negligible friction. A child moves from the center out to the rim of the merry-go-round platform. Let the system be the merry-go-round plus the child. Which of these quantities change: angular velocity of the system, rotational kinetic energy of the
The figure shows a balancing toy with weights extending on either side. The toy is extremely stable. It can be pushed quite far off center one way or the other but it does not fall over? Explain why it is so stable.
Explain why the posture taken by defensive football linemen makes them more difficult to push out of the way. Consider both the height of the center of gravity and the size of the support base (the area on the ground bounded by the hands and feet touching the ground). In order to knock a person
The center of gravity of the upper body of a bird is located below the hips; in a human, the center of gravity of the upper body is located well above the hips. Since the upper body is supported by the hips, are birds or humans more stable? Consider what happens if the upper body is displaced a
An astronaut wants to remove a bolt from a satellite in orbit. He positions himself so that he is at rest with respect to the satellite, then pulls out a wrench and attempts to remove the bolt. What is wrong with his method? How can he remove the bolt?
Your door is hinged to close automatically after being opened. Where is the best place to put a wedge-shaped door stopper on a slippery floor in order to hold the door open? Should it be placed close to the hinge or far from it?
You are riding your bicycle and approaching a rather steep hill. Which gear should you use to go uphill, a low gear or a high gear? With a low gear the wheel rotates less than with a high gear for one rotation of the pedals.
Explain why it is easier to drive a wood screw using a screwdriver with a large diameter handle rather than one with a thin handle?
One way to find the center of gravity of an irregular flat object is to suspend it from various points so that it is free to rotate. When the object hangs inEquilibrium, a vertical line is drawn downward from the support point. After drawing lines from several different support points, the center
One of the effects of significant global warming would be the melting of part or all of the polar ice caps. This, in turn, would change the length of the day (the period of the Earth's rotation). Explain why. Would the day get longer or shorter?

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