(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?
> 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 cutting tool under microprocessor control has several forces acting on it. One force is
> 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
> 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
> How might you determine experimentally the moment of inertia of an irregularly shaped body about a given axis?
> In a completely inelastic collision between two objects, where the objects stick together after the collision, is it possible for the final kinetic energy of the system to be zero? If so, give an example in which this would occur. If the final kinetic en
> (a) If the momentum of a single point object is equal to zero, must the object’s kinetic energy also be zero? (b) If the momentum of a pair of point objects is equal to zero, must the kinetic energy of those objects also be zero? (c) If the kinetic energ
> When rain falls from the sky, what happens to its momentum as it hits the ground? Is your answer also valid for Newton’s famous apple?
> When an object breaks into two pieces (explosion, radioactive decay, recoil, etc.), the lighter fragment gets more kinetic energy than the heavier one. This is a consequence of momentum conservation, but can you also explain it by using Newton’s laws of
> At the highest point in its parabolic trajectory, a shell explodes into two fragments. Is it possible for both fragments to fall straight down after the explosion? Why or why not?
> Suppose you catch a baseball and then someone invites you to catch a bowling ball with either the same momentum or the same kinetic energy as the baseball. Which would you choose? Explain.
> A very heavy SUV collides head-on with a very light compact car. Which of these statements about the collision are correct? (a) The amount of kinetic energy lost by the SUV is equal to the amount of kinetic energy gained by the compact; (b) the amount of
> A 1.20-kg piece of cheese is placed on a vertical spring of negligible mass and force constant k = 1800 N/m that is compressed 15.0 cm. When the spring is released, how high does the cheese rise from this initial position? (The cheese and the spring are
> Two objects of mass M and 5M are at rest on a horizontal, frictionless table with a compressed spring of negligible mass between them. When the spring is released, which of the following statements are true? (a) The two objects receive equal magnitudes o
> Two pieces of clay collide and stick together. During the collision, which of these statements are true? (a) Only the momentum of the clay is conserved; (b) only the mechanical energy of the clay is conserved; (c) both the momentum and the mechanical ene
> An apple falls from a tree and feels no air resistance. As it is falling, which of these statements about it are true? (a) Only its momentum is conserved; (b) only its mechanical energy is conserved; (c) both its momentum and its mechanical energy are co
> The net force on a particle of mass m has the potential­ energy function graphed in Fig. 7.24a. If the total energy is E1, graph the speed v of the particle versus its position x. At what value of x is the speed greatest? Sketch v versus x if
> A particle is in neutral equilibrium if the net force on it is zero and remains zero if the particle is displaced slightly in any direction. Sketch the potential energy function near a point of neutral equilibrium for the case of one dimensional moti
> Explain why the points x = A and x = -A in Fig. 7.23b are called turning points. How are the values of E and U related at a turning point? Fig. 7.23b: (b) On the graph, the limits of motion are the points where the U curve intersects the horizontal
> An egg is released from rest from the roof of a building and falls to the ground. As the egg falls, what happens to the momentum of the system of the egg plus the earth?
> A tennis player hits a tennis ball with a racket. Consider the system made up of the ball and the racket. Is the total momentum of the system the same just before and just after the hit? Is the total momentum just after the hit the same as 2 s later, whe
> Figure 7.22a shows the potential ­ energy function for the force Fx = -kx. Sketch the potential ­ energy function for the force Fx = +kx. For this force, is x = 0 a point of equilibrium? Is this equilibrium stable or unstable? Expla
> Since only changes in potential energy are important in any problem, a student decides to let the elastic potential energy of a spring be zero when the spring is stretched a distance x1. The student decides, therefore, to let U = 1 2 k(x - x1)2. Is this
> A spring of negligible mass has force constant k = 800 N/m. (a) How far must the spring be compressed for 1.20 J of potential energy to be stored in it? (b) You place the spring vertically with one end on the floor. You then lay a 1.60-kg book on top of
> In each of Examples 8.10, 8.11, and 8.12 (Section 8.4), verify that the relative velocity vector of the two bodies has the same magnitude before and after the collision. In each case, what happens to the direction of the relative velocity vector? Exampl
> A box slides down a ramp and work is done on the box by the forces of gravity and friction. Can the work of each of these forces be expressed in terms of the change in a potential energy function? For each force explain why or why not.
> In Fig. 8.23b, the kinetic energy of the Ping-Pong ball is larger after its interaction with the bowling ball than before. From where does the extra energy come? Describe the event in terms of conservation of energy. Fig. 8.23b: (b) Moving bowling
> Two objects with different masses are launched vertically into the air by placing them on identical compressed springs and then releasing the springs. The two springs are compressed by the same amount before launching. Ignore air resistance and the masse
> A 1.0kg stone and a 10.0kg stone are released from rest at the same height above the ground. Ignore air resistance. Which of these statements about the stones are true? Justify each answer. (a) Both have the same initial gravitational potential energy.
> (a) A block of wood is pushed against a spring, which is compressed 0.080 m. Does the force on the block exerted by the spring do positive or negative work? Does the potential energy stored in the spring increase or decrease? (b) A block of wood is place
> (a) A book is lifted upward a vertical distance of 0.800 m. During this displacement, does the gravitational force acting on the book do positive work or negative work? Does the gravitational potential energy of the book increase or decrease? (b) A can o
> In Example 8.7 (Section 8.3), where the two gliders of Fig. 8.18 stick together after the collision, the collision is inelastic because K2 < K1 . In Example 8.5 (Section 8.2), is the collision inelastic? Explain. Example 8.7: We repeat the collision de
> A woman holding a large rock stands on a frictionless, horizontal sheet of ice. She throws the rock with speed v0 at an angle a above the horizontal. Consider the system consisting of the woman plus the rock. Is the momentum of the system conserved? Why
> Is it possible for a friction force to increase the mechanical energy of a system? If so, give examples.
> A slingshot will shoot a 10-g pebble 22.0 m straight up. (a) How much potential energy is stored in the slingshot’s rubber band? (b) With the same potential energy stored in the rubber band, how high can the slingshot shoot a 25-g pebble? (c) What physic
> A physics teacher had a bowling ball suspended from a very long rope attached to the high ceiling of a large lecture hall. To illustrate his faith in conservation of energy, he would back up to one side of the stage, pull the ball far to one side until t
> An egg is released from rest from the roof of a building and falls to the ground. Its fall is observed by a student on the roof of the building, who uses coordinates with origin at the roof, and by a student on the ground, who uses coordinates with origi
> An object is released from rest at the top of a ramp. If the ramp is frictionless, does the object’s speed at the bottom of the ramp depend on the shape of the ramp or just on its height? Explain. What if the ramp is not frictionless?
> A proton with mass m moves in one dimension. The potential-energy function is U(x)=(a/x2)-(b/x), where a and b are positive constants. The proton is released from rest at x0 = a/b. (a) Show that U(x) can be written as Graph U(x). Calculate U(x0) and th
> Use the methods of Challenge Problem 8.104 to calculate the x- and y-coordinates of the center of mass of a semicircular metal plate with uniform density r and thickness t. Let the radius of the plate be a. The mass of the plate is thus M = 1/2 rpa2t. Us
> In Section 8.5 we calculated the center of mass by considering objects composed of a finite number of point masses or objects that, by symmetry, could be represented by a finite number of point masses. For a solid object whose mass distribution does not
