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physics
mechanics

Questions and Answers of Mechanics

A baseball is thrown from the roof of a 22.0-m-tall building with an initial velocity of magnitude 12.0 m/s and directed at an angle of 53.10 above the horizontal. (a) What is the speed of the ball
A crate of mass M starts from rest at the top of a frictionless ramp inclined at an angle a above the horizontal. Find its speed at the bottom of the ramp, a distance d from where it started. Do this
Answer part (b) of Example 7.6 (Section 7.1) by applying Eq. (7.7) to points 2 and 3, rather than to points 1 and 3 as was done in the example.
An empty crate is given an initial push down a ramp, starting it with a speed vo and reaches the bottom with speed v and kinetic energy K. Some books are now placed in the crate, so that the total
A Small rock with mass 0.20 kg is released from rest at point A, which is at the top edge of a large, hemispherical bowl with radius R = 050 m (Fig. 7.25) Assume that the size of the rock is small
A stone of mass m is thrown upward at an angle θ above the horizontal and feels no appreciable air resistance. Use conservation of energy to show that at its highest point, it is a distance V02
You are testing a new amusement park roller coaster with an empty car with mass 120 kg. One part of the track is a vertical loop with radius 12.0 m. At the bottom of the loop (point A) the car has
Tarzan and Jane Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 m that makes an angle of 45° with the vertical, steps off his tree limb, and swings down
A 10.0-kg microwave oven is pushed 8.00 m up the sloping surface of a loading ramp inclined at an angle of 36.9° above the horizontal, by a constant force F with a magnitude 110 N and acting
Pendulum a small rock with mass 0.12 kg is fastened to a mass less string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45° with the vertical. Air
A force of 800 N stretches a certain spring a distance of 0.200 m. (a) What is the potential energy of the spring when it is stretched 0.200 m? (b) What is its potential energy when it is
An ideal spring of negligible mass is 12.00 cm long when nothing is attached to it. When you hang a 3.15-kg weight from it, you measure its length to be 13.40 cm. If you wanted to store 10.0 J of
A spring stores potential energy Uo when it is compressed a distance xo from its uncompressed length. (a) In terms of Uo, how much energy does it store when it is compressed (i) twice as much and
A slingshot will shoot a l0-g pebble 22.0 m straight up. (a) How much potential energy is stored in the slingshot's rubber band? (b) With the same potential energy stored in the rubber band, how
A spring of negligible mass has force constant k = 1600 N/m. (a) How far must the spring be compressed for 3.20 J of potential energy to be stored in it? (b) You place the spring vertically with
A 1.20-kg piece of cheese is placed on a vertical spring of negligible mass and force constant k = 1800 N/m that is compressed 15.0 cm. When the spring is released, how high does the cheese rise from
Consider the glider of Example 7.7 (Section 7.2) 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
Consider the glider of Example 7.7 (Section 7.2) 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
A 2.50-kg mass is pushed against a horizontal spring of force constant 25.0 N/cm on a frictionless air table. The spring is attached to the tabletop, and the mass is not attached to the spring in any
(a) For the elevator of Example 7.9 (Section 7.2), 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 elevators 1.00 m below point 1 in
You are asked to design a spring that will give a 1160-kg satellite a speed of 2.50 m/ s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5.00g.
A 75-kg roofer climbs a vertical 7.0-m ladder to the flat roof of a house. He then walks 12 m on the roof, climbs down another vertical 7.0-m ladder, and finally walks on the ground back to his
A 10.0-kg box is palled by a horizontal wire in a circle on a rough horizontal surface for which the coefficient of kinetic friction is 0.250. Calculate the work done by friction during one complete
In an experiment, one of the forces exerted on a proton is F = -ax2i, where a = 12 N/m2. (a) How much work does F do when the proton moves along the straight-line path from the point (0.10m, 0) to
A 0.60-kg book slides on a horizontal table. The kinetic friction force on the book has magnitude 1.2 N. (a) How much work is done on the book by friction during a displacement of 3.0 m to the
You are three friends stand at the comers of a square whose sides are S.O m long in the middle of the gym floor, as shown in Fig. 7.26. You rake your physics book and push it from one person to the
A block with mass m is attached to an ideal spring that has force constant k. (a) The block moves from x, to x" where x, > x,. How much work does the spring force do during this disparagement?
The potential energy of a pair of hydrogen atoms separated by a large distance X is given by Vex) = -c61x6, where Co is a positive constant. What is the force that one atom exerts on the other? Is
A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy vex) given by v(x) = ax', where a = 1.20 11m'. What is the force (magnitude and
Gravity in One Dimension two point masses, ml and m2, lie on the x-axis, with m, held in place at the origin and m, at position x and free to move. The gravitational potential energy of these masses
Gravity in Two Dimensions Two point masses, m, and m2, lie in the xy-plane, with m, held in place at the origin and m2 free to move a distance r away at a point P having coordinates X and y (Fig.
An object moving in the xy-plane is acted on by a conservative force described by the potential-energy function V(x, y) = aUlx2 + l/y2), where a is a positive constant. Derive an expression for the
The potential energy of two atoms in a diatomic molecule is approximated by V(r) = a/r12 - b/r2, where r is the spacing between atoms and a and b are positive constants. (a) Find the force F( r) on
A marble moves along the x-axis. The potential-energy function is shown in Fig.(a) At which of the labeled x-coordinates is the force on the marble zero?(b) Which of the labeled x-coordinates is a
At a construction site, a 65.O-kg bucket of concrete hangs from a light (but strong) cable that passes over a light friction-free pulley and is connected to an SO.O-kg box on a horizontal roof (Fig.
Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. The masses are released from rest, and the
Legal Physics In an auto accident, a car hit a pedestrian and the driver then slammed on the brakes to stop the car. During the subsequent trial, the driver's lawyer claimed that he was obeying the
A 2.00-kg block is pushed against a spring with negligible mass and force constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, horizontal surface
A block with mass 0.50 kg is forced against a horizontal spring of negligible mass, compressing the spring a distance of 0.20 m (Fig. 7.31). When released, the block moves 00 a horizontal tabletop
On a horizontal surface, a crate with mass 50.0 kg is placed against a spring that stores 360 of energy. The spring is released, and the crate slides 5.60 m before coming to rest. What is the speed
Bouncing Ball A 650-gram rubber ball is dropped from an initial height of 250 m, and on each bounce it returns to 75% of its previous height (a) What is the initial mechanical energy of the ball,
Riding a Loop-the-Loop A car in an amusement park ride rolls without friction around the track shown in Fig. 7.32. It starts from rest at point A at a height h above the bottom of the loop. Treat the
A 2.9-kg piece of wood slides on the surface shown in Fig. 7.33 The curved sides are perfectly smooth, but the rough horizontal bottom is 30 m long and has a kinetic friction coefficient of 0.20 with
Up and Down the Hill. A 28-kg rock approaches the foot of a hill with a speed of 15 m/s. This hill slopes upward at a constant angle of 40.0" above the horizontal. The coefficients of static and
A 15.0-kg stone slides down a snow-covered hill (Fig. 7.34), leaving point A with a speed of 10.0 m/s. There is no friction on the hill between points A and B, but there is friction on the level
A 2.8-kg block slides over the smooth, icy hill shown in Fig. 7.35. The top of the hill is horizontal and 70 m higher than its base. What minimum speed must the block have at the base of the hill so
Bungee Jump a bungee cord is 30.0 m long and, when stretched a distance x, it exerts a restoring force of magnitude. Your father-in-law (mass 95.0 kg) stands on a platform 45.0 m above the ground,
Ski Jump Ramp. You are designing a ski jump ramp for the next Water Olympics. You need to calculate the vertical height h from the starting gate to the bottom of the ramp. The skiers push off hard
The Great Sandini is a 6O-kg circus performer who is shot from a cannon (actually a spring gun). You don't find many men of his caliber, so you help him design a new gun. This new gun has a very
You are designing a delivery ramp for crates containing exercise equipment The l470-N crates will move at 1.8 m/s at the top of a ramp that slopes downward at 22.0°. The ramp exerts a 550-N kinetic
A system of two paint buckets connected by a lightweight rope is released from rest with the 12.0-kg bucket 2.00 m above the floor (Fig. 7.36). Use the principle of conservation of energy to find the
A 1500-kg rocket is to be launched with an initial upward speed of 50.0 m/s. In order to assist its engines, the engineers will start it from rest on a ramp that rises 53° above the horizontal
A machine part of mass m is attached to a horizontal ideal spring of force constant k that is attached to the edge of a friction free horizontal surface. The part is pushed against the spring,
A wooden rod of negligible mass and length 80.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.500 kg clings to one end of the stick, and a mouse with mass 0.200 kg
A O.100-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
These data are from 8 computer simulation for 8 batted baseballs with mass 0.1451rg, including air resistance:(a) How much work was done by the air on the baseball as it moved from its initial
Down the Pole a fireman of mass m slides a distance d down 8 poles he starts from rest. Removes as fast at the bottom as if he had stepped off a platform a distance h s d shoves the ground and
A 6Cl.O-kg skier starts from rest at the top of a ski slope 65.0 m high. (a) H frictional forces do 10.5 k1 of work on her as she descends bow fast is she going at 1he bottom of 1he slope? (b)
A skier starts at the top of a very large, frictionless snowball, with a very small initial speed, and skis straight down 1he side (Fig. 7.38). At what point does she lose contact with the snowball
A rock is tied to a cord and the other end of the cord is held fixed. The rock is given an initial tangential velocity that causes it to rotate in a vertical circle. Prove that the tension in the
In a truck-loading station at a post office a small O.200-kg Package is released from rest at point A on a track that is one-quarter of a circle with radius 1.60 m (Fig. 7.39). The size of the
A truck with mass m has a brake failure while going down an icy mountain road of constant downward slope angle a (Fig. 7.40). Initially the truck is moving downhill at speed vo. After careening
A certain spring is found not to obey Hooke's law; it exerts a restoring force Fx(x) = -ax _1Jx2 if it is stretched or compressed where a - 60.0 N/m and f3 - 18.0 N/m2. The mass of 1he spring is
A variable force F is maintained tangent to a frictionless, semicircular surface (Fig. 7 AI). By slow variations in the force a block with weight w is moved, and the spring to which it is attached is
A 0.150-kg block of ice is placed against a horizontal, compressed spring mounted on a horizontal tabletop that is 1.20 m above the floor. The spring has force constant 1900 N/m and is initially
A 3.00-kg block is connected to two ideal horizontal springs having force constants k, = 25.0 N/cm and k2 = 20.0N/cm (Fig. 7.42). The system is initially in equilibrium on a horizontal, frictionless
An experimental apparatus with mass m is placed on a vertical spring of negligible mass and pushed down until the spring is compressed a distance x. The apparatus is then released and reaches its
If a fish is attached to a vertical spring and slowly lowered to its equilibrium position, it is found to stretch the spring by an amount d. If the same fish is attached to the end of the unscratched
A wooden block with mass 1.50 kg is placed against a compressed spring at the bottom of an incline of slope 30.00 (point A). When the spring is released, it projects the block up the incline. At
A 2.00-kg package is released on a 53.10 incline 4.00 m from a long spring with force constant 120 N/m that is attached at the bottom of the incline (Fig. 7.43). The coefficients of friction between
A 0.500-kg block, attached to a spring with length 0.60 m and force constant 40.0 N/m, is at rest with the back of the block at point A on a frictionless, horizontal air table (Fig. 7.44). The mass
Fraternity Physics the brothers of Iota Eta Pi fraternity build a platform, supported at all four comers by vertical springs, in the basement of their frat house. A brave fraternity brother wearing a
A particle with mass m is acted on by a conservative force and moves along a path given by x = xo cos w0t and y = yosinwot, where x, yo, and wo are constants. (a) Find the components of the force
When it is burned, 1 gallon of gasoline produces 1.3 x 108 I of energy. A 1500-kg car accelerates from rest to 37 m/s in 10 s. The engine of this car is only 15% efficient (which is typical), meaning
A hydroelectric dam holds back a lake of surface area 3.0 X 106 m2 that has vertical sides below the water level. The water level in the lake is 150 m above the base of the dam. When the water passes
How much total energy is stored in the lake in Problem 7.79? As in that problem, take the gravitational potential energy to be zero at the base of the dam. Express your answer in joules and in
Gravity in Three Dimensions a point mass ml is held in place at the origin, and another point mass m2 is free to move a distance r away at a point P having coordinates x, y, and z. The gravitational
(a) Is the force F = Cy2j, where C is a negative constant with units of N/m2 , conservative or non-conservative? Justify your answer. (b) Is the force F = Cy2i, where C is a negative constant with
A cutting tool under microprocessor control has several forces acting on it. One force is F = _axy2j, a force in the negative y-direction whose magnitude depends on the position of the tool. The
An object has several forces acting on it. One force is F = axfi, a force in the x-
A Hooke's law force -Toe and a constant conservative force F in the +x-direction act on an atomic ion (a) Show that a possible potential-energy function for this combination of forces is U(x) = Toe
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. 7.45. The particle is
A proton with mass m moves in one dimension. The potential-energy function is U(x) = alx2- B/x, where a and p are positive constants. The proton is released from rest at Xo = alp.(a) Show that U(x)
(a) What is the magnitude of the momentum of a 10,000-kg truck whose speed is 12.0 m/s? (b) What speed would a 2,000-kg SUV have to attain in order to have (i) the same moment? (ii) the same
In Conceptual Example 8.1 (Section 8.1), show that the iceboat with mass 2m has V 2 times as much moment at the finish line as does the iceboat with mass m.
(a) Show that the kinetic energy K and the momentum magnitude p of a particle with mass m are related by K = p2/2m. (b) A 0.040-kg cardinal (Richmondena cardinalis) and a 0.145-kg baseball have the
In a certain men's track and field event, the shotput has a mass of 7.30 kg and is released with a speed of 15.0 m/s at 40.0 above the horizontal over a man's straight left leg. What are the initial
One 110-kg football lineman is running to the right at 2.75 m/s while another 125-kg lineman is running directly toward him at 2.60 m/s. What are? (a) The magnitude and direction of the net
Two vehicles are approaching an intersection. One is a 2500- kg pickup traveling at 14.0 m/s from east to west (the - x-direction), and the other is a 1500-kg sedan going from south to north (the
Force of B Golf Swing A 0.0450-kg golf ball initially at rest is given a speed of 25.0 m/s when a club strikes. If the club and ball are in contact for 2.00 ms, what average force acts on the ball?
Force of B Baseball Swing A baseball has mass 0.145 kg. (a) If the velocity of a pitched ball has a magnitude of 45.0 m/s and the batted ball's velocity is 55.0 m/s in the opposite direction, find
A 0.160-kg hockey puck is moving on an icy, frictionless, horizontal surface. At t = 0, the puck is moving to the right at 3.00 m/s. (a) Calculate the velocity of the puck (magnitude and direction)
An engine of the orbital maneuvering system (OMS) on a space shuttle exerts a force of (26,700 N)j for 3.90 s, exhausting a negligible mass of fuel relative to the 95,000-kg mass of the shuttle. (a)
At time t = 0, a 2150-kg rocket in outer space fires an engine that exerts an increasing force on it in the + x-direction. This force obeys the equation F. = At2, where t is time, and has a magnitude
A bat strikes a 0.145-kg baseball. Just before impact, the ball is traveling horizontally to the right at 50.0 m/s, and it leaves the bat traveling to the left at an angle of 30° above horizontal
A 2.00-kg stone is sliding to the right on a frictionless horizontal surface at 5.00 m/s when it is suddenly struck by an object that exerts a large horizontal force on it for a short period of time.
A 68.5-kg astronaut is doing a repair in space on the orbiting space station. She throws a 2.25-kg tool away from her at 3.20 m/s relative to the space station. With what speed and in what direction
Animal Propulsion Squids and octopuses propel themselves by expelling water. They do this by keeping water in a cavity and then suddenly contracting the cavity to force out the water through an
You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.400-kg ball that is
On a frictionless, horizontal air table, puck A (with mass 0.250 kg) is moving toward puck B (with mass 0.350 kg), which is initially at rest. After the collision, puck A has a velocity of 0.120m/s

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