A cutting tool under microprocessor control has several forces acting on it. One force is
> A circular saw blade with radius 0.120 m starts from rest and turns in a vertical plane with a constant angular acceleration of 2.00 rev>s2. After the blade has turned through 155 rev, a small piece of the blade breaks loose from the top of the blade. Af
> A uniform disk with radius R = 0.400 m and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to
> A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.992 kg that rests on a frictionless, horizontal surface and is attached to a coil spring (Fig. P8.79). The impact compresses the spring 15.0 cm. Calibration of the spring sh
> A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.0400 m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm (Fig. P8.78). Find the maximum distance the frame moves downward from its initial eq
> A 1500-kg sedan goes through a wide intersection traveling from north to south when it is hit by a 2200-kg SUV traveling from east to west. The two cars become enmeshed due to the impact and slide as one thereafter. On-the scene measurements show that th
> You are called as an expert witness to analyze the following auto accident: Car B, of mass 1900 kg, was stopped at a red light when it was hit from behind by car A, of mass 1500 kg. The cars locked bumpers during the collision and slid to a stop with bra
> Two blocks have a spring compressed between them, as in Exercise 8.24. The spring has force constant 720 N/m and is initially compressed 0.225 m from its original length. For each block, what is (a) the acceleration just after the blocks are released; (b
> Block B (mass 4.00 kg) is at rest at the edge of a smooth platform, 2.60 m above the floor. Block A (mass 2.00 kg) is sliding with a speed of 8.00 m/s along the platform toward block B. A strikes B and rebounds with a speed of 2.00 m/s. The collision pro
> A 5.00-kg chunk of ice is sliding at 12.0 m/s on the floor of an ice-covered valley when it collides with and sticks to another 5.00-kg chunk of ice that is initially at rest (Fig. P8.73). Since the valley is icy, there is no friction. After the collisio
> A 62.0-kg skier is moving at 6.50 m/s on a frictionless, horizontal, snow-covered plateau when she encounters a rough patch 4.20 m long. The coefficient of kinetic friction between this patch and her skis is 0.300. After crossing the rough patch and retu
> A small wooden block with mass 0.800 kg is suspended from the lower end of a light cord that is 1.60 m long. The block is initially at rest. A bullet with mass 12.0 g is fired at the block with a horizontal velocity v0. The bullet strikes the block and b
> An 8.00-kg block of wood sits at the edge of a frictionless table, 2.20 m above the floor. A 0.500-kg blob of clay slides along the length of the table with a speed of 24.0 m/s, strikes the block of wood, and sticks to it. The combined object leaves the
> You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 80.0 kg, is given a push and slides eastward. Abigail, with mass 50.0 kg, is sent sliding northward. They collide, and a
> Spheres A (mass 0.020 kg), B (mass 0.030 kg), and C (mass 0.050 kg) are approaching the origin as they slide on a frictionless air table. The initial velocities of A and B are given in Fig. P8.69. All three spheres arrive at the origin at the same time
> A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of 200 kg and is traveling east with a velocity of magnitude 5.00 m/s. Find the
> Blocks A (mass 2.00 kg) and B (mass 10.00 kg, to the right of A) move on a frictionless, horizontal surface. Initially, block B is moving to the left at 0.500 m>s and block A is moving to the right at 2.00 m/s. The blocks are equipped with ideal spring b
> Three identical pucks on a horizontal air table have repelling magnets. They are held together and then released simultaneously. Each has the same speed at any instant. One puck moves due west. What is the direction of the velocity of each of the other t
> Just before it is struck by a racket, a tennis ball weighing 0.560 N has a velocity of (20.0 m/s)
> A steel ball with mass 40.0 g is dropped from a height of 2.00 m onto a horizontal steel slab. The ball rebounds to a height of 1.60 m. (a) Calculate the impulse delivered to the ball during impact. (b) If the ball is in contact with the slab for 2.00 ms
> For the Texas Department of Public Safety, you are investigating an accident that occurred early on a foggy morning in a remote section of the Texas Panhandle. A 2012 Prius traveling due north collided in a highway intersection with a 2013 Dodge Durango
> In an experiment, one of the forces exerted on a proton is
> In your job in a police lab, you must design an apparatus to measure the muzzle velocities of bullets fired from handguns. Your solution is to attach a 2.00-kg wood block that rests on a horizontal surface to a light horizontal spring. The other end of t
> A 2004 Prius with a 150-lb driver and no passengers weighs 3071 lb. The car is initially at rest. Starting at t = 0, a net horizontal force Fx(t) in the +x-direction is applied to the car. The force as a function of time is given in Fig. P8.100. (a) For
> An outlaw cuts loose a wagon with two boxes of gold, of total mass 300 kg, when the wagon is at rest 50 m up a 6.0° slope. The outlaw plans to have the wagon roll down the slope and across the level ground, and then fall into a canyon where hi
> A 12.0-kg shell is launched at an angle of 55.0° above the horizontal with an initial speed of 150 m>s. At its highest point, the shell explodes into two fragments, one three times heavier than the other. The two fragments reach the ground at the same ti
> A fireworks rocket is fired vertically upward. At its maximum height of 80.0 m, it explodes and breaks into two pieces: one with mass 1.40 kg and the other with mass 0.28 kg. In the explosion, 860 J of chemical energy is converted to kinetic energy of th
> A 20.0-kg projectile is fired at an angle of 60.0° above the horizontal with a speed of 80.0 m/s. At the highest point of its trajectory, the projectile explodes into two fragments with equal mass, one of which falls vertically with zero initial speed. I
> A 7.0-kg shell at rest explodes into two fragments, one with a mass of 2.0 kg and the other with a mass of 5.0 kg. If the heavier fragment gains 100 J of kinetic energy from the explosion, how much kinetic energy does the lighter one gain?
> In a fireworks display, a rocket is launched from the ground with a speed of 18.0 m>s and a direction of 51.0° above the horizontal. During the flight, the rocket explodes into two pieces of equal mass (see Fig. 8.32). (a) What horizontal distance from t
> You are standing on a concrete slab that in turn is resting on a frozen lake. Assume there is no friction between the slab and the ice. The slab has a weight five times your weight. If you begin walking forward at 2.00 m/s relative to the ice, with what
> A 45.0-kg woman stands up in a 60.0-kg canoe 5.00 m long. She walks from a point 1.00 m from one end to a point 1.00 m from the other end (Fig. P8.92). If you ignore resistance to motion of the canoe in the water, how far does the canoe move during this
> A 0.60-kg book slides on a horizontal table. The kinetic friction force on the book has magnitude 1.8 N. (a) How much work is done on the book by friction during a displacement of 3.0 m to the left? (b) The book now slides 3.0 m to the right, returning t
> Friends Burt and Ernie stand at opposite ends of a uniform log that is floating in a lake. The log is 3.0 m long and has mass 20.0 kg. Burt has mass 30.0 kg; Ernie has mass 40.0 kg. Initially, the log and the two friends are at rest relative to the shore
> Jonathan and Jane are sitting in a sleigh that is at rest on frictionless ice. Jonathan’s weight is 800 N, Jane’s weight is 600 N, and that of the sleigh is 1000 N. They see a poisonous spider on the floor of the sleigh and immediately jump off. Jonathan
> In beta decay, a nucleus emits an electron. A 210Bi (bismuth) nucleus at rest undergoes beta decay to 210Po (polonium). Suppose the emitted electron moves to the right with a momentum of 5.60 × 10-22 kg # m/s. The 210Po nucleus, with mass 3.50 × 10-25 kg
> A neutron at rest decays (breaks up) to a proton and an electron. Energy is released in the decay and appears as kinetic energy of the proton and electron. The mass of a proton is 1836 times the mass of an electron. What fraction of the total energy rele
> In a shipping company distribution center, an open cart of mass 50.0 kg is rolling to the left at a speed of 5.00 m/s (Fig. P8.87). Ignore friction between the cart and the floor. A 15.0-kg package slides down a chute that is inclined at 37°
> A 5.00-g bullet is shot through a 1.00-kg wood block suspended on a string 2.00 m long. The center of mass of the block rises a distance of 0.38 cm. Find the speed of the bullet as it emerges from the block if its initial speed is 450 m/s.
> A 4.00-g bullet, traveling horizontally with a velocity of magnitude 400 m/s, is fired into a wooden block with mass 0.800 kg, initially at rest on a level surface. The bullet passes through the block and emerges with its speed reduced to 190 m/s. The bl
> A 20.00-kg lead sphere is hanging from a hook by a thin wire 2.80 m long and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.00-kg steel dart that embeds itself in the lead sphere. What must be the minimum initial speed o
> A ball with mass M, moving horizontally at 4.00 m/s, collides elastically with a block with mass 3M that is initially hanging at rest from the ceiling on the end of a 50.0-cm wire. Find the maximum angle through which the block swings after it is hit.
> Two identical masses are released from rest in a smooth hemispherical bowl of radius R from the positions shown in Fig. P8.82. Ignore friction between the masses and the surface of the bowl. If the masses stick together when they collide, how high above
> 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 starting point. How much work is done on him by gravity (a)
> A movie stuntman (mass 80.0 kg) stands on a window ledge 5.0 m above the floor (Fig. P8.81). Grabbing a rope attached to a chandelier, he swings down to grapple with the movie’s villain (mass 70.0 kg), who is standing directly under the chandelier. (Assu
> A 0.100-kg stone rests on a frictionless, horizontal surface. A bullet of mass 6.00 g, traveling horizontally at 350 m>s, strikes the stone and rebounds horizontally at right angles to its original direction with a speed of 250 m/s. (a) Compute the magni
> A single conservative force F1x2 acts on a small sphere of mass m while the sphere moves along the x-axis. You release the sphere from rest at x = -1.50 m. As the sphere moves, you measure its velocity as a function of position. You use the velocity data
> A long ramp made of cast iron is sloped at a constant angle u = 52.0o above the horizontal. Small blocks, each with mass 0.42 kg but made of different materials, are released from rest at a vertical height h above the bottom of the ramp. In each case the
> You are designing a pendulum for a science museum. The pendulum is made by attaching a brass sphere with mass m to the lower end of a long, light metal wire of (unknown) length L. A device near the top of the wire measures the tension in the wire and tra
> 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. P7.76. The particle is released from rest at point A. (a) What is the direction
> A small object with mass m = 0.0900 kg moves along the +x-axis. The only force on the object is a conservative force that has the potential-energy function U(x)= -ax2 + bx3, where a = 2.00 J/m2 and b = 0.300 J/m3. The object is released from rest at smal
> A wooden block with mass 1.50 kg is placed against a compressed spring at the bottom of an incline of slope 30.0° (point A). When the spring is released, it projects the block up the incline. At point B, a distance of 6.00 m up the incline from A, the bl
> A small rock with mass 0.12 kg is fastened to a massless 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 resistance is negligible. (a) What is the speed of the rock when t
> 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. The spring’s mass, the recoil kinetic energy of the shutt
> A small block with mass 0.0500 kg slides in a vertical circle of radius R = 0.800 m on the inside of a circular track. There is no friction between the track and the block. At the bottom of the block’s path, the normal force the track exerts on the block
> A small block with mass 0.0400 kg slides in a vertical circle of radius R = 0.500 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the normal force exerted on the block
> 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. P7.69). The mass of the spring is negligible. You move the block to t
> You are designing an amusement park ride. A cart with two riders moves horizontally with speed v = 6.00 m/s. You assume that the total mass of cart plus riders is 300 kg. The cart hits a light spring that is attached to a wall, momentarily comes to rest
> A 3.00-kg fish is attached to the lower end of a vertical spring that has negligible mass and force constant 900 N/m. The spring initially is neither stretched nor compressed. The fish is released from rest. (a) What is its speed after it has descended 0
> A basket of negligible weight hangs from a vertical spring scale of force constant 1500 N/m. (a) If you suddenly put a 3.0-kg adobe brick in the basket, find the maximum distance that the spring will stretch. (b) If, instead, you release the brick from 1
> You are an industrial engineer with a shipping company. As part of the package-handling system, a small box with mass 1.60 kg is placed against a light spring that is compressed 0.280 m. The spring has force constant k = 45.0 N/m. The spring and box are
> 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 unstretched spring and then allowed to fall from rest, through wha
> 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 compressed 0.045 m. The mass of the spring is negligible. T
> A 3.00-kg block is connected to two ideal horizontal springs having force constants k1 = 25.0 N/cm and k2 = 20.0 N/cm (Fig. P7.62). The system is initially in equilibrium on a horizontal, frictionless surface. The block is now pushed 15.0 cm to the right
> A 2.50-kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0300 m. The spring has force constant 840 N/m. The coefficient of kinetic friction between the floor and the block is
> A conservative force F is in the +x-direction and has magnitude F(x)= a/(x + x0)2, where a = 0.800 N#m2 and x0 = 0.200 m. (a) What is the potential-energy function U1x2 for this force? Let U(x) → 0 as x → ∞. (b) An object with mass m = 0.500 kg is relea
> A sled with rider having a combined mass of 125 kg travels over a perfectly smooth icy hill (Fig. P7.60). How far does the sled land from the foot of the cliff? Fig. P7.60: Figure P7.60 11.0 m Cliff 22.5 m/s
> A certain spring found not to obey Hooke’s law exerts a restoring force Fx(x)= -ax - bx2 if it is stretched or compressed, where a = 60.0 N/m and b = 18.0 N/m2. The mass of the spring is negligible. (a) Calculate the potential-energy function U(x) for th
> A truck with mass m has a brake failure while going down an icy mountain road of constant downward slope angle a (Fig. P7.58). Initially the truck is moving downhill at speed v0. After careening downhill a distance L with negligible friction, the truck d
> In a truck-loading station at a post office, a small 0.200-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. P7.57). The size of the package is much less than 1.60 m, so the package can be tre
> A ball is thrown upward with an initial velocity of 15 m/s at an angle of 60.0° above the horizontal. Use energy conservation to find the ball’s greatest height above the ground.
> A skier starts at the top of a very large, frictionless snowball, with a very small initial speed, and skis straight down the side (Fig. P7.55). At what point does she lose contact with the snowball and fly off at a tangent? That is, at the instant she l
> A 60.0-kg skier starts from rest at the top of a ski slope 65.0 m high. (a) If friction forces do -10.5 kJ of work on her as she descends, how fast is she going at the bottom of the slope? (b) Now moving horizontally, the skier crosses a patch of soft sn
> A 0.300-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 string pulled taut, and is then released. (a) What is t
> During the calibration process, the cantilever is observed to deflect by 0.10 nm when a force of 3.0 pN is applied to it. What deflection of the cantilever would correspond to a force of 6.0 pN? (a) 0.07 nm; (b) 0.14 nm; (c) 0.20 nm; (d) 0.40 nm.
> 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 way. When the spring has been compressed enough to sto
> The fish shoots the drop of water at an insect that hovers on the water’s surface, so just before colliding with the insect, the drop is still moving at the speed it had when it left the fish’s mouth. In the collision, the drop sticks to the insect, and
> A new species of eel is found to have the same mass but one-quarter the length and twice the diameter of the American eel. How does its moment of inertia for spinning around its long axis compare to that of the American eel? The new species has (a) half
> The eel has a certain amount of rotational kinetic energy when spinning at 14 spins per second. If it swam in a straight line instead, about how fast would the eel have to swim to have the same amount of kinetic energy as when it is spinning? (a) 0.5 m/s
> The eel is observed to spin at 14 spins per second clockwise, and 10 seconds later it is observed to spin at 8 spins per second counterclockwise. What is the magnitude of the eel’s average angular acceleration during this time? (a) 6/10 rad/s2; (b) 6
> The stage moves at a constant speed while stretching the DNA. Which of the graphs in Fig. P7.84 best represents the power supplied to the stage versus time? Fig. P7.84: Figure P7.84 (a) (b) (d) Time Time Time Time Power
> Based on Fig. P7.82, how much elastic potential energy is stored in the DNA when it is stretched 50 nm? (a) 2.5 × 10-19 J; (b) 1.2 × 10-19 J; (c) 5.0 × 10-12 J; (d) 2.5 × 10-12 J. Figure P7.82:
> A segment of DNA is put in place and stretched. Figure P7.82 shows a graph of the force exerted on the DNA as a function of the displacement of the stage. Based on this graph, which statement is the best interpretation of the DNA’s beha
> A projectile has the same initial kinetic energy no matter what the angle of projection. Why doesn’t it rise to the same maximum height in each case?
> Which of the following formulas is valid if the angular acceleration of an object is not constant? Explain your reasoning in each case. (a) v = rw; (b) atan = ra; (c) w = w0 + at; (d) atan = rw2; (e) K = 1 2 Iw2.
> Can you think of a body that has the same moment of inertia for all possible axes? If so, give an example, and if not, explain why this is not possible. Can you think of a body that has the same moment of inertia for all axes passing through a certain po
> (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 elevator is 1.00 m below point 1 in Fig. 7.17, what is its acceleration?
> The food calorie, equal to 4186 J, is a measure of how much energy is released when the body metabolizes food. A certain fruitandcereal bar contains 140 food calories. (a) If a 65kg hiker eats one bar, how high a mountain must he climb to “work off” t
> You are designing a flywheel to store kinetic energy. If all of the following uniform objects have the same mass and same angular velocity, which one will store the greatest amount of kinetic energy? Which will store the least? Explain. (a) A solid spher
> What is the purpose of the spin cycle of a washing machine? Explain in terms of acceleration components.
> A flywheel rotates with constant angular velocity. Does a point on its rim have a tangential acceleration? A radial acceleration? Are these accelerations constant in magnitude? In direction? In each case give your reasoning.
> What is the difference between tangential and radial acceleration for a point on a rotating body?
> Estimate your own moment of inertia about a vertical axis through the center of the top of your head when you are standing up straight with your arms outstretched. Make reasonable approximations and measure or estimate necessary quantities.
> A wheel is rotating about an axis perpendicular to the plane of the wheel and passing through the center of the wheel. The angular speed of the wheel is increasing at a constant rate. Point A is on the rim of the wheel and point B is midway between the r
> A diatomic molecule can be modeled as two point masses, m1 and m2, slightly separated (Fig. Q9.2). If the molecule is oriented along the y-axis, it has kinetic energy K when it spins about the x-axis. What will its kinetic energy (in terms of K) be if it
> You can use any angular measure—radians, degrees, or revolutions—in some of the equations in Chapter 9, but you can use only radian measure in others. Identify those for which using radians is necessary and those for which it is not, and in each case giv
> An elaborate pulley consists of four identical balls at the ends of spokes extending out from a rotating drum (Fig. Q9.18). A box is connected to a light, thin rope wound around the rim of the drum. When it is released from rest, the box acquires a speed
> Two identical balls, A and B, are each attached to very light string, and each string is wrapped around the rim of a frictionless pulley of mass M. The only difference is that the pulley for ball A is a solid disk, while the one for ball B is a hollow di
> 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 one end on the floor. You then drop a 1.20-kg book onto it
> For the equations for I given in parts (a) and (b) of Table 9.2 to be valid, must the rod have a circular cross section? Is there any restriction on the size of the cross section for these equations to apply? Explain. Table 9.2: TABLE 9.2 Moments o
> Describe how you could use part (b) of Table 9.2 to derive the result in part (d). Table 9.2: TABLE 9.2 Moments of Inertia of Various Bodies (a) Slender rod, axis through center (b) Slender rod, axis through one end (c) Rectangular plate, axis thro
