A man of mass m1 = 70.0 kg is skating at v1 = 8.00 m/s behind his wife of mass m2 = 50.0 kg, who is skating at v2 = 4.00 m/s. Instead of passing her, he inadvertently collides with her. He grabs her around the waist, and they maintain their balance. (a) Sketch the problem with before - and - after diagrams, representing the skaters as blocks. (b) Is the collision best described as elastic, inelastic, or perfectly inelastic? Why? (c) Write the general equation for conservation of momentum in terms of m1, v1, m2, v2, and final velocity vf. (d) Solve the momentum equation for vf. (e) Substitute values, obtaining the numerical value for vf, their speed after the collision.
> Two blocks collide on a frictionless surface. After the collision, the blocks stick together. Block A has a mass M and is initially moving to the right at speed v. Block B has a mass 2M and is initially at rest. System C is composed of both blocks. (a) D
> A cannon is rigidly attached to a carriage, which can move along horizontal rails, but is connected to a post by a large spring, initially unstretched and with force constant k = 2.00 x 104 N/m, as in Figure P6.75. The cannon fires a 2.00 x 102-kg projec
> A car of mass m moving at a speed v1 collides and couples with the back of a truck of mass 2m moving initially in the same direction as the car at a lower speed v2. (a) What is the speed vf of the two vehicles immediately after the collision? (b) What is
> A small block of mass m1 = 0.500 kg is released from rest at the top of a curved wedge of mass m2 = 3.00 kg, which sits on a frictionless horizontal surface as in Figure P6.73a. When the block leaves the wedge, its velocity is measured to be 4.00 m/s to
> Two objects of masses m and 3m are moving toward each other along the x-axis with the same initial speed v0. The object with mass m is traveling to the left, and the object with mass 3m is traveling to the right. They undergo an elastic glancing collisio
> A block with mass m1 = 0.500 kg is released from rest on a frictionless track at a distance h1 = 2.50 m above the top of a table. It then collides elastically with an object having mass m2 = 1.00 kg that is initially at rest on the table, as shown in Fig
> Two blocks of masses m1 = 2.00 kg and m2 = 4.00 kg are each released from rest at a height of h = 5.00 m on a frictionless track, as shown in Figure P6.70, and undergo an elastic headon collision. (a) Determine the velocity of each block just before the
> A rigid body is rotating counterclockwise about a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid body. Which of the sets can occur only if the rigid body rotates thro
> Two blocks of masses m1 and m2 approach each other on a horizontal table with the same constant speed, v0, as measured by a laboratory observer. The blocks undergo a perfectly elastic collision, and it is observed that m1 stops but m2 moves opposite its
> An unstable nucleus of mass 1.7 x 10-26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 = 5.0 x 10-27 kg, moves in the positive y- direction with speed v1 = 6.0 x 106 m/s.
> A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2-kg physics textbook horizontally toward t
> A 0.400-kg blue bead slides on a frictionless, curved wire, starting from rest at point â’¶ in Figure P6.66, where h = 1.50 m. At point â’·, the bead collides elastically with a 0.600-kg green bead at rest. Find the maxi
> An amateur skater of mass M is trapped in the middle of an ice rink and is unable to return to the side where there is no ice. Every motion she makes causes her to slip on the ice and remain in the same spot. She decides to try to return to safety by rem
> A bullet of mass m and speed v passes completely through a pendulum bob of mass M as shown in Figure P6.64. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod of length, and negligible mass. What is the minimum value of
> A 2.0-g particle moving at 8.0 m/s makes a perfectly elastic head-on collision with a resting 1.0-g object. (a) Find the speed of each particle after the collision (b) Find the speed of each particle after the collision if the stationary particle has a m
> Consider a frictionless track as shown in Figure P6.62. A block of mass m1 = 5.00 kg is released from â’¶. It makes a head-on elastic collision at â’· with a block of mass m2 = 10.0 kg that is initially at rest. Calculat
> Most of us know intuitively that in a head-on collision between a large dump truck and a subcompact car, you are better off being in the truck than in the car. Why is this? Many people imagine that the collision force exerted on the car is much greater t
> In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a person’s heart in one stroke. This information can be obtained by means of a ballistocardiograph. The instrument works as follows: The subject
> Suppose an asteroid has a semimajor axis of 4 AU. How long does it take the asteroid to go around the Sun? (a) 2 years (b) 4 years (c) 6 years (d) 8 years
> A spaceship’s orbital maneuver requires a speed increase of 1.20 x 103 m/s. If its engine has an exhaust speed of 2.50 x 103 m/s, determine the required ratio Mi/Mf of its initial mass to its final mass. (The difference Mi - Mf equals the mass of the eje
> A spaceship at rest relative to a nearby star in interplanetary space has a total mass of 2.50 x 104 kg. Its engines fire at t = 0, steadily burning fuel at 76.7 kg/s with an exhaust speed of 4.25 x 103 m/s. Calculate the spaceship’s (a) Acceleration at
> A typical person begins to lose consciousness if subjected to accelerations greater than about 5g (49.0 m/s2) for more than a few seconds. Suppose a 3.00 x 104-kg manned spaceship’s engine has an exhaust speed of 2.50 x 103 m/s. What maximum burn rate |Δ
> NASA’s Saturn V rockets that launched astronauts to the moon were powered by the strongest rocket engine ever developed, providing 6.77 x 106 N of thrust while burning fuel at a rate of 2.63 x 103 kg/s. Calculate the engine’s exhaust speed.
> One of the first ion engines on a commercial satellite used Xenon as a propellant and could eject the ionized gas at a rate of 3.03 x 10-6 kg/s with an exhaust speed of 3.04 x 104 m/s. What instantaneous thrust could the engine provide?
> The Merlin rocket engines developed by SpaceX produce 8.01 x 105 N of instantaneous thrust with an exhaust speed of 3.05 x 103 m/s in vacuum. What mass of fuel does the engine burn each second?
> A billiard ball moving at 5.00 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.33 m/s at an angle of 30.0° with respect to the original line of motion. (a) Find the velocity (magnitude and direction) of the
> Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 13.0 m/s toward the east, and the other is traveling north with velocity v2i. Neither driver sees the other. The vehicles collide in the intersection and stick
> A 2.00 x 103-kg car moving east at 10.0 m/s collides with a 3.00 x 103-kg car moving north. The cars stick together and move as a unit after the collision, at an angle of 40.0° north of east and a speed of 5.22 m/s. Find the speed and direction of the 3.
> Identical twins, each with mass 55.0 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass 12.0 kg. She throws it horizontally at 3.00 m/s to Twin B. Neglecting any gravity effects,
> A planet has two moons with identical mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. The magnitude of the gravitational force exerted by the planet on Moon 2 is (a) Four times as large (b) Twice as large (c)
> A 90.0-kg fullback running east with a speed of 5.00 m/s is tackled by a 95.0-kg opponent running north with a speed of 3.00 m/s. (a) Why does the tackle constitute a perfectly inelastic collision? (b) Calculate the velocity of the players immediately af
> A billiard ball rolling across a table at 1.50 m/s makes a headon elastic collision with an identical ball. Find the speed of each ball after the collision (a) When the second ball is initially at rest, (b) When the second ball is moving toward the first
> A 25.0-g object moving to the right at 20.0 cm/s overtakes and collides elastically with a 10.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision.
> A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m1 = 48.0 kg travels in the positive x - direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane
> A tennis ball of mass 57.0 g is held just above a basketball of mass 590 g. With their centers vertically aligned, both balls are released from rest at the same time, falling through a distance of 1.20 m, as shown in Figure P6.45. (a) Find the magnitude
> A 1200-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9000-kg truck moving in the same direction at 20.0 m/s (Fig. P6.44). The velocity of the car right after the collision is 18.0 m/s to the e
> A 12.0-g bullet is fired horizontally into a 100-g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 150 N/m. The bullet becomes embedded in the block. If the bullet– block system
> An bullet of mass m = 8.00 g is fired into a block of mass M = 250 g that is initially at rest at the edge of a table of height h = 1.00 m (Fig. P6.42). The bullet remains in the block, and after the impact the block lands d = 2.00 m from the bottom of t
> A 0.030-kg bullet is fired vertically at 200 m/s into a 0.15-kg baseball that is initially at rest. How high does the combined bullet and baseball rise after the collision, assuming the bullet embeds itself in the ball?
> Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at 5.00 m/s as in Figure P6.4
> A ball is falling toward the ground. Which of the following statements are false? (a) The force that the ball exerts on Earth is equal in magnitude to the force that Earth exerts on the ball. (b) The ball undergoes the same acceleration as Earth. (c) The
> In a Broadway performance, an 80.0-kg actor swings from a 3.75-m-long cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55.0-kg costar in an inelastic collision. What maximum height do they reach after their upward swing?
> A cue ball traveling at 4.00 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The target ball deflects the cue ball so that its subsequent motion makes an angle of 30.0° with respect to its original dire
> Consider the ballistic pendulum device discussed in Example 6.5 and illustrated in Figure 6.13. (a) Determine the ratio of the momentum immediately after the collision to the momentum immediately before the collision. (b) Show that the ratio of the kinet
> A railroad car of mass M moving at a speed v1 collides and couples with two coupled railroad cars, each of the same mass M and moving in the same direction at a speed v2. (a) What is the speed vf of the three coupled cars after the collision in terms of
> A railroad car of mass 2.00 x 104 kg moving at 3.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) What is the speed of the three coupled cars after the c
> A 75.0-kg ice skater moving at 10.0 m/s crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 5.00 m/s. Suppose the average force a skater can experience without breaking a bone is 4500 N. If the impact ti
> Gayle runs at a speed of 4.00 m/s and dives on a sled, initially at rest on the top of a frictionless, snow- covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back, and they continue d
> An archer shoots an arrow toward a 3.00 x 102 - g target that is sliding in her direction at a speed of 2.50 m/s on a smooth, slippery surface. The 22.5-g arrow is shot with a speed of 35.0 m/s and passes through the target, which is stopped by the impac
> A pail of water is rotated in a vertical circle of radius 1.00 m. (a) What two external forces act on the water in the pail? (b) Which of the two forces is most important in causing the water to move in a circle? (c) What is the pail’s minimum speed at t
> An object moves in a circular path with constant speed v. Which of the following statements is true concerning the object? (a) Its velocity is constant, but its acceleration is changing. (b) Its acceleration is constant, but its velocity is changing. (c)
> A woman places her briefcase on the backseat of her car. As she drives to work, the car negotiates an unbanked curve in the road that can be regarded as an arc of a circle of radius 62.0 m. While on the curve, the speed of the car is 15.0 m/s at the inst
> A snowboarder drops from rest into a halfpipe of radius R and slides down its frictionless surface to the bottom (Fig. P7.28). Show that (a) The snowboarder’s speed at the bottom of the halfpipe is v = √2gR (b) The sno
> An air puck of mass m1 = 0.25 kg is tied to a string and allowed to revolve in a circle of radius R = 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m2 = 1.0 kg is tie
> A space habitat for a long space voyage consists of two cabins each connected by a cable to a central hub as shown in Figure P7.26. The cabins are set spinning around the hub axis, which is connected to the rest of the spacecraft to generate artificial g
> A 50.0-kg child stands at the rim of a merry-go-round of radius 2.00 m, rotating with an angular speed of 3.00 rad/s. (a) What is the magnitude of the child’s centripetal acceleration? (b) What is the magnitude of the minimum force between her feet and t
> A sample of blood is placed in a centrifuge of radius 15.0 cm. The mass of a red blood cell is 3.0 x 10-16 kg, and the magnitude of the force acting on it as it settles out of the plasma is 4.0 x 10-11 N. At how many revolutions per second should the cen
> A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve having a radius of 75.0 m?
> A 40.0-kg child swings in a swing supported by two chains, each 3.00 m long. The tension in each chain at the lowest point is 350 N. Find (a) The child’s speed at the lowest point and (b) The force exerted by the seat on the child at the lowest point. (I
> A 55.0-kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.800 m around the pole. (a) Determine the force exerted by the horizontal rope on her ar
> Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g - suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness. (a) If a human centrifug
> A racetrack is constructed such that two arcs of radius 80 m at â’¶ and 40 m at â’· are joined by two stretches of straight track as in Figure 7.8. In a particular trial run, a driver travels at a constant speed of 50 m/
> One end of a cord is fixed and a small 0.500-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.00 m, as shown in Figure P7.19. When θ = 20.0°, the speed of the object is 8.00 m/s
> An adventurous archeologist (m = 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.0 m long, and his speed at the bottom of the swing is 8.00 m/s. The archeologist doesn’t know that the vine has a breaking strength of 1000 N. Does h
> (a) What is the tangential acceleration of a bug on the rim of a 10.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular velocity of 78.0 rev/min in 3.00 s? (b) When the disk is at its final speed, what is the tangential velocity
> It has been suggested that rotating cylinders about 10 mi long and 5.0 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall accelerat
> A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in Figure P7.15. The length of the arc ABC is 235 m, and the car completes the turn in 36.0 s. (a) Determine the car’s speed. (b) W
> An electric motor rotating a workshop grinding wheel at a rate of 1.00 x 102 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude 2.00 rad/s2. (a) How long does it take for the grinding wheel to stop? (b) Th
> A rotating wheel requires 3.00 s to rotate 37.0 revolutions. Its angular velocity at the end of the 3.00-s interval is 98.0 rad/s. What is the constant angular acceleration (in rad/s2) of the wheel?
> A child is practicing for a BMX race. His speed remains constant as he goes counterclockwise around a level track with two nearly straight sections and two nearly semicircular sections, as shown in the aerial view of Figure CQ7.12. (a) What are the direc
> A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2 after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tire
> A car of mass m follows a truck of mass 2m around a circular turn. Both vehicles move at speed v. (a) What is the ratio of the truck’s net centripetal force to the car’s net centripetal force? (b) At what new speed vtruck will the net centripetal force a
> When the merry-go-round of Quick Quiz 7.4 is rotating at a constant angular speed, Andrea’s tangential speed is (a) Twice Chuck’s (b) The same as Chuck’s (c) Half of Chuck’s (d) Impossible to determine. Data From Quick Quiz 7.4: Andrea and Chuck are rid
> The diameters of the main rotor and tail rotor of a singleengine helicopter are 7.60 m and 1.02 m, respectively. The respective rotational speeds are 450 rev/min and 4138 rev/ min. Calculate the speeds of the tips of both rotors. Compare these speeds wit
> Describe the path of a moving object in the event that the object’s acceleration is constant in magnitude at all times and (a) Perpendicular to its velocity; (b) Parallel to its velocity.
> A bicyclist starting at rest produces a constant angular acceleration of 1.60 rad/s2 for wheels that are 38.0 cm in radius. (a) What is the bicycle’s linear acceleration? (b) What is the angular speed of the wheels when the bicyclist reaches 11.0 m/s? (c
> Because of Earth’s rotation about its axis, you weigh slightly less at the equator than at the poles. Explain.
> A dentist’s drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate of 2.51 x 104 rev/min. (a) Find the drill’s angular acceleration. (b) Determine the angle (in radians) through which the drill rotates during this perio
> Objects moving along a circular path have a centripetal acceleration provided by a net force directed towards the center. Identify the force(s) providing the centripetal acceleration in each of these cases: (a) A planet in circular orbit around its sun;
> A potter’s wheel moves uniformly from rest to an angular velocity of 1.00 rev/s in 30.0 s. (a) Find its angular acceleration in radians per second per second. (b) Would doubling the angular acceleration during the given period have doubled final angular
> A bicycle tire is spinning clockwise at 2.50 rad/s. During a time period Δt = 1.25 s, the tire is stopped and spun in the opposite (counterclockwise) direction, also at 2.50 rad/s. Calculate (a) The change in the tire’s angular velocity Δw and (b) The ti
> The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60000 miles. (a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period. (b) How many revolutions of the tire are equivalent
> A model airplane of mass 0.750 kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 60.0-m control wire as shown in Figure P7.60a. The forces exerted on the airplane are shown in Figure P7.60b; the tension in the control wire, Î
> In Robert Heinlein’s The Moon Is a Harsh Mistress, the colonial inhabitants of the Moon threaten to launch rocks down onto Earth if they are not given independence (or at least representation). Assuming a gun could launch a rock of mass m at twice the lu
> A roller coaster travels in a circular path. (a) Identify the forces on a passenger at the top of the circular loop that cause centripetal acceleration. Show the direction of all forces in a sketch. (b) Identify the forces on the passenger at the bottom
> Because of Earth’s rotation about its axis, a point on the equator has a centripetal acceleration of 0.034 0 m/s2, whereas a point at the poles has no centripetal acceleration. (a) Show that, at the equator, the gravitational force on an object (the obje
> Keratinocytes are the most common cells in the skin’s outer layer. As these approximately circular cells migrate across a wound during the healing process, they roll in a way that reduces the frictional forces impeding their motion. (a) Given a cell body
> A car moves at speed v across a bridge made in the shape of a circular arc of radius r. (a) Find an expression for the normal force acting on the car when it is at the top of the arc. (b) At what minimum speed will the normal force become zero (causing t
> A 0.400-kg pendulum bob passes through the lowest part of its path at a speed of 3.00 m/s. (a) What is the tension in the pendulum cable at this point if the pendulum is 80.0 cm long? (b) When the pendulum reaches its highest point, what angle does the c
> The Solar Maximum Mission Satellite was placed in a circular orbit about 150 mi above Earth. Determine (a) The orbital speed of the satellite and (b) The time required for one complete revolution.
> The dung beetle is known as one of the strongest animals for its size, often forming balls of dung up to 10 times their own mass and rolling them to locations where they can be buried and stored as food. A typical dung ball formed by the species K. nigro
> An athlete swings a 5.00-kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.800 m at an angular speed of 0.500 rev/s. What are (a) The tangential speed of the ball and (b) Its centripetal acceleration? (c) If the maximum te
> Suppose an alien civilization has a space station in circular orbit around its home planet. The station’s orbital radius is twice the planet’s radius. (a) If an alien astronaut has weight w just before launch from the surface, will she be weightless when
> A digital audio compact disc (CD) carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies 0.6 mm of the track. A CD player turns the disc to carry the track counterclockwise above a len
> One method of pitching a softball is called the “windmill” delivery method, in which the pitcher’s arm rotates through approximately 360° in a vertical plane before the 198- gram ball is released at the lowest point of the circular motion. An experienced
> Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the grea
> (a) One of the moons of Jupiter, named Io, has an orbital radius of 4.22 x 108 m and a period of 1.77 days. Assuming the orbit is circular, calculate the mass of Jupiter. (b) The largest moon of Jupiter, named Ganymede, has an orbital radius of 1.07 x 10
> A synchronous satellite, which always remains above the same point on a planet’s equator, is put in circular orbit around Jupiter to study that planet’s famous red spot. Jupiter rotates once every 9.84 h. Use the data
> A comet has a period of 76.3 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.610 AU. Find (a) The semimajor axis of the comet and (b) An estimate of the comet’s maximum distance from the Sun, both in astr
> A 600-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth’s mean radius. Find (a) The satellite’s orbital speed, (b) The period of its revolution, and (c) The gravitational force acting on it.
