A surgeon is using material from a donated heart to repair a patients damaged aorta and needs to know the elastic characteristics of this aortal material. Tests performed on a 16.0-cm strip of the...
A 2.0-kg box and a 3.0-kg box on a perfectly smooth horizontal floor have a spring of force constant 250 N/m compressed between them. If the initial compression of the spring is 6.0 cm, find the...
Three identical 6.40-kg masses are hung by three identical springs, as shown in Fig. E6.33. Each spring has a force constant of and was 12.0 cm long before any masses were attached to it. (a) Draw a...
A crate on a motorized cart starts from rest and moves with a constant eastward acceleration of = 2.80 m/s 2 . A worker assists the cart by pushing on the crate with a force that is eastward and has...
It is 5.0 km from your home to the physics lab. As part of your physical fitness program, you could run that distance at 10 km h (which uses up energy at the rate of 700 W), or you could walk it...
A 20.0-kg crate sits at rest at the bottom of a 15.0-m-long ramp that is inclined at 34.0 above the horizontal. A constant horizontal force of 290 N is applied to the crate to push it up the ramp....
A 5.00-kg package slides 1.50 m down a long ramp that is inclined at 24.0 below the horizontal. The coefficient of kinetic friction between the package and the ramp is Calculate (a) The work done on...
When a car is hit from behind, its passengers undergo sudden forward acceleration, which can cause a severe neck injury known as whiplash. During normal acceleration, the neck muscles play a large...
A block of ice with mass 4.00 kg is initially at rest on a frictionless, horizontal surface. A worker then applies a horizontal force F to it. As a result, the block moves along the x-axis such that...
You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200-kg car moving at 0.65 m/s is to compress the spring no more than 0.090 m before stopping. What should...
All birds, independent of their size, must maintain a power output of 1025 watts per kilogram of body mass in order to fly by flapping their wings. (a) The Andean giant hummingbird (Patagona gigas)...
The food calorie, equal to 4186 J, is a measure of how much energy is released when food is metabolized by the body. A certain brand of fruit-and-cereal bar contains 140 food calories per bar. (a) If...
The maximum energy that a bone can absorb without breaking depends on its characteristics, such as its cross-sectional area and its elasticity. For healthy human leg bones of approximately 6.0 cm2...
Tendons are strong elastic fibers that attach muscles to bones. To a reasonable approximation, they obey Hookes law. In laboratory tests on a particular tendon, it was found that, when a 250-g object...
A 2.50-kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0300 m. The spring has force constant 840 N/m. The coefficient of kinetic friction between the...
Consider the glider of Example 7.7 and Fig. 7.16. As in the example, the glider is released from rest with the spring stretched 0.100 m. What is the displacement x of the glider from its equilibrium...
Consider the glider of Example 7.7 and Fig. 7.16. (a) As in the example, the glider is released from rest with the spring stretched 0.100 m. What is the speed of the glider when it returns to x = 0?...
(a) For the elevator of Example 7.9, what is the speed of the elevator after it has moved downward 1.00 m from point 1 in Fig. 7.17? (b) When the elevator is 1.00 m below point 1 in Fig. 7.17, what...
A 15.0-kg stone slides down a snow-covered hill (Fig. P7.49), leaving point A with a speed of 10.00 m/s. There is no friction on the hill between points A and B, but there is friction on the level...
A 0.300-kg potato is tied to a string with length 2.50 m, and the other end of the string is tied to a rigid support. The potato is held straight out horizontally from the point of support, with the...
A sled with rider having a combined mass of 125 kg travels over the perfectly smooth icy hill shown in Fig. 7.68. How far does the sled land from the foot of the cliff? Figure 7.68: 11.0m Cliff 22.5...
A 3.00-kg fish is attached to the lower end of a vertical spring that has negligible mass and force constant 900 N/m. The spring initially is neither stretched nor compressed. The fish is released...
A basket of negligible weight hangs from a vertical spring scale of force constant 1500 N/m. (a) If you suddenly put a 3.0-kg adobe brick in the basket, find the maximum distance that the spring will...
A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis. The force corresponds to the potential-energy function graphed in Fig. P7.86. The particle is...
The mass of a regulation tennis ball is 57 g (although it can vary slightly), and tests have shown that the ball is in contact with the tennis racket for 30 ms. (This number can also vary, depending...
Experimental tests have shown that bone will rupture if it is subjected to a force density of 1.03 10 8 N/m 2 . Suppose a 70.0-kg person carelessly rollerskates into an overhead metal beam that hits...
To warm up for a match, a tennis player hits the 57.0-g ball vertically with her racket. If the ball is stationary just before it is hit and goes 5.50 m high, what impulse did she impart to it?
Two identical 1.50-kg masses are pressed against opposite ends of a light spring of force constant compressing the spring by 20.0 cm from its normal length. Find the speed of each mass when it has...
In a volcanic eruption, a 2400-kg boulder is thrown vertically upward into the air. At its highest point, it suddenly explodes (due to trapped gases) into two fragments, one being three times the...
A 1500-kg blue convertible is traveling south, and a 2000-kg red SUV is traveling west. If the total momentum of the system consisting of the two cars is 7200 kg m/s directed at 60.0 west of south,...
An 8.00-kg block of wood sits at the edge of a frictionless table, 2.20 m above the floor. A 0.500-kg blob of clay slides along the length of the table with a speed of 24.0 m/s, strikes the block of...
A small wooden block with mass 0.800 kg is suspended from the lower end of a light cord that is 1.60 m long. The block is initially at rest. A bullet with mass 12.0 g is fired at the block with a...
A 5.00-kg chunk of ice is sliding at 12.0 m/s on the floor of an ice-covered valley when it collides with and sticks to another 5.00-kg chunk of ice that is initially at rest. Since the valley is...
(a) When an object is in a circular orbit of radius r around the earth (mass ), the period of the orbit is T, given by Eq. (13.12), and the orbital speed is given by Eq. (13.10). Show that when the...
A shaft is drilled from the surface to the center of the earth (see Fig. 13.24). As in Example 13.10 (Section 13.6), make the unrealistic assumption that the density of the earth is uniform. With...
A 5000-kg spacecraft is in a circular orbit 2000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the...
An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and...
An object in the shape of a thin ring has radius a and mass M. A uniform sphere with mass m and radius R is placed with its center at a distance x to the right of the center of the ring, along a line...
In Example 13.10 (Section 13.6) we saw that inside a planet of uniform density (not a realistic assumption for the earth) the acceleration due to gravity increases uniformly with distance from the...
Two stars, with masses M 1 and M 2 , are in circular orbits around their center of mass. The star with mass has M 1 an orbit of radius R 1 ; the star with mass M 2 has an orbit of radius R 2 . (a)...
In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting very close to the star HD 179949 (hence the term hot Jupiter). The orbit was 1/9 just the distance of Mercury from...
Two satellites are in circular orbits around a planet that has radius 9.00 10 6 m. One satellite has mass 68.0 kg, orbital radius 5.00 10 7 m, and orbital speed 4800 m s. The second satellite has...
If a satellite is in a sufficiently low orbit, it will encounter air drag from the earths atmosphere. Since air drag does negative work (the force of air drag is directed opposite the motion), the...
Find the gravitational force that the earth exerts on a 10.0-kg mass if it is placed at the following locations. Consult Fig. 13.9, and assume a constant density through each of the interior regions...
A spacecraft is to be launched from the surface of the earth so that it will escape from the solar system altogether. (a) Find the speed relative to the center of the earth with which the spacecraft...
Jupiters moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of...
Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth. (a) What is the acceleration due to gravity at the surface of Titania? (b) What is...
Find the magnitude and direction of the net gravitational force on mass A due to masses B and C in Fig. E13.6. Each mass is 2.00 kg. Figure E13.6: (a) 10 -* 40 cm (b) K10 cm- 40 cm cm-
A car travels in the +x-direction on a straight and level road. For the first 4.00 s of its motion, the average velocity of the car is u av-x = 6.25 m/s. How far does the car travel in 4.00 s?
The 0.100-kg sphere in Fig. P13.62 is released from rest at the position shown in the sketch, with its center 0.400 m from the center of the 5.00-kg mass. Assume that the only forces on the 0.100-kg...
Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: A 2.50-kg stone thrown upward from the ground at 12.0 m/s...
An experiment is performed in deep space with two uniform spheres, one with mass 50.0 kg and the other with mass 100.0 kg. They have equal radii, r = 0.20 m. The spheres are released from rest with...
Use the results of Example 13.5 (Section 13.3) to calculate the escape speed for a spacecraft (a) From the surface of Mars and (b) From the surface of Jupiter. Use the data in Appendix F. (c) Why is...
Starting from the front door of your ranch house, you walk 60.0 m due east to your windmill, and then you turn around and slowly walk 40.0 m west to a bench where you sit and watch the sunrise. It...
A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them together. One of them has a mass of 65 kg and the other a mass of 72 kg, and they start from...
In the Cavendish balance apparatus shown in Fig. 13.4, suppose that m 1 = 1.10 kg, m 2 = 25.0 kg, and the rod connecting the pairs is 30.0 cm long. If, in each pair, m 1 and m 2 are 12.0 cm apart...
Prevention of Hip Fractures. Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hips speed at impact is about 2.0 m/s. If this can be reduced...
A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by v = [5.00 m/s (0.0180 m/s 3 )t 2 ]i + [2.00 m/s + (0.550 m/s 2 )t]j. (a) What are...
A rookie quarterback throws a football with an initial upward velocity component 12.0 m/s of and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (a) How much time is required for...
Dizziness. Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose a dancer (or skater) is spinning at a very...
An athlete starts at point A and runs at a constant speed 6.0 m/s of around a circular track 100 m in diameter, as shown in Fig. P3.40. Find the x and y-components of this runners average velocity...
The position of a dragonfly that is flying parallel to the ground is given as a function of time by r = [2.90 m + (0.0900 m/s 2 )t 2 ]i (0.0150 m/s 3 )t 3 j. (a) At what value of t does the velocity...
Spiraling Up. It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant...
A jungle veterinarian with a blow-gun loaded with a tranquilizer dart and a sly 1.5-kg monkey are each 25 m above the ground in trees 70 m apart. Just as the hunter shoots horizontally at the monkey,...
A toy rocket is launched with an initial velocity of 12.0 m s in the horizontal direction from the roof of a 30.0-m-tall building. The rockets engine produces a horizontal acceleration of (1.60 m/s 3...
An Errand of Mercy. An airplane is dropping bales of hay to cattle stranded in a blizzard on the Great Plains. The pilot releases the bales at 150 m above the level ground when the plane is flying at...
A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.63. Use information from the figure to find (a) The initial speed of the grasshopper and (b) The height of the...
A World Record. In the shot put, a standard track and-field event, a 7.3-kg object (the shot) is thrown by releasing it at approximately 40 over a straight left leg. The world record for distance,...
Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 6.00 m s. The velocity of the ball relative to Mia is 5.00 m/s in a direction...
Jaw Injury. Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the...
Boxes A and B are in contact on a horizontal, friction less surface, as shown in Fig. E4.23. Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 100 N is exerted on box A. What is...
A 4.80-kg bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 75.0 N. If the bucket starts from rest, what is the minimum time required to raise the bucket a...
Human Biomechanics. The fastest pitched baseball was measured at Typically, a baseball has a mass of 145 g. If the pitcher exerted his force (assumed to be horizontal and constant) over a distance of...
Human Biomechanics. The fastest served tennis ball, served by Big Bill Tilden in 1931, was measured at 73.14 m/s. The mass of a tennis ball is 57 g, and the ball is typically in contact with the...
Are We Martians? It has been suggested, and not facetiously, that life might have originated on Mars and been carried to the earth when a meteor hit Mars and blasted pieces of rock (perhaps...
Two stones are thrown vertically upward from the ground, one with three times the initial speed of the other. (a) If the faster stone takes 10 s to return to the ground, how long will it take the...
A uniform sphere with mass 28.0 kg and radius 0.380 m is rotating at constant angular velocity about a stationary axis that lies along a diameter of the sphere. If the kinetic energy of the sphere is...
Given two vectors and A = 4.00i + 7.00i and B = 5.00i 2.00i, (a) Find the magnitude of each vector; (b) Write an expression for the vector difference A B using unit vectors; (c) Find the magnitude...
Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed. (a) A thin 2.50-kg rod of length 75.0 cm, about an axis perpendicular...
A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.890 rad/s 2...
Suppose the solid cylinder in the apparatus described in Example 9.8 (Section 9.4) is replaced by a thin-walled, hollow cylinder with the same mass M and radius R. The cylinder is attached to the...
A bucket of mass m is tied to a massless cable that is wrapped around the outer rim of a frictionless uniform pulley of radius R, similar to the system shown in Fig. E9.47. In terms of the stated...
A flywheel has angular acceleration z (t) = 8.60 rad/s 2 (2.30 rads/s 3 )t, where counterclockwise rotation is positive. (a) If the flywheel is at rest at t = 0, what is its angular velocity at...
A uniform disk with radius R = 0.400 and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has...
A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is...
A classic 1957 Chevrolet Corvette of mass 1240 kg starts from rest and speeds up with a constant tangential acceleration of 2.00 m/s 2 on a circular test track of radius 60.0 m. Treat the car as a...
A vacuum cleaner belt is looped over a shaft of radius 0.45 cm and a wheel of radius 1.80 cm. The arrangement of the belt, shaft, and wheel is similar to that of the chain and sprockets in Fig. Q9.4....
A meter stick with a mass of 0.180 kg is pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released. As it swings...
A sphere with radius R = 0.200 m has density that decreases with distance r from the center of the sphere according to = 3.00 10 3 kg/m 3 (9.00 10 3 kg/m 4 )r. (a) Calculate the total mass of the...
As an intern with an engineering firm, you are asked to measure the moment of inertia of a large wheel, for rotation about an axis through its center. Since you were a good physics student, you know...
In the system shown in Fig. 9.17, a 12.0-kg mass is released from rest and falls, causing the uniform 10.0-kg cylinder of diameter 30.0 cm to turn about a frictionless axle through its center. How...
A dancer is spinning at 72 rpm about an axis through her center with her arms outstretched, as shown in Fig. P9.92. From biomedical measurements, the typical distribution of mass in a human body is...
In Fig. E10.7, forces A, B, C, and D each have magnitude 50 N and act at the same point on the object. (a) What torque (magnitude and direction) does each of these forces exert on the object about...
A uniform disk with mass 40.0 kg and radius 0.200 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force F =...
A bicycle racer is going downhill at 11.0 m/s when, to his horror, one of his 2.25-kg wheels comes off as he is 75.0 m above the foot of the hill. We can model the wheel as a thin-walled cylinder...
If a person of mass M simply moved forward with speed V, his kinetic energy would be 1/2 MV 2 , However, in addition to possessing a forward motion, various parts of his body (such as the arms and...
Using Problem 9.93 as a guide, apply it to a person running at 12 km h, with his arms and legs each swinging through 30 in s. As before, assume that the arms and legs are kept straight. Problem...
A size-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 5.00 m above the base of the hill. We can model this ball as a thin-walled...
(a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. Is it reasonable to model it as a particle? (b) Calculate the magnitude of the angular momentum of...
A uniform, 4.5-kg, square, solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1-kg raven flying horizontally at 5.0 m/s flies into...