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physics
mechanics

Questions and Answers of Mechanics

A high diver of mass 70.0 kg jumps off a board 10.0 m above the water. If his downward motion is stopped 2.00 s after he enters the water, what average upward force did the water exert on him?
A crate of weight Fg is pushed by a force P on a horizontal floor. (a) If the coefficient of static friction is -s and P is directed at angle μ below the horizontal, show that the minimum
A block of mass m = 2.00 kg is released from rest at h = 0.500 m above the surface of a table, at the top of a θ = 30.0° incline as shown in Figure P5.58. The frictionless incline is fixed
In Larry Niven€™s science-fiction novel Ringworld, a rigid ring of material rotates about a star (Fig. P13.51) The tangential speed of the ring is 1.25 X 106 m/s, and its radius is 1.53 X
A 1.30-kg toaster is not plugged in. The coefficient of static friction between the toaster and a horizontal countertop is 0.350. To make the toaster start moving, you carelessly pull on its electric
(a) Show that the rate of change of the free-fall acceleration with distance above the Earth’s surface is dg/dr = 2GME/RE3 This rate of change over distance is called a gradient. (b) If h is
Materials such as automobile tire rubber and shoe soles are tested for coefficients of static friction with an apparatus called a James tester. The pair of surfaces for which μs is to be measured
What horizontal force must be applied to the cart shown in Figure P5.61 in order that the blocks remain stationary relative to the cart? Assume all surfaces, wheels, and pulley is frictionless.
A ring of matter is a familiar structure in planetary and stellar astronomy. Examples include Saturn€™s rings and a ring nebula. Consider a uniform ring of mass 2.36 X 1020 kg and radius
A student is asked to measure the acceleration of a cart on a “frictionless” inclined plane as in Figure 5.11, using an air track, a stopwatch, and a meter stick. The height of the incline is
Voyagers 1 and 2 surveyed the surface of Jupiter’s moon Io and photographed active volcanoes spewing liquid sulfur to heights of 70 km above the surface of this moon. Find the speed with which the
Initially the system of objects shown in Figure P5.61 is held motionless. All surfaces, pulley, and wheels are frictionless. Let the force F is zero and assume that m2 can move only vertically. At
As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and find yourself returning to your spacecraft from the opposite
One block of mass 5.00 kg sits on top of a second rectangular block of mass 15.0 kg, which in turn is on a horizontal table. The coefficients of friction between the two blocks are μs = 0.300
A 1.00-kg glider on a horizontal air track is pulled by a string at an angle θ. The taut string runs over a pulley and is attached to a hanging object of mass 0.500 kg as in Fig. P5.65. (a)
A certain quaternary star system consists of three stars, each of mass m, moving in the same circular orbit of radius r about a central star of mass M. The stars orbit in the same sense, and are
Cam mechanisms are used in many machines. For example, cams open and close the valves in your car engine to admit gasoline vapor to each cylinder and to allow the escape of exhaust. The principle is
A cylindrical habitat in space 6.00 km in diameter and 30 km long has been proposed (by G. K. O’Neill, 1974) Such a habitat would have cities, land, and lakes on the inside surface and air and
Newton’s law of universal gravitation is valid for distances covering an enormous range, but it is thought to fail for very small distances, where the structure of space itself is uncertain. Far
Any device that allows you to increase the force you exert is a kind of machine. Some machines, such as the prybar or the inclined plane, are very simple. Some machines do not even look like
Show that the escape speed from the surface of a planet of uniform density is directly proportional to the radius of the planet.
Two blocks of mass 3.50 kg and 8.00 kg are connected by a Mass less string that passes over a frictionless pulley (Fig.P5.68). The inclines are frictionless. Find (a) the magnitude of the
Many people assume that air resistance acting on a moving object will always make the object slow down. It can actually be responsible for making the object speed up. Consider a 100-kg Earth
A van accelerates down a hill (Fig. P5.69), going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy (m =0.100 kg) hangs by a string from the van€™s ceiling. The acceleration
Two hypothetical planets of masses m1 and m2 and radii r1 and r2, respectively, are nearly at rest when they are an infinite distance apart. Because of their gravitational attraction, they head
In Figure P5.58 the incline has mass M and is fastened to the stationary horizontal tabletop. The block of mass m is placed near the bottom of the incline and is released with a quick push that sets
The maximum distance from the Earth to the Sun (at our aphelion) is 1.521 X 1011 m, and the distance of closest approach (at perihelion) is 1.471 X 1011 m. If the Earth’s orbital speed at
A magician pulls a tablecloth from under a 200-g mug located 30.0 cm from the edge of the cloth. The cloth exerts a friction force of 0.100 N on the mug, and the cloth is pulled with a constant
(a) Determine the amount of work (in joules) that must be done on a 100-kg payload to elevate it to a height of 1 000 km above the Earth’s surface. (b) Determine the amount of additional work
An 8.40-kg object slides down a fixed, frictionless inclined plane. Use a computer to determine and tabulate the normal force exerted on the object and its acceleration for a series of incline angles
X-ray pulses from Cygnus X-1, a celestial x-ray source, have been recorded during high-altitude rocket flights. The signals can be interpreted as originating when a blob of ionized matter orbits a
A mobile is formed by supporting four metal butterflies of equal mass m from a string of length L. The points of support are evenly spaced a distance θ apart as shown in Figure P5.73. The string
Studies of the relationship of the Sun to its galaxy—the Milky Way—have revealed that the Sun is located near the outer edge of the galactic disk, about 30 000 light-years from the center. The
The oldest artificial satellite in orbit is Vanguard I, launched March 3, 1958. Its mass is 1.60 kg. In its initial orbit, its minimum distance from the center of the Earth was 7.02 Mm, and its speed
Astronomers detect a distant meteoroid moving along a straight line that, if extended, would pass at a distance 3RE from the center of the Earth, where RE is the radius of the Earth. What minimum
A spherical planet has uniform density P Show that the minimum period for a satellite in orbit around it is Tmin = √3π/Gp independent of the radius of the planet.
Two stars of masses M and m, separated by a distance d, revolve in circular orbits about their center of mass (Fig. P13.69). Show that each star has a period given by T2 = 4π2d3/G (M + m) Proceed
(a) A 5.00-kg object is released 1.20 X 107 m from the center of the Earth. It moves with what acceleration relative to the Earth? (b) What If? A 2.00 X 1024 kg object is released 1.20 X 107 m from
The acceleration of an object moving in the gravitational field of the Earth is a = ─ GMEr/r3 where r is the position vector directed from the center of the Earth toward the object. Choosing
A motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.00-min trip, find (a) The
During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t2, where θ is in radians and t is in seconds. Determine the angular
A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by the following expressions: x = (18.0 m/s) t And y = (4.00 m/s) t ─ (4.90
A dentist’s drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate of 2.51 + 104 rev/min. (a) Find the drill’s angular acceleration. (b) Determine the angle
A sailor drops a wrench from the top of a sailboat’s mast while the boat is moving rapidly and steadily in a straight line. Where will the wrench hit the deck? (Galileo posed this question.)
A wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of 12.0 rad/s in 3.00 s. Find (a) The magnitude of the angular acceleration of the wheel and (b)
The coordinates of an object moving in the xy plane vary with time according to the equations x=─ (5.00 m) sin (wt) and y= (4.00 m) ─ (5.00 m) cos (wt), where w is a constant and t is in
An airliner arrives at the terminal, and the engines are shut off. The rotor of one of the engines has an initial clockwise angular speed of 2 000 rad/s. The engine’s rotation slows with an angular
An electric motor rotating a grinding wheel at 100 rev/min is switched off. With constant negative angular acceleration of magnitude 2.00 rad/s2, (a) How long does it take the wheel to stop? (b)
At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi = (3.00i ─ 2.00ˆj) m/s and is at the origin. At t = 3.00 s, the particle’s velocity is v = (9.00i
A centrifuge in a medical laboratory rotates at an angular speed of 3 600 rev/min. When switched off, it rotates 50.0 times before coming to rest. Find the constant angular acceleration of the
The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 8.00 s, at which time it is turning at 5.00 rev/s. At this point the person doing the laundry
The vector position of a particle varies in time according to the expression r = (3.00i─ 6.00t2 j) m. (a) Find expressions for the velocity and acceleration as functions of time. (b)
A rotating wheel requires 3.00 s to rotate through 37.0 revolutions. Its angular speed at the end of the 3.00-s interval is 98.0 rad/s. What is the constant angular acceleration of the wheel?
(a) Find the angular speed of the Earth’s rotation on its axis. As the Earth turns toward the east, we see the sky turning toward the west at this same rate. (b) The rainy Pleiads wester And
A fish swimming in a horizontal plane has velocity vi = (4.00i + 1.00j) m/s at a point in the ocean where the position relative to a certain rock is ri = (10.0i ─ 4.00j) m. After the fish swims
A merry-go-round is stationary. A dog is running on the ground just outside its circumference, moving with a constant angular speed of 0.750 rad/s. The dog does not change his pace when he sees what
A particle initially located at the origin has an acceleration of a = 3.00j m/s2 and an initial velocity of vi = 500i m/s. Find (a) The vector position and velocity at any time t and (b) The
Make an order-of-magnitude estimate of the number of revolutions through which a typical automobile tire turn s in 1 yr. State the quantities you measure or estimate and their values.
A racing car travels on a circular track of radius 250 m. If the car moves with a constant linear speed of 45.0 m/s, find (a) its angular speed and (b) the magnitude and direction of its acceleration.
A wheel 2.00 m in diameter lies in a vertical plane and rotates with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on
It is not possible to see very small objects, such as viruses, using an ordinary light microscope. An electron microscope can view such objects using an electron beam instead of a light beam.
Figure P10.14 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady angular rate of 76.0 rev/min. The chain engages with
To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. It explodes on the mountainside 42.0 s after firing. What
A discus thrower (Fig P10.15) accelerates a discus from rest to a speed of 25.0 m/s by whirling it through 1.25 rev. Assume the discus moves on the arc of a circle 1.00 m in radius.(a) Calculate the
A car accelerates uniformly from rest and reaches a speed of 22.0 m/s in 9.00 s. If the diameter of a tire is 58.0 cm, find (a) The number of revolutions the tire makes during this motion, assuming
In a local bar, a customer slides an empty beer mug down the counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor
A disk 8.00 cm in radius rotates at a constant rate of 1 200 rev/min about its central axis. Determine (a) Its angular speed, (b) the tangential speed at a point 3.00 cm from its center, (c) the
A car traveling on a flat (unbanked) circular track accelerates uniformly from rest with a tangential acceleration of 1.70 m/s2. The car makes it one quarter of the way around the circle before it
Consider a tall building located on the Earth’s equator. As the Earth rotates, a person on the top floor of the building moves faster than someone on the ground with respect to an inertial
Rigid rods of negligible mass lying along the y axis connect three particles (Fig. P10.20). If the system rotates about the x axis with an angular speed of 2.00 rad/s, find(a) The moment of inertia
In a local bar, a customer slides an empty beer mug down the counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor
The four particles in Figure P10.21 are connected by rigid rods of negligible mass. The origin is at the center of the rectangle. If the system rotates in the xy plane about the z axis with an
Two balls with masses M and m are connected by a rigid rod of length L and negligible mass as in Figure P10.22. For an axis perpendicular to the rod, show that the system has the minimum moment of
One strategy in a snowball fight is to throw a snowball at a high angle over level ground. While your opponent is watching the first one, a second snowball is thrown at a low angle timed to arrive
Three identical thin rods, each of length L and mass m, are welded perpendicular to one another as shown in Figure P10.23. The assembly is rotated about an axis that passes through the end of one rod
Figure P10.24 shows a side view of a car tire. Model it as having two sidewalls of uniform thickness 0.635 cm and a tread wall of uniform thickness 2.50 cm and width 20.0 cm. Assume the rubber has
A uniform thin solid door has height 2.20 m, width 0.870 m, and mass 23.0 kg. Find its moment of inertia for rotation on its hinges. Is any piece of data unnecessary?
An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 15.0 m if her initial speed is 3.00 m/s. What is the free-fall acceleration on the planet?
Attention! About face! Compute an order-of-magnitude estimate for the moment of inertia of your body as you stand tall and turn about a vertical axis through the top of your head and the point
The density of the Earth, at any distance r from its center, is approximately p = [14.2 ─ 11.6(r/R)] X 103 kg/m3 Where R is the radius of the Earth, Show that this density leads to a moment
A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection?
Calculate the moment of inertia of a thin plate, in the shape of a right triangle, about an axis that passes through one end of the hypotenuse and is parallel to the opposite leg of the triangle, as
Many machines employ cams for various purposes, such as opening and closing valves. In Figure P10.29, the cam is a circular disk rotating on a shaft that does not pass through the center of the disk.
The fishing pole in Figure P10.30 makes an angle of 20.0' with the horizontal. What is the torque exerted by the fish about an axis perpendicular to the page and passing through the
A rock is thrown upward from the level ground in such a way that the maximum height of its flight is equal to its horizontal range d. (a) At what angle ' is the rock thrown? (b) What If? Would
Find the net torque on the wheel in Figure P10.31 about the axle through O if a =10.0 cm and b = 25.0 cm.
A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.00 m/s at an angle of 20.0° below the horizontal. It strikes the ground 3.00 s later. (a) How
The tires of a 1 500-kg car are 0.600 m in diameter, and the coefficients of friction with the road surface are 7s = 0.800 and 7k = 0.600. Assuming that the weight is evenly distributed on the four
The small archerfish (length 20 to 25 cm) lives in brackish waters of Southeast Asia from India to the Philippines. This aptly named creature captures its prey by shooting a stream of water drops at
Suppose the car in Problem 32 has a disk brake system. Each wheel is slowed by the friction force between a single brake pad and the disk-shaped rotor. On this particular car, the brake pad contacts
A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves
A grinding wheel is in the form of a uniform solid disk of radius 7.00 cm and mass 2.00 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.600 N,m that the
A model airplane with mass 0.750 kg is tethered by a wire so that it flies in a circle 30.0 m in radius. The airplane engine provides a net thrust of 0.800 N perpendiculars to the tethering wire.
The combination of an applied force and a friction force produces a constant total torque of 36.0 N,m on a wheel rotating about a fixed axis. The applied force acts for 6.00 s. During this time the
A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle i above the horizontal as in Figure P4.20. If the initial speed of the stream is vi, at what
A playground is on the flat roof of a city school, 6.00 m above the street below. The vertical wall of the building is 7.00 m high, to form a meter-high railing around the playground. A ball has
A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a mass less string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. These
A dive bomber has a velocity of 280 m/s at an angle θ below the horizontal. When the altitude of the aircraft is 2.15 km, it releases a bomb, which subsequently hits a target on the ground. The
A potter’s wheel—a thick stone disk of radius 0.500 m and mass 100 kg—is freely rotating at 50.0 rev/min. The potter can stop the wheel in 6.00 s by pressing a wet rag against the rim and
An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley that is rigidly attached to the flywheel, as shown in Figure P10.39. The flywheel is a solid disk

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