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physics
mechanics
Physics 9th edition John D. Cutnell, Kenneth W. Johnson - Solutions
Refer to Multiple-Concept Example 10 for help in solving problems like this one. An ice skater is gliding horizontally across the ice with an initial velocity of +6.3 m/s. The coefficient of kinetic friction between the ice and the skate blades is 0.081, and air resistance is negligible. How much
The three objects in the drawing are connected by strings that pass over mass less and friction free pulleys. The objects move, and the coefficient of kinetic friction between the middle object and the surface of the table is 0.100.(a) What is the acceleration of the three objects?(b) Find the
A car travels at a constant speed around a circular track whose radius is 2.6 km. The car goes once around the track in 360 s. What is the magnitude of the centripetal acceleration of the car?
How long does it take a plane, traveling at a constant speed of 110 m/s, to fly once around a circle whose radius is 2850 m?
Computer-controlled display screens provide drivers in the Indianapolis 500 with a variety of information about how their cars are performing. For instance, as a car is going through a turn, a speed of 221 mi/h (98.8 m/s) and centripetal acceleration of 3.00 g (three times the acceleration due to
Review Example, which deals with the bobsled in Figure. Also, review Conceptual Example. The mass of the sled and its two riders in Figure is 350 kg. Find the magnitude of the centripetal force that acts on the sled during the turn with a radius of(a) 33 m and(b) 24m.
The hammer throw is a track-and-field event in which a 7.3-kg ball (the “hammer”) is whirled around in a circle several times and released. It then moves upward on the familiar curving path of projectile motion and eventually returns to earth some distance away. The world record for this
A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.70 × 104 m/s, and the radius of the orbit is 5.25 × 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.60 × 106 m. What is
A satellite moves on a circular earth orbit that has a radius of 6.7 × 106 m. A model airplane is flying on a 15-m guideline in a horizontal circle. The guideline is parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.
A motorcycle has a constant speed of 25.0 m/s as it passes over the top of a hill whose radius of curvature is 126 m. The mass of the motorcycle and driver is 342 kg. Find the magnitudes of.(a) The centripetal force and(b) The normal force that acts on the cycle.
For the normal force in Figure to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points. Suppose, for example, that the track has a radius of 3.0 m and that the driver goes past point 1 at the bottom with a speed of
In a skating stunt known as crack-the-whip, a number of skaters hold hands and form a straight line. They try to skate so that the line rotates about the skater at one end, who acts as the pivot. The skater farthest out has a mass of 80.0 kg and is 6.10 m from the pivot. He is skating at a speed of
A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to twice her weight as she goes through the dip. If r = 20.0 m, how fast is the roller coaster traveling at the bottom of
Each of the space shuttle’s main engines is fed liquid hydrogen by a high-pressure pump. Turbine blades inside the pump rotate at 617 rev/s. A point on one of the blades traces out a circle with a radius of 0.020 m as the blade rotates.(a) What is the magnitude of the centripetal acceleration
Redo Example 5, assuming that there is no upward lift on the plane generated by its wings. Without such lift, the guideline slopes downward due to the weight of the plane. For purposes of significant figures, use 0.900 kg for the mass of the plane, 17.0 m for the length of the guideline, and 19.0
During a tug-of-war, team A pulls on team B by applying a force of 1100 N to the rope between them. The rope remains parallel to the ground. How much work does team A do if they pull team B toward them a distance of 2.0 m?
Suppose in Figure that +1.10 × 103 J of work is done by the force F→ (magnitude = 30.0 N) in moving the suitcase a distance of 50.0 m. At what angle θ is the force oriented with respect to theground?
The drawing shows a plane diving toward the ground and then climbing back upward. During each of these motions, the lift L†’ force acts perpendicular to the displacement, which has the same magnitude, 1.7 × 103 m, in each case? The engines of the plane exert a thrust, which
It takes 185 kJ of work to accelerate a car from 23.0 m/s to 28.0 m/s. What is the car is mass?
The hammer throw is a track-and-field event in which a 7.3-kg ball (the “hammer”) starting from rest is whirled around in a circle several times and released. It then moves upward on the familiar curving path of projectile motion. In one throw, the hammer is given a speed of 29 m/s. For
A 6200-kg satellite is in a circular earth orbit that has a radius of 3.3 × 107 m. A net external force must act on the satellite to make it change to a circular orbit that has a radius of 7.0 × 106 m. What work W must the net external force do? Note that the work determined here is not the work
A sled is being pulled across a horizontal patch of snow. Friction is negligible. The pulling force points in the same direction as the sled’s displacement, which is along the + x-axis. As a result, the kinetic energy of the sled increases by 38%. By what percentage would the sled’s kinetic
A bicyclist rides 5.0 km due east, while the resistive force from the air has a magnitude of 3.0 N and points due west. The rider then turns around and rides 5.0 km due west, back to her starting point. The resistive force from the air on the return trip has a magnitude of 3.0 N and points due
A 55.0-kg skateboarder starts out with a speed of 1.80 m/s. He does + 80.0 J of work on himself by pushing with his feet against the ground. In addition, friction does - 265 J of work on him. In both cases, the forces doing the work are neoconservative. The final speed of the skateboarder is 6.00
A gymnast is swinging on a high bar. The distance between his waist and the bar is 1.1 m, as the drawing shows. At the top of the swing, his speed is momentarily zero. Ignoring friction and treating the gymnast as if all of his mass is located at his waist, find his speed at the bottom of theswing.
The drawing shows a skateboarder moving at 5.4 m/s along a horizontal section of a track that is slanted upward by 48° above the horizontal at its end, which is 0.40 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air
Two pole-vaulters just clear the bar at the same height. The first lands at a speed of 8.90 m/s, and the second lands at a speed of 9.00 m/s. The first vaulter clears the bar at a speed of 1.00 m/s. Ignore air resistance and friction and determines the speed at which the second vaulter clears the
A projectile of mass 0.750 kg is shot straight up with an initial speed of 18.0 m/s.(a) How high would it go if there were no air resistance?(b) If the projectile rises to a maximum height of only 11.8 m, determine the magnitude of the average force due to air resistance.
The (nonconservative) force propelling a 1.50 × 103-kg car up a mountain road does 4.70 × 106 J of work on the car. The car starts from rest at sea level and has a speed of 27.0 m/s at an altitude of 2.00 × 102 m above sea level. Obtain the work done on the car by the combined forces of friction
A truck is traveling at 11.1 m/s down a hill when the brakes on all four wheels lock. The hill makes an angle of 15.0° with respect to the horizontal. The coefficient of kinetic friction between the tires and the road is 0.750. How far does the truck skid before coming to a stop?
Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by seven-time-winner Lance Armstrong (m = 75.0 kg) is 6.50 W per kilogram of his body mass.(a) How much work does he do during a 135-km race in which his average speed
The motor of a ski boat generates an average power of 7.50 × 104 W when the boat is moving at a constant speed of 12 m/s. When the boat is pulling a skier at the same speed, the engine must generate an average power of 8.30 × 104 W. What is the tension in the towrope that is pulling the skier?
The drawing shows the force€“displacement graph for two different bows. These graphs give the force that an archer must apply to draw the bowstring.(a) For which bow is more work required to draw the bow fully from s = 0 to s = 0.50 m? Give your reasoning.(b) Estimate the additional work
A 2.00-kg rock is released from rest at a height of 20.0 m. Ignore air resistance and determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the following heights: 20.0, 10.0, and 0 m.
A water-skier, moving at a speed of 9.30 m/s, is being pulled by a towrope that makes an angle of 37.00 with respect to the velocity of the boat (see the drawing). The towrope is parallel to the water. The skier is moving in the same direction as the boat. If the tension in the towrope is 135 N,
A basketball of mass 0.60 kg is dropped from rest from a height of 1.05 m. It rebounds to a height of 0.57 m.(a) How much mechanical energy was lost during the collision with the floor?(b) A basketball player dribbles the ball from a height of 1.05 m by exerting a constant downward force on it for
A 46-kg skater is standing still in front of a wall. By pushing against the wall, she propels herself backward with a velocity of -1.2 m/s. Her hands are in contact with the wall for 0.80 s. Ignore friction and wind resistance. Find the magnitude and direction of the average force she exerts on the
A volleyball is spiked so that it incoming velocity of + 4.0 m/s is changed to an outgoing velocity of - 21 m/s. The mass of the volleyball is 0.35 kg. What impulse does the player apply to the ball?
A lumberjack (mass = 98 kg) is standing at rest on one end of a floating log (mass = 230 kg) that is also at rest. The lumberjack runs to the other end of the log, attaining a velocity of + 3.6 m/s relative to the shore, and then hops onto an identical floating log that is initially at rest.
A two-stage rocket moves in space at a constant velocity of 4900 m/s. The two stages are then separated by a small explosive charge placed between them. Immediately after the explosion, the velocity of the 1200-kg upper stage is 5700 m/s in the same direction as before the explosion. What is the
By accident, a large plate is dropped and breaks into three pieces. The pieces fly apart parallel to the floor. As the plate falls, its momentum has only a vertical component and no component parallel to the floor. After the collision, the component of the total momentum parallel to the floor must
A cannon of mass 5.80 × 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires an 85.0-kg shell horizontally with an initial velocity of + 551 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. What would
Batman (mass = 91 kg) jumps straight down from a bridge into a boat (mass = 510 kg) in which a criminal is fleeing. The velocity of the boat is initially + 11 m/s. What is the velocity of the boat after Batman lands in it?
A 5.00-kg ball, moving to the right at a velocity of +2.00 m/s on a frictionless table, collides head-on with a stationary 7.50-kg ball. Find the final velocities of the balls if the collision is.(a) Elastic and(b) Completely inelastic.
A projectile (mass = 0.20 kg) is fired at and embeds itself in a stationary target (mass = 2.50 kg). With what percentage of the projectile’s incident kinetic energy does the target (with the projectile in it) fly off after being struck?
A 50.0-kg skater is traveling due east at a speed of 3.00 m /s. A 70.0-kg skater is moving due south at a speed of 7.00 m/s. They collide and hold on to each other after the collision, managing to move off at an angle θ south of east, with a speed of vf. Find(a) The angle θ and(b) The speed vf,
Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a 1.50-kg ball swings downward and strikes a 4.60-kg ball that is at rest, as the drawing shows.(a) Using the principle of conservation of mechanical energy, find the speed of the 1.50 kg ball just before impact.(b) Assuming that
Consider the two moving boxcars in Example. Determine the velocity of their center of mass.(a) Before and(b) After the collision.(c) Should your answer in part (b) be less than, greater than, or equal to the common velocity vf of the two coupled cars after the collision? Justify your answer.
Two friends, Al and Jo, have a combined mass of 168 kg. At an ice skating rink, they stand close together on skates, at rest and facing each other, with a compressed spring between them. The spring is kept from pushing them apart because they are holding each other. When they release their arms, Al
One average force F→1 has a magnitude that is three times as large as that of another average force F→2. Both forces produce the same impulse. The average force F→1 acts for a time interval of 3.2ms. For what time interval does the average force F→2 act?
Two people are standing on a 2.0-m-long stationary platform, one at each end. The platform floats parallel to the ground on a cushion of air, like a hovercraft. One person throws a 6.0-kg ball to the other, who catches it. The ball travels nearly horizontally. Excluding the ball, the total mass of
A pitcher throws a curveball that reaches the catcher in 0.60 s. The ball curves because it is spinning at an average angular velocity of 330 rev/min (assumed constant) on its way to the catcher’s mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher
In Europe, surveyors often measure angles in grads. There are 100 grads in one-quarter of a circle. How many grads are in one radian?
A Ferris wheel rotates at an angular velocity of 0.24 rad/s. Starting from rest, it reaches its operating speed with an average angular acceleration of 0.030 rad/s2. How long does it take the wheel to come up to operating speed?
A stroboscope is a light that flashes on and off at a constant rate. It can be used to illuminate a rotating object, and if the flashing rate is adjusted properly, the object can be made to appear stationary. (a) What is the shortest time between flashes of light that will make a three-bladed
A gymnast is performing a floor routine. In a tumbling run, she spins through the air, increasing her angular velocity from 3.00 to 5.00 rev/s while rotating through one-half of a revolution. How much time does this maneuver take?
The wheels of a bicycle have an angular velocity of +20.0 rad/s. Then, the brakes are applied. In coming to rest, each wheel makes an angular displacement of +15.92 revolutions.(a) How much time does it take for the bike to come to rest?(b) What is the angular acceleration (in rad/s2) of each wheel?
A motorcyclist is traveling along a road and accelerates for 4.50 s to pass another cyclist. The angular acceleration of each wheel is +6.70 rad/s2, and, just after passing, the angular velocity of each wheel is +74.5 rad/s, where the plus signs indicate counterclockwise directions. What is the
A child, hunting for his favorite wooden horse, is running on the ground around the edge of a stationary merry-go-round. The angular speed of the child has a constant value of 0.250 rad/s. At the instant the child spots the horse, one-quarter of a turn away, the merry-go-round begins to move (in
A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon “string” that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 47rev/s, and its tip has a tangential speed of 54 m/s. What is the length of the rotating
A baseball pitcher throws a baseball horizontally at a linear speed of 42.5 m/s (about 95 mi/h). Before being caught, the baseball travels a horizontal distance of 16.5 m and rotates through an angle of 49.0 rad. The baseball has a radius of 3.67 cm and is rotating about an axis as it travels, much
A racing car travels with a constant tangential speed of 75.0 m/s around a circular track of radius 625m. Find (a) The magnitude of the car’s total acceleration and (b) The direction of its total acceleration relative to the radial direction.
The earth orbits the sun once a year (3.16 × 107s) in a nearly circular orbit of radius 1.50 × 1011 m. With respect to the sun, determine (a) The angular speed of the earth, (b) The tangential speed of the earth, and (c) The magnitude and direction of the earth’s centripetal acceleration.
The sun has a mass of 1.99 × 1030 kg and is moving in a circular orbit about the center of our galaxy, the Milky Way. The radius of the orbit is 2.3 × 104 light-years (1 light-year = 9.5 × 1015 m), and the angular speed of the sun is 1.1 × 10-15 rad/s.(a) Determine the tangential speed of the
A motorcycle accelerates uniformly from rest and reaches a linear speed of 22.0 m/s in a time of 9.00 s. The radius of each tire is 0.280 m. What is the magnitude of the angular acceleration of each tire?
The penny-farthing is a bicycle that was popular between 1870 and 1890. As the drawing shows, this type of bicycle has a large front wheel and a small rear wheel. During a ride, the front wheel (radius = 1.20 m) makes 276 revolutions. How many revolutions does the rear wheel (radius = 0.340 m)make?
A 220-kg speedboat is negotiating a circular turn (radius = 32 m) around a buoy. During the turn, the engine causes a net tangential force of magnitude 550 N to be applied to the boat. The initial tangential speed of the boat going into the turn is 5.0 m/s. (a) Find the tangential acceleration. (b)
An electric fan is running on HIGH. After the LOW button is pressed, the angular speed of the fan decreases to 83.8 rad/s in 1.75 s. The deceleration is 42.0 rad/s2. Determine the initial angular speed of the fan.
A compact disc (CD) contains music on a spiral track. Music is put onto a CD with the assumption that, during playback, the music will be detected at a constant tangential speed at any point. Since vT = rω, a CD rotates at a smaller angular speed for music near the outer edge and a larger angular
The wheel of a car has a radius of 0.350 m. The engine of the car applies a torque of 295 N · m to this wheel, which does not slip against the road surface. Since the wheel does not slip, the road must be applying a force of static friction to the wheel that produces a counter torque. Moreover,
You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has a magnitude of 45 N · m. Using the data in the drawing, determine the magnitude F of the force that you must exert on thewrench.
The drawing shows a jet engine suspended beneath the wing of an airplane. The weight W†’ of the engine is 10 200 N and acts as shown in the drawing. In flight the engine produces a thrust T†’ of 62 300 N that is parallel to the ground. The rotational axis in the drawing is
A pair of forces with equal magnitudes, opposite directions, and different lines of action is called a €œcouple.€ When a couple acts on a rigid object, the couple produces a torque that does not depend on the location of the axis. The drawing shows a couple acting on a tire
A hiker, who weighs 985 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3610 N, and rests on two concrete supports, one at each end. He stops one-fifth of the way along the bridge. What is the magnitude of the force that a concrete support
Review Multiple-Concept Example before beginning this problem. A sport utility vehicle (SUV) and a sports car travel around the same horizontal curve. The SUV has a static stability factor of 0.80 and can negotiate the curve at a maximum speed of 18 m/s without rolling over. The sports car has a
A uniform board is leaning against a smooth vertical wall. The board is at an angle θ above the horizontal ground. The coefficient of static friction between the ground and the lower end of the board is 0.650. Find the smallest value for the angle θ, such that the lower end of the board does not
A 1220-N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A 1960-N crate hangs from the far end of the beam. Using the data shown in the drawing, find(a) The magnitude of the tension in the wire and(b) The magnitudes of the horizontal and vertical
Two vertical walls are separated by a distance of 1.5 m, as the drawing shows. Wall 1 is smooth, while wall 2 is not smooth. A uniform board is propped between them. The coefficient of static friction between the board and wall 2 is 0.98. What is the length of the longest board that can be propped
Multiple-Concept Example offers useful background for problems like this. A cylinder is rotating about an axis that passes through the center of each circular end piece. The cylinder has a radius of 0.0830 m, an angular speed of 76.0 rad/s, and a moment of inertia of 0.615 kg · m2. A brake shoe
A particle is located at each corner of an imaginary cube. Each edge of the cube is 0.25 m long, and each particle has a mass of 0.12 kg. What is the moment of inertia of these particles with respect to an axis that lies along one edge of the cube?
Two thin rectangular sheets (0.20 m × 0.40 m) are identical. In the first sheet the axis of rotation lies along the 0.20-m side, and in the second it lies along the 0.40-m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 8.0
A stationary bicycle is raised off the ground, and its front wheel (m = 1.3 kg) is rotating at an angular velocity of 13.1 rad /s (see the drawing). The front brake is then applied for 3.0 s, and the wheel slows down to 3.7 rad/s. Assume that all the mass of the wheel is concentrated in the rim,
Three objects lie in the x, y plane. Each rotates about the z-axis with an angular speed of 6.00 rad/s. The mass m of each object and its perpendicular distance r from the z-axis are as follows: (1) m1 = 6.00 kg and r1 = 2.00 m, (2) m2 = 4.00 kg and r2 = 1.50 m, (3) m3 = 3.00 kg and r3 = 3.00 m.
A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned
A bowling ball encounters a 0.760-m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 3.50 m/s at the bottom of the rise. Find the translational
Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.4 kg·m2 and an angular velocity of +7.2 rad/s. Disk B is rotating with an angular velocity of -9.8 rad/s. The two disks are then linked together without the aid of any external torques, so that they rotate as a single
The drawing shows a lower leg being exercised. It has a 49-N weight attached to the foot and is extended at an angle θ with respect to the vertical. Consider a rotational axis at the knee.(a) When θ = 90.0°, find the magnitude of the torque that the weight creates.(b)
A rotating door is made from four rectangular sections, as indicated in the drawing. The mass of each section is 85 kg. A person pushes on the outer edge of one section with a force of F = 68 N that is directed perpendicular to the section. Determine the magnitude of the door’s
In outer space, two identical space modules are joined together by a mass less cable. These modules are rotating about their center of mass, which is at the center of the cable because the modules are identical (see the drawing). In each module, the cable is connected to a motor, so that the
A hand exerciser utilizes a coiled spring. A force of 89.0 N is required to compress the spring by 0.0191 m. Determine the force needed to compress the spring by 0.0508 m.
A person who weighs 670 N steps onto a spring scale in the bathroom, and the spring compresses by 0.79 cm.(a) What is the spring constant?(b) What is the weight of another person who compresses the spring by 0.34 cm?
In 0.750 s, a 7.00-kg block is pulled through a distance of 4.00 m on a frictionless horizontal surface, starting from rest. The block has a constant acceleration and is pulled by means of a horizontal spring that is attached to the block. The spring constant of the spring is 415 N/m. By how much
A small ball is attached to one end of a spring that has an unstrained length of 0.200 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 3.00 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch
When responding to sound, the human eardrum vibrates about its equilibrium position. Suppose an eardrum is vibrating with amplitude of 6.3 × 10-7 m and a maximum speed of 2.9 × 10-3 m/s.(a) What is the frequency (in Hz) of the eardrum’s vibration?(b) What is the maximum acceleration of the
A spring stretches by 0.018 m when a 2.8-kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is f = 3.0 Hz?
A vertical spring with a spring constant of 450 N/m is mounted on the floor. From directly above the spring, which is unstrained, a 0.30-kg block is dropped from rest. It collides with and sticks to the spring, which is compressed by 2.5 cm in bringing the block to a momentary halt. Assuming air
A 1.00 × 10-2 -kg block is resting on a horizontal frictionless surface and is attached to a horizontal spring whose spring constant is 124 N/m. The block is shoved parallel to the spring axis and is given an initial speed of 8.00 m/s, while the spring is initially unstrained. What is the
A spring is compressed by 0.0620 m and is used to launch an object horizontally with a speed of 1.50 m/s. If the object were attached to the spring, at what angular frequency (in rad/s) would it oscillate?
A 70.0-kg circus performer is fired from a cannon that is elevated at an angle of 40.0 above the horizontal. The cannon use strong elastic bands to propel the performer, much in the same way that a slingshot fires a stone. Setting up for this stunt involves stretching the bands by 3.00 m from their
A tow truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 0.50 cm. When the car just begins to move, the tension in the cable is 890 N. How much has the cable stretched?
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