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university physics

Questions and Answers of University Physics

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 to
A lunar lander is descending toward the moon’s surface. Until the lander reaches the surface, its height above the surface of the moon is given by y(t) = b – ct + dt2, where b = 800 m is the
A typical male sprinter can maintain his maximum acceleration for 2.0 s and his maximum speed is 10 m/s. After reaching this maximum speed, his acceleration becomes zero and then he runs at constant
Flying Leap of the Flea. High-speed motion pictures (3500 frames/second) of a jumping, 210-Î¼g flea yielded the data used to plot the graph given in Fig. E2.54. (See €œThe
Given two vectors and A = 4.00î + 7.00î and B = 5.00î – 2.00î,(a) Find the magnitude of each vector;(b) Write an expression for the vector difference A – B using unit vectors;(c) Find the
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
Two cars, A and B, move along the x-axis. Figure E2.32 is a graph of the positions of A and B versus time.Figure E2.32(a) In motion diagrams (like Figs. 2.13b and 2.14b), show the position, velocity,
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 crates, one with mass 4.00 kg and the other with mass 6.00 kg, sit on the friction less surface of a frozen pond, connected by a light rope (Fig. P4.43). A woman wearing golf shoes (so she can
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
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
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
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
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
Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in Fig. E4.2.(a) Find the x- and y-components of each
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
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,
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
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 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 rocket’s engine produces a horizontal acceleration of (1.60
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,
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 small toy airplane is flying in the xy-plane parallel to the ground. In the time interval to t = 0 to t = 1.00 s, its velocity as a function of time is given by v = (1.20 m/s2)tî + [12.0 m/s –
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/s2)t2]î – (0.0150 m/s3)t3ĵ.(a) At what value of t does the velocity
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 runner€™s average
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
The Champion Jumper of the Insect World. The froghopper, Philaenus spumarius, holds the world record for insect jumps. When leaping at an angle of 58.0° above the horizontal, some of the tiny
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
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/s3)t2]î + [2.00 m/s + (0.550 m/s2)t]ĵ.(a) What are
The position of a squirrel running in a park is given by r = [(0.280 m/s)t + (0.0360 m/s2)t2]î + (0.0190 m/s3)t3 ĵ.(a) What are and ux(t) and uy(t), the x- and y-components of the velocity of the
Prevention of Hip Fractures. Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hip’s speed at impact is about 2.0 m/s. If this can be
Air-Bag Injuries. During an auto accident, the vehicle’s air bags deploy and slow down the passengers more gently than if they had hit the windshield or steering wheel. According to safety
If a pilot accelerates at more than 4g, he begins to “gray out” but doesn’t completely lose consciousness.(a) Assuming constant acceleration, what is the shortest time that a jet pilot starting
A jet fighter pilot wishes to accelerate from rest at a constant acceleration of 5g to reach Mach 3 (three times the speed of sound) as quickly as possible. Experimental tests reveal that he will
A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car’s motion, the eastward component of the car’s velocity is given by Ux(t) = (0.860
A test car travels in a straight line along the x-axis. The graph in Fig. E2.11 shows the car€™s position x as a function of time. Find its instantaneous velocity at points A through
A bird is flying due east. Its distance from a tall building is given by x(t) = 28.0 m + (12.4 m/s)t – (0.0450 m/s3)t3. What is the instantaneous velocity of the bird when t = 8.00 s?
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 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 uav-x = 6.25 m/s. How far does the car travel in 4.00 s?
In the Cavendish balance apparatus shown in Fig. 13.4, suppose that m1= 1.10 kg, m2= 25.0 kg, and the rod connecting the pairs is 30.0 cm long. If, in each pair, m1and m2are 12.0 cm apart center to
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
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) К10 ст-* 40 cm (b) K10 cm- 40 cm cm-
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 the
Jupiter’s 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
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 the
Two satellites are in circular orbits around a planet that has radius 9.00 × 106 m. One satellite has mass 68.0 kg, orbital radius 5.00 × 107 m, and orbital speed 4800 m s. The second satellite has
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
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
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 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
In Example 13.5 (Section 13.3) we ignored the gravitational effects of the moon on a spacecraft en route from the earth to the moon. In fact, we must include the gravitational potential energy due to
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
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
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
If a satellite is in a sufficiently low orbit, it will encounter air drag from the earth’s atmosphere. Since air drag does negative work (the force of air drag is directed opposite the motion), the
Two stars, with masses M1and M2, are in circular orbits around their center of mass. The star with mass has M1an orbit of radius R1; the star with mass M2has an orbit of radius R2.(a) Show that the
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
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 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
A thin, uniform rod has length L and mass M. Calculate the magnitude of the gravitational force the rod exerts on a particle with mass m that is at a point along the axis of the rod a distance x from
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) 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 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 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
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 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 60.0º west of
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
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
Starting at t = 0, a horizontal net force F(0.280 N/s)tî + (–0.450 N/s2)t2ĵ is applied to a box that has an initial momentum p = (– 3.00 kg ∙ m/s)î + (4.00 kg ∙ m/s)ĵ. What is
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?
Experimental tests have shown that bone will rupture if it is subjected to a force density of 1.03 × 108 N/m2. Suppose a 70.0-kg person carelessly rollerskates into an overhead metal beam that hits
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
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
A small block with mass 0.0400 kg slides in a vertical circle of radius R = 0.500 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of
A small block with mass 0.0500 kg slides in a vertical circle of radius R = 0.800 on the inside of a circular track. There is no friction between the track and the block. At the bottom of the
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 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 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 ball is thrown upward with an initial velocity of 15 m/s at an angle of 60.0° above the horizontal. Use energy conservation to find the ball’s greatest height above the ground?
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 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 350-kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop shown in Fig. P7.45.(a) How fast is this roller coaster moving at point B?(b) How hard does it press
While a roofer is working on a roof that slants at 36° above the horizontal, he accidentally nudges his 85.0-N toolbox, causing it to start sliding downward, starting from rest. If it starts 4.25 m
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
(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 is
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 =
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
Tendons are strong elastic fibers that attach muscles to bones. To a reasonable approximation, they obey Hooke’s law. In laboratory tests on a particular tendon, it was found that, when a 250-g
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
For its size, the common flea is one of the most accomplished jumpers in the animal world. A 2.0-mm-long, 0.50-mg critter can reach a height of 20 cm in a single leap.(a) Neglecting air drag, what is
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 height a typical human can jump from a crouched start is about 60 cm. By how much does the gravitational potential energy increase for a 72-kg person in such a jump? Where does this
All birds, independent of their size, must maintain a power output of 10–25 watts per kilogram of body mass in order to fly by flapping their wings.(a) The Andean giant hummingbird (Patagona gigas)
Consider the system shown in Fig. P6.86. The rope and pulley have negligible mass, and the pulley is frictionless. Initially the 6.00-kg block is moving downward and the 8.00-kg block is moving to
Your cat “Ms.” (mass 7.00 kg) is trying to make it to the top of a frictionless ramp 2.00 m long and inclined upward 30.0º at above the horizontal. Since the poor cat can’t get any traction on
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
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
A net force along the x-axis that has x-component Fx = –12.0 N + (0.300 N/m2)x2 is applied to a 5.00-kg object that is initially at the origin and moving in the –x-direction with a speed of 6.00
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 5.00-kg package slides 1.50 m down a long ramp that is inclined at 24.0º below the horizontal. The coefficient of kinetic friction between the package and the ramp is Calculate(a) The work done on

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