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physics
mechanics
Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions
Two blocks, of weights 3.6 N and 7.2 N, are connected by a mass less string and slide down a 30o inclined plane. The coefficient of kinetic friction between the lighter block and the plane is 0.10; that between the heavier block and the plane is 0.20. Assuming that the lighter block leads,
Figure shows three crates being pushed over a concrete floor by a horizontal force F of magnitude 440N. The masses of the crates are m1= 30.0kg, m2= 10.0kg, and m3= 20.0kg. The coefficient of kinetic friction between the floor and each of the crates is 0.700.? (a) What is the magnitude F32 of the
Body A in Figure weighs 102 N, and body B weighs 32 N. The coefficients of friction between A and the incline are ?s= 0.56 and ?k= 0.25. Angle θ is 40o. Let the positive direction of an x axis be up the incline. In unit-vector notation, what is the acceleration of A it A is initially (a) At
In Figure two blocks are connected over a pulley. The mass of block A is 10 kg, and the coefficient of kinetic friction between A and the incline is 0.20. Angle θ of the incline is 30o. Block 4 slides down the incline at constant speed. What is the mass of block B?
In Figure, blocks A and B have weights of 44 N and 22 N, respectively.? (a) Determine the minimum weight of block C to keep A from sliding if ?s between A and the table is 0.20.? (b) Block C suddenly is lifted off A. What is the acceleration of block A if ?k between A and the table is 0.15?
A toy chest and its contents have a combined weight of 180N. The coefficient of static friction between toy chest and floor is 0.42.The child in Figure attempts to move the chest across the floor by pulling on an attached rope. (a) If θ is 42o, what is the magnitude of the force F that the child
The two blocks (m = 16 kg and M = 88 kg) in Fig. 6-39 are not attached to each other. The coefficient of static friction between the blocks is ?s= 0.38, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force F required to keep the smaller
In Figure, a slab of mass m1= 40 kg rests on a frictionless floor, and a block of mass m2= 10 kg rests on top of the slab. Between block and slab, the coefficient of static friction is 0.60, and the coefficient of kinetic friction is 0.40. The block is pulled by a horizontal force F- of magnitude
A 1000 kg boat is traveling at 90 km/h when its engine is shut off. The magnitude of the frictional force f k between boat and water is proportional to the speed v of the boat: fk = 70v, where y is in meters per second and fk is in new tons. Find the time required for the boat to slow to 45
The terminal speed of a sky diver is 160 km/h in the spread-eagle position and 310 km/h in the nosedive position. Assuming that the diver's drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in the
Calculate the ratio of the drag force on a jet flying at 1000 km/h at an altitude of 10 km to the drag force on a prop-driven transport flying at half that speed and altitude. The density of air is 0.38 kg/m3 at 10 km and 0.67 kg/m3 at 5.0 km. Assume that the airplanes have the same effective
In downhill speed sking a skier is retarded by both the air drag force on the body and the kinetic frictional force on the skis. (a) Suppose the slope angle is θ = 40.0o, the snow is dry snow with a coefficient of kinetic friction µk = 0.0400, the mass of the skier and equipment is m = 85.0 kg,
Continuation of Problem 2, now assume that Eq. 6-14 gives the magnitude of the air drag force on the typical 20 kg stone, which presents to the wind a vertical cross-sectional area of 0.040 m2 and has a drag coefficient C of 0.80. Take the air density to be 1.21 kg/m3, and the coefficient of
Assume Eq. 6-14 gives the drag force on a pilot plus ejection seat just after they are ejected from a plane traveling horizontally at 1300 km/h. Assume also that the mass of the seat is equal to the mass of the pilot and that the drag coefficient is that of a sky diver. Making a reasonable guess of
What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29 km/h and the p, between tires and track is 0.32?
During an Olympic bobsled run, the Jamaican team makes a turn of radius 7.6 m at a speed of 96.6 km/h. What is their acceleration in terms of g?
A cat dozes on a stationary merry-go-round, at a radius of 5 .4 m from the center of the ride. Then the operator turns on the ride and brings it up to its proper turning rate of one complete rotation every 6.0 s. What is the least coefficient of static friction between the cat and the
Suppose the coefficient of static friction between the road and the tires on a car is 0.60 and the car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level curve of 30.5 m radius?
A circular-motion addict of mass 80 kg rides a Ferris wheel around in a vertical circle of radius 10 m at a constant speed of 6.1m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through? (b) The highest point of the
A roller-coaster car has a mass of 1200 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 18 m, its speed is not changing. At the top of the hill, what are the(a) Magnitude Fry and(b) Direction (up or down) of the normal force on the car from the
In Figure a car is driven at constant speed over a circular hill and then into a circular valley with the same radius. At the top of the hill, the normal force on the driver from the car seat is 0. The driver's mass is 70.0kg. What is the magnitude of the normal force on the driver from the seat
A police officer in hot pursuit drives her car through a circular turn of radius 300 m with a constant speed of 80.0 km/h. Her mass is 55.0 kg. What are? (a) The magnitude and (b) The angle (relative to vertical) of the net force of the officer on the car seat?
A student of weight 667 N rides a steadily rotatingFerris wheel (the student sits upright).At the highest point, the magnitude of the normal force F1u. on the student from the seat is 556 N.(a) Does the student feel "light" or "heavy" there? (b) What is the magnitude of Fr at the lowest point?
An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is 5.0kN, and the circle's radius is 10 m. At the top of the circle, what are the (a) Magnitude FB and (b) Direction (up or down) of the
An old streetcar rounds a flat corner of radius 9.1m, at 16km/h. What angle with the vertical will be made by the loosely hanging hand straps?
In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass m riding around a horizontal circle of radius r at speed v. What is the variation dF in the net force
An airplane is flying in a horizontal circle at a speed of 480 km/h (Figure). If its wings are tilted at angle ? = 40 to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an "aerodynamic lift" that is perpendicular
An 85.0 kg passenger is made to move along a circular path of radius r = 3.50 m in uniform circular motion.(a) Figure (a) is a plot of the required magnitude F of the net centripetal force for a range of possible values of the passenger's speed y. What is the plot's slope at v = 8.30 m/s?(b) Figure
A puck of mass m = 1.50kg slides in a circle of radius r = 20.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 2.50 kg by a cord through a hole in the table (Figure). What speed keeps the cylinder atrest?
Brake or turn? Figure 6-45 depicts an overhead view of a car's path as the car travels toward a wall. Assume that the driver begins to brake the car when the distance to the wall is d = 107 m, and take the car's mass as m = 1400 kg, its initial speed as v0 = 35 m/s, and the coefficient of static
A bolt is threaded onto one end of a thin horizontal rod, and the rod is then rotated horizontally about its other end. An engineer monitors the motion by flashing a strobe lamp onto the rod and bolt, adjusting the strobe rate until the bolt appears to be in the same eight places during each full
A banked circular highway curve is designed for traffic moving at 60 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off
In Figure a 1.34kg ball is connected by means of two mass less strings, each of length L = 1.70 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.70 m and are taut. The tension in the upper string is 35 N. What are the(a) Tension in the lower string,(b) Magnitude
Figure shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.040 kg, the string has length L = 0.90 m and negligible mass, and the bob
Continuation of Problems 2 and 39, another explanation is that the stones move only when the water dumped on the playa during a storm freezes into a large, thin sheet of ice. The stones are trapped in place in the ice. Then, as air flows across the ice during a wind, the air-drag forces on the ice
Engineering a highway curve if a car goes through a curve too fast, the car tends to slide out of the curve. For a banked curve with friction, a frictional force acts on a fast car to oppose the tendency to slide out of the curve; the force is directed down the bank (in the direction water would
In Figure the coefficient of kinetic friction between the block and inclined plane is 0.20, and angle ? is 60o. What are the(a) Magnitude a and(b) Direction (up or down the plane) of the block's acceleration if the block is sliding down the plane? What are?(c) A and(d) The direction if the block is
In Figure, block 1 of mass m1= 2.0kg and block 2 of mass m2= 3.0kg are connected by a string of negligible mass and are initially held in place. Block 2 is one a frictionless surface tilted at θ = 30o. The coefficient of kinetic friction between block 1 and the horizontal surface is 0.25. The
A block of mass m1= 4.0 kg is put on top of a block of mass mb= 5.0 kg. To cause the top block to slip on the bottom one while the bottom one is held fixed, a horizontal force of at least 12 N must be applied to the top block. The assembly of blocks is now placed on a horizontal, frictionless table
A box of canned goods slides down a ramp from street level into the basement of a grocery store with acceleration 0.15 m/s2 directed down the ramp. The ramp makes an angle of 40° with the horizontal. What is the coefficient of kinetic friction between the box and the ramp?
An 8.00 kg block of steel is at rest on a horizontal table. The coefficient of static friction between the block and the table is 0.450. A force is to be applied to the block. To three significant figures, what is the magnitude of that applied force if it puts the block on the verge of sliding when
In Figure a box of ant aunts (total mass m1= 1.65 kg) and a box of ant uncles (total mass m2= 3.30 kg) slide down an inclined plane while attached by a mass less rod parallel to the plane. The angle of incline is θ = 30.0o. The coefficient of kinetic friction between the aunt box and the incline
In Figure a crate slides down an inclined right-angled trough. The coefficient of kinetic friction between the crate and the trough ir ?k.What is the acceleration of the crate in terrns of ?k, θ, and g?
A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches 30°, the box starts to slip, and it then slides 2.5
A locomotive accelerates a 25-car train along a level track. Every car has a mass of 5.0 x 104 kg and is subject to a frictional force f = 250v, where the speed v is in meters per second and the force f is in Newton’s. At the instant when the speed of the train is 30 km/h, the magnitude of its
A house is built on the top of a hill with a nearby slope at angle θ = 45o(Figure). An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the coefficient of static friction between two such layers
What is the terminal speed of a 6.00 kg spherical ball that has a radius of 3.00 cm and a drag coefficient of 1.60? The density of the air through which the ball falls is 1.20 kg/m3.
A high-speed railway car goes around a flat, horizontal circle of radius 470 m at a constant speed. The magnitudes of the horizontal and vertical components of the force of the car on a 51.0 kg passenger are 210N and 500N, respectively.(a) What is the magnitude of the net force (of all the forces)
An 11 kg block of steel is at rest on a horizontal table. The coefficient of static friction between block and table is 0.52. (a) What is the magnitude of the horizontal force that will put the block on the verge of moving? (b) What is the magnitude of a force acting upward 60o from the horizontal
Calculate the magnitude of the drag force on a missile 53 cm in diameter cruising at 250 m/s at low altitude, where the density of air is 1.2 kg/m3. Assume C = 0.75.
A bicyclist travels in a circle of radius 25.0 m at a constant speed of 9.00 m/s. The bicycle-rider mass is 85.0 kg. Calculate the magnitudes of (a) The force of friction on the bicycle from the road and (b) The net force on the bicycle from the road.
A 110 g hockey puck sent sliding over ice is stopped in 15 m by the frictional force on it from the ice. (a) If its initial speed is 6.0m/s, what is the magnitude of the frictional force?(b) What is the coefficient of friction between the puck and the ice?
In Figure a 49 kg rock climber is climbing a "chimney." The coefficient of static friction between her shoes and the rock is 1.2; between her back and the rock is 0.80. She has reduced her push against the rock until her back and her shoes are on the verge of slipping.(a) Draw a free-body diagram
A 5.00 kg stone is rubbed across the horizontal ceiling of a cave passageway (Fig. 6-56). If the coefficient of kinetic friction is 0.65 and the force applied to the stone is angled at θ = 10.0?, what must the magnitude of the force be for the stone to move at constant velocity?
Block A in Figure has mass mA = 4.0kg, and block B has mass mB = 2.0kg. The coefficient of kinetic friction between block B and the horizontal plane is ?k = 0.50. The inclined plane is frictionless and at angle ? = 30o. The pulley serves only to change the direction of the cord connecting the
A ski that is placed on snow will stick to the snow. However, when the ski is moved along the snow, the rubbing warms and partially melts the snow, reducing the coefficient of kinetic friction and promoting sliding. Waxing the ski makes it water repellent and reduces friction with the resulting
Playing near a road construction site, a child falls over a barrier and down onto a dirt slope that is angled downward at 35o to the horizontal. As the child slides down the slope, he has an acceleration that has a magnitude of 0.50 m/s2 and that is directed up the slope. What is the coefficient of
In Figure a stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius R = 250 m. What is the greatest speed at which he can drive without the car leaving the road at the top of thehill?
A car weighing 10.7kN and traveling at 13.4 m/s without negative lift attempts to round an unbanked curve with a radius of 61.0 m. (a) What magnitude of the frictional force on the tires is required to keep the car on its circular path? (b) If the coefficient of static friction between the tires
A 100 N force, directed at an angle θ above a horizontal floor, is applied to a25.0 kg chair sitting on the floor. If θ = 0o, what are (a) The horizontal component Fh of the applied force and (b) The magnitude Fry of the normal force of the floor on the chair? If θ = 30.0o, what
A student, crazed by final exams, uses a force P of magnitude 80 N and angle ? = 70o to push a 5.0 kg block across the ceiling of his room (Figure). If the coefficient of kinetic friction between the block and the ceiling is 0.40, what is the magnitude of the block's acceleration?
A certain string can withstand a maximum tension of 40 N without breaking. A child ties a 0.37 kg stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.91 m, slowly increasing the speed until the string breaks. (a) Where is the stone on its path when the
You must push a crate across a floor to a docking bay. The crate weighs 165 N. The coefficient of static friction between crate and floor is 0.510, and the coefficient of kinetic friction is 0.32. Your force on the crate is directed horizontally.(a) What magnitude of your push puts the crate on the
A child weighing 140 N sits at rest at the top of a playground slide that makes an angle of 25o with the horizontal. The child keeps from sliding by holding onto the sides of the slide. After letting go of the sides, the child has a constant acceleration of 0.86 m/s2 (down the slide, of course).
A filing cabinet weighing 556N rests on the floor. The coefficient of static friction between it and the floor is 0.68, and the coefficient of kinetic friction is 0.56. In four different attempts to move it, it is pushed with horizontal forces of magnitudes? (a) 222N, (b) 334N, (c) 445N, and (d)
A sling-thrower puts a stone (0.250 kg) in the sling's pouch (0.010 kg) and then begins to make the stone and pouch move in a vertical circle of radius 0.650 m. The cord between the pouch and the person's hand has negligible mass and will break when the tension in the cord is 33.0 N or more.
A four-person bobsled (total mass = 630 kg) comes down a straightaway at the start of a bobsled run. The straightaway is 80.0m long and is inclined at a constant angle of 10.2o with the horizontal Assume that the combined effects of friction and air drag produce on the bobsled a constant force of
In Figure force F is applied to a crate of mass m on a floor where the coefficient of static friction between crate and floor is ?s. Angle ? is initially 0o but is gradually increased so that the force vector rotates clockwise in the figure. During the rotation, the magnitude F of the force is
In the early afternoon, a car is parked on a street that runs down a steep hill, at an angle of 35.0o relative to the horizontal. Just then the coefficient of static friction between the tires and the street surface is 0.725. Later, after nightfall, a sleet storm hits the area, and the coefficient
In Figure block 1 of mass m1 = 2.0 kg and block 2 of mass m2 = 2.0 are connected by a string of negligible mass. Block 2 is pushed by force F of magnitude 20N and angle ? = 35o. The coefficient of kinetic friction between each block and the horizontal surface is 0.20. What is the tension in the
In Figure a fastidious worker pushes directly along the handle of a mop with a force F. The handle is at an angle ? with the vertical, and ?s and ?k are the coefficients of static and kinetic friction between the head of the mop and the floor. Ignore the mass of the handle and assume that all the
A circular curve of highway is designed for traffic moving at 60 km/h. Assume the traffic consists of cars without negative lift. (a) If the radius of the curve is 150 m, what is the correct angle of banking of the road? (b) If the curve were not banked, what would be the minimum coefficient of
A block slides with constant velocity down an inclined plane that has slope angle 0. The block is then projected up the same plane with an initial speed v0. (a) How far up the plane will it move before coming to rest?(b) After the block comes to rest, will it slide down the plane again? Give an
In Fig. 6-63, a block weighing 22 N is held at rest against a vertical wall by a horizontal force F of magnitude 60 N. The coefficient of static friction between the wall and the block is 0.55, and the coefficient of kinetic friction between them is 0.38. In six experiments, a second force P is
When a small 2.0 g coin is placed at a radius of 5.0 cm on a horizontal turntable that makes three full revolutions in 3.14 s, the coin does not slip. What are? (a) The coin's speed, the (b) Magnitude and (c) Direction (radially inward or outward) of the coin's acceleration, and the (d) Magnitude
A child places a picnic basket on the outer rim of a merry-go-round that has a radius of 4.6 m and revolves once every 30 s. (a) What is the speed of a point on that rim?(b) What is the lowest value of the coefficient of static friction between basket and merry-go-round that allows the basket to
A 1.5 kg box is initially at rest on a horizontal surface n at t = 0 a horizontal force F = (1.8t)i N (with t in seconds) is applied to the box. The acceleration of the box as a function of time t is given by a = 0 for 0 < t < 2.8s and a = (1.2t – 2.4)i m/s2 for t > 2.8 s. (a) What is the
A trunk with a weight of 220 N rests on the floor. The coefficient of static friction between the trunk and the floor is 0.41, and the coefficient of kinetic friction is 0.32. (a) What is the magnitude of the minimum horizontal force with which a person must push on the trunk to start it moving?
A warehouse worker exerts a constant horizontal force of magnitude 85 N on a 40 kg box that is initially at rest on the horizontal floor of the warehouse. When the box has moved a distance of 1.4 m, its speed is 1.0 m/s. What is the coefficient of kinetic friction between the box and the floor?
Imagine that the standard kilogram is placed on Earth's equator, where it moves in a circle of radius 6.40 x 106 m (Earth's radius) at a constant speed of 465 m/s due to Earth's rotation. (a) What is the magnitude of the centripetal force on the standard kilogram during the rotation? Imagine that
As a 40 N block slides down a plane that is inclined at 25o to the horizontal its acceleration is 0.80 m/s2, directed up the plane. What is the coefficient of kinetic friction between the block and the plane?
Luggage is transported from one location to another in an airport by a conveyor belt. At a certain location, the belt moves down an incline that makes an angle of.2.5o with the horizontal. Assume that with such a slight angle there is no slipping of the luggage. Determine the magnitude of the
In Figure a 5.0 kg block is sent sliding up a plane inclined at ? = 37o while a horizontal force F of magnitude 50 N acts on it. The coefficient of kinetic friction between block and plane is 0.30. What are the?(a) Magnitude and?(b) Direction (up or down the plane) of the block's acceleration? The
On August 10, 1912, a large meteorite skipped across the atmosphere above the western United States and western Canada, much like a stone skipped across water. The accompanying fireball was so bright that it could be seen in the daytime sky and was brighter than the usual meteorite trail. The
If a Saturn V rocket with an Apollo spacecraft attached had a combined mass of 2.9 x 105 kg and reached a speed of 2.9 x 105 km/s, how much kinetic energy would it then have?
A proton (mass m = 1.67 x 10-27 kg) is being accelerated along a straight line at 3.6 x 1015 m/s2 in a machine. If the proton has an initial speed of 2.4 x 107 m/s and travels 3.5 cm, what then is? (a) Its speed and (b) The increase in its kinetic energy?
A force Fa is applied to a bead as the bead is moved along a straight wire through displacement + 5.0cm. The magnitude of Fa is set at a certain value, but the angle ? between Fa and the bead??s displacement can be chosen. Figure gives the work W done by Fa on the bead for a range ? values; W0 =
A father racing his son has half the kinetic energy of the son, who has half the mass of the father. The father speeds up by 1.0 m/s and then has the same kinetic energy as the son. What are the original speeds of? (a) The father and (b) The son?
A bead with mass 1.8 x 10-2kg is moving along a wire in the positive direction of an x axis. Beginning at time t = 0, when the bead passes through x = 0 with speed 12 m/s, a constant force acts on the bead. Figure indicates the bead's position at times t0?= 0, t1= 1.0 s, t2= 2.0 s, and t3?= 3.0 s.
The only force acting on a 2.0kg canister that is moving in an xy plane has a magnitude of 5.0 N. The canister initially has a velocity of 4.0 m/s in the positive x direction and some time later has a velocity of 6.0 m/s in the positive y direction. How much work is done on the canister by the 5.0N
A coin slides over a frictionless plane and across an xy coordinate system from the origin to a point with xy coordinates (3.0 m, 4.0 m) while a constant force acts on it. The force has magnitude 2.0 N and is directed at a counterclockwise angle of 100" from the positive direction of the x axis.
A 3.0 kg body is at rest on a frictionless horizontal air track when a constant horizontal force F acting in the positive direction of an x axis along the track is applied to the body. A stroboscopic graph of the position of the body as it slides to the right is shown in Figure. The force F is
A floating ice block is pushed through a displacement d = (15 m)i – (12m)j along a straight embankment by rushing water, which exerts a force F = (210 N)i – (150 N)j on the block. How much work does the force do on the block during the displacement?
A luge and its rider, with a total mass of 85 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 37 m/s. If a force slows them to a stop at a constant rate of 2.0 m/s2, (a) What magnitude F is required for the force, (b) What distance d do they travel while
An 8.0 kg object is moving in the positive direction of an x axis. When it passes through x = 0, a constant force directed along the axis begins to act on it. Figure gives its kinetic energy K versus position x as it moves from x = 0 to x = 5.0 m; K0 = 30.0J. The force continues to act. What is v
Figure shows three forces applied to a trunk that moves leftward by 3.00 m over a frictionless floor. The force magnitudes ate F1 = 5.00N, F2 = 9.00N, and F3 = 3.00 N, and the indicated angle is ? = 60.0o. During the displacement,(a) What is the net work done on the trunk by the three forces an(b)
A can of bolts and nuts is pushed 2.00 m along an x axis by a broom along the greasy (frictionless) floor of a car repair shop in a version of shuffleboard. Figure 7-29 gives the work W done on the can by the constant horizontal force from the broom, versus the can's position x. The scale of the
A 12.0 N force with a fixed orientation does work on a particle as the particle moves through displacement d = (2.00i – 4.00i + 3.00k) m. What is the angle between the force and the displacement if the change in the particle's kinetic energy is? (a) + 30.0 J and (b) – 30.0 J?
Figure 7 -30 shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but now moves across a frictionless floor. The force magnitudes are F1 = 3.00 N, F2 = 4.00 N, and F3 = l0.0 N, and the indicated angles are ?2 = 50.0o and ?3 = 35.0o. What is the
A helicopter lifts a72 kg astronaut 15 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/10. How much work is done on the astronaut by?(a) The force from the helicopter and (b) The gravitational force on her? Just before she reaches the helicopter, what is her?
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