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physics
mechanics
Physics 5th edition James S. Walker - Solutions
(a) What is the magnitude of the momentum of a 0.0053-kg marble whose speed is 0.65 m/s? (b) What is the speed of a 0.132-kg baseball whose momentum has a magnitude of 3.28 kg ∙ m/s?
One study suggests that a brain concussion can occur if a person's head is subjected to an acceleration as small as 60g, where g is the acceleration of gravity.(a) If the mass of the person's head is 4.8 kg, what is the magnitude of the force?(b) If the impulse delivered to the person's head is 18
A 0.14-kg baseball moves toward home plate with a velocity v(vector)i = (–36 m/s)x̂. After striking the bat, the ball moves vertically upward with a velocity v(vector)f = (18 m/s)ŷ.(a) Find the direction and magnitude of the impulse delivered to the ball by the bat. Assume that the ball and
A player bounces a 0.43-kg soccer ball off her head, changing the velocity of the ball from v(vector)i = (8.8 m/s)x̂ + (– 2.3 m/s)ŷ to v(vector)f = (5.2 m/s)x̂ + (3.7 m/s)ŷ. If the ball is in contact with the player’s head for 6.7 ms, what are(a) The direction(b) The magnitude of the
Two ice skaters stand at rest in the center of an ice rink. When they push off against one another the 45-kg skater acquires a speed of 0.62 m/s. If the speed of the other skater is 0.89 m/s, what is this skater's mass?
A 0.042-kg pet lab mouse sits on a 0.35-kg air-track cart, as shown in FIGURE 9-27. The cart is at rest, as is a second cart with a mass of 0.25 kg. The lab mouse now jumps to the second cart. After the jump, the 0.35-kg cart has a speed of v1 = 0.88 m/s. What is the speed v2 of the mouse and the
An object initially at rest breaks into two pieces as the result of an explosion. One piece has twice the kinetic energy of the other piece. What is the ratio of the masses of the two pieces? Which piece has the larger mass?
A 92-kg astronaut and a 1200-kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.14 m/s directly away from the shuttle. Seven and a half seconds later the astronaut comes into contact with the shuttle. What was the initial distance
The recoil of a shotgun can be significant. Suppose a 3.3-kg shotgun is held tightly by an arm and shoulder with a combined mass of 15.0 kg. When the gun fires a projectile with a mass of 0.038 kg and a speed of 385 m/s, what is the recoil velocity of the shotgun and arm-shoulder combination?
A plate drops onto a smooth floor and shatters into three pieces of equal mass. Two of the pieces go off with equal speeds v at right angles to one another. Find the speed and direction of the third piece.
Suppose the car in Example 9-13 has an initial speed of 20.0 m/s and that the direction of the wreckage after the collision is 40.0° above the x axis. Find the initial speed of the minivan and the final speed of the wreckage.
A 54-kg person walks due north with a speed of 1.2 m/s, and her 6.9-kg dog runs directly toward her, moving due south, with a speed of 1.7 m/s. What is the magnitude of the total momentum of this system?
Two 78.5-kg hockey players skating at 4.47 m/s collide and stick together. If the angle between their initial directions was 105°, what is their speed after the collision?
An air-track cart with mass m1 = 0.32 kg and initial speed v0 = 0.85 m/s collides with and sticks to a second cart that is at rest initially. If the mass of the second cart is m2 = 0.44 kg, how much kinetic energy is lost as a result of the collision?
A bullet with a mass of 4.0 g and a speed of 650 m/s is fired at a block of wood with a mass of 0.095 kg. The block rests on a frictionless surface, and is thin enough that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is 23 m/s.(a)
The human head can be considered as a 3.3-kg cranium protecting a 1.5-kg brain, with a small amount of cerebrospinal fluid that allows the brain to move a little bit inside the cranium. Suppose a cranium at rest is subjected to a force of 2800 N for 6.5 ms in the forward direction.(a) What is the
Two objects moving with a speed v travel in opposite directions in a straight line. The objects stick together when they collide, and move with a speed of v/4 after the collision.(a) What is the ratio of the final kinetic energy of the system to the initial kinetic energy?(b) What is the ratio of
In the apple-orange collision in Example 9-16, suppose the final velocity of the orange is 1.03 m/s in the negative y direction. What are the final speed and direction of the apple in this case?
A 732-kg car stopped at an intersection is rear-ended by a 1720-kg truck moving with a speed of 15.5 m/s. If the car was in neutral and its brakes were off, so that the collision is approximately elastic, find the final speed of both vehicles after the collision.
The collision between a hammer and a nail can be considered to be approximately elastic. Calculate the kinetic energy acquired by a 7.2-g nail when it is struck by a 450-g hammer moving with an initial speed of 8.8 m/s.
A charging bull elephant with a mass of 5240 kg comes directly toward you with a speed of 4.55 m/s. You toss a 0.150-kg rubber ball at the elephant with a speed of 7.81 m/s.(a) When the ball bounces back toward you, what is its speed?(b) How do you account for the fact that the ball's kinetic
In a nuclear reactor, neutrons released by nuclear fission must be slowed down before they can trigger additional reactions in other nuclei. To see what sort of material is most effective in slowing (or moderating) a neutron, calculate the ratio of a neutron's final kinetic energy to its initial
A 26.2-kg dog is running northward at 2.70 m/s, while a 5.30-kg cat is running eastward at 3.04 m/s. Their 74.0-kg owner has the same momentum as the two pets taken together. Find the direction and magnitude of the owner's velocity.
The three air carts shown in FIGURE 9-28 have masses, reading from left to right, of 4m, 2m, and m, respectively.The most massive cart has an initial speed of v0; the other two carts are at rest initially. All carts are equipped with spring bumpers that give elastic collisions.(a) Find the final
An air-track cart with mass m = 0.25 kg and speed v0 = 1.2 m/s approaches two other carts that are at rest and have masses 2m and 3m, as indicated in FIGURE 9-29. The carts have bumpers that make all the collisions elastic. Find the final speed of each of the carts, assuming the air track extends
A stalactite in a cave has drops of water falling from it to the cave floor below. The drops are equally spaced in time and come in rapid succession, so that at any given moment there are many drops in midair.(a) Is the center of mass of the midair drops higher than, lower than, or equal to the
A baseball bat balances when placed on a fulcrum in the position shown in FIGURE 9-30. Is the mass of the bat to the left of the fulcrum greater than, less than, or equal to the mass of the bat to the right of the fulcrum? Explain.
Find the x coordinate of the center of mass of the bricks shown in FIGURE 9-31.
You are holding a shopping basket at the grocery store with two 0.62-kg cartons of cereal at the left end of the basket. The basket is 0.61 m long. Where should you place a 1.9-kg half gallon of milk, relative to the left end of the basket, so that the center of mass of your groceries is at the
A pencil standing upright on its eraser end falls over and lands on a table. As the pencil falls, its eraser does not slip. The following questions refer to the contact force exerted on the pencil by the table. Let the positive x direction be in the direction the pencil falls, and the positive y
Suppose the human body can be reduced to individual point masses as shown in FIGURE 9-32. If mL = 14.0 kg, yL = 0.65 m, mA = 9.00 kg, yA = 1.20 m, mT = 24.5 kg, yT = 1.25 m, mH = 6.50 kg, and yH = 1.65 m, what is the vertical height of the center of mass?
The location of the center of mass of the partially eaten, 12-inch-diameter pizza shown in FIGURE 9-33 is Xcm = - 1.4 in. and Ycm = -1.4 in. Assuming each quadrant of the pizza to be the same, find the center of mass of the uneaten pizza above the x axis (that is, the portion of the pizza in the
Sulfur dioxide (SO2) consists of two oxygen atoms (each of mass 16 u, where u is defined in Problem 39) and a single sulfur atom (of mass 32 u). The center to-center distance between the sulfur atom and either of the oxygen atoms is 0.143 nm, and the angle formed by the three atoms is 120°, as
Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.28 kg and a speed of 0.97 m/s. Cart 2 has a mass of 0.64 kg.(a) What speed must cart 2 have if the total momentum of the system is to be zero?(b) Since the momentum of the system is zero, does it follow that the
Three uniform metersticks, each of mass m, are placed on the floor as follows: stick 1 lies along the y axis from y = 0 to y = 1.0 m, stick 2 lies along the x axis from x = 0 to x = 1.0 m, stick 3 lies along the x axis from x = 1.0 m to x = 2.0 m.(a) Find the location of the center of mass of the
A 0.726-kg rope 2.00 meters long lies on a floor. You grasp one end of the rope and begin lifting it upward with a constant speed of 0.710 m/s. Find the position and velocity of the rope's center of mass from the time you begin lifting the rope to the time the last piece of rope lifts off the
Consider the system shown in FIGURE 9-35. Assume that after the string breaks the ball falls through the liquid with constant speed. If the mass of the bucket and the liquid is 1.20 kg, and the mass of the ball is 0.150 kg, what is the reading on the scale(a) Before(b) After the string breaks?
A metal block of mass m is attached to the ceiling by a spring. Connected to the bottom of this block is a string that supports a second block of the same mass m, as shown in FIGURE 9-36. The string connecting the two blocks is now cut.(a) What is the net force acting on the two-block system
During a rescue operation, a 5300-kg helicopter hovers above a fixed point. The helicopter blades send air downward with a speed of 62 m/s. What mass of air must pass through the blades every second to produce enough thrust for the helicopter to hover?
A child sits in a wagon with a pile of 0.34-kg rocks. If she can throw each rock with a speed of 9.5 m/s relative to the ground, causing the wagon to move, how many rocks must she throw per minute to maintain a constant average speed against a 3.4-N force of friction?
A 57.8-kg person holding two 0.880-kg bricks stands on a 2.10-kg skateboard. Initially, the skateboard and the person are at rest. The person now throws the two bricks at the same time so that their speed relative to the person is 17.0 m/s. What is the recoil speed of the person and the skateboard
A fire hose can expel water at a rate of 9.5 kg/s (150 gallons/ minute) with a speed of 24 m/s. How much force must the firefighters exert on the hose in order to hold it steady?
A 0.540-kg bucket rests on a scale. Into this bucket you pour sand at the constant rate of 56.0 g/s. If the sand lands in the bucket with a speed of 3.20 m/s,(a) What is the reading of the scale when there is 0.750 kg of sand in the bucket?(b) What is the weight of the bucket and the 0.750 kg of
Holding a long rope by its upper end, you lower it onto a scale. The rope has a mass of 0.13 kg per meter of length, and is lowered onto the scale at the constant rate of 1.4 m/s.(a) Calculate the thrust exerted by the rope as it lands on the scale.(b) At the instant when the amount of rope at rest
A 0.145-kg baseball is dropped from rest. If the magnitude of the baseball's momentum is 1.55 kg ∙ m/s just before it lands on the ground, from what height was it dropped?
Object A has a mass m, object B has a mass 2m, and object C has a mass m/2. Rank these objects in order of increasing kinetic energy, given that they all have the same momentum. Indicate ties where appropriate.
Object A has a mass m, object B has a mass 4m, and object C has a mass m/4. Rank these objects in order of increasing momentum, given that they all have the same kinetic energy. Indicate ties where appropriate.
A juggler performs a series of tricks with three bowling balls while standing on a bathroom scale. Is the average reading of the scale greater than, less than, or equal to the weight of the juggler plus the weight of the three balls? Explain.
A golfer attempts a birdie putt, sending the 0.045-kg ball toward the hole with a speed of 1.2 m/s. Unfortunately, the ball does a "horseshoe" and goes halfway around the rim of the hole. The ball ends up heading back toward the golfer with a speed of 1.1 m/s. If we take the positive direction to
Two trucks drive directly away from one another on a straight line, as indicated in FIGURE 9-37. The trucks drive with their speeds adjusted precisely so that the center of mass (CM) of the two trucks remains stationary-that is, the velocity of the center of mass is zero. The mass and speed of
FIGURE 9-38 shows a block of mass 2m at rest on a horizontal, frictionless table. Attached to this block by a string that passes over a pulley is a second block, with a mass m. The initial position of the center of mass of the blocks is indicated by the point i.The blocks are now released and
A 1.35-kg block of wood sits at the edge of a table, 0.782 m above the floor. A 0.0105-kg bullet moving horizontally with a speed of 715 m/s embeds itself within the block. What horizontal distance does the block cover before hitting the ground?
In a stunt, three people jump off a platform and fall 9.9 m onto a large air bag. A fourth person at the other end of the air bag, the "flier," is launched 17 m vertically into the air. Assume all four people have a mass of 75 kg.(a) What fraction of the mechanical energy of the three jumpers is
The carton of eggs shown in FIGURE 9-39 is filled with a dozen eggs, each of mass m. Initially, the center of mass of the eggs is at the center of the carton.(a) Does the location of the center of mass of the eggs change more if egg 1 is removed or if egg 2 is removed? Explain.(b) Find the center
During a severe storm in Palm Beach, FL, on January 2, 1999, 31 inches of rain fell in a period of nine hours. Assuming that the raindrops hit the ground with a speed of 10 m/s, estimate the average upward force exerted by one square meter of ground to stop the falling raindrops during the storm.
A 285-g ball falls vertically downward, hitting the floor with a speed of 2.5 m/s and rebounding upward with a speed of 2.0 m/s.(a) Find the magnitude of the change in the ball's momentum.(b) Find the change in the magnitude of the ball's momentum.(c) Which of the two quantities calculated in parts
An experiment is performed in which two air carts collide on an air track. Position-versus-time data from a video of the experiment is shown in FIGURE 9-40.(a) Is the collision elastic or inelastic? Explain.(b) What is the speed of the center of mass of the two carts?
Figure 9-40 shows position-versus-time data from an experiment in which two air carts collide on an air track. If the mass of the air cart that is moving initially is 0.24 kg, what is the mass of the other cart?
To balance a 35.5-kg automobile tire and wheel, a mechanic must place a 50.2-g lead weight 25.0 cm from the center of the wheel. When the wheel is balanced, its center of mass is exactly at the center of the wheel. How far from the center of the wheel was its center of mass before the lead weight
A hoop of mass M and radius R rests on a smooth, level surface. The inside of the hoop has ridges on either side, so that it forms a track on which a ball can roll, as indicated in FIGURE 9-41. If a ball of mass 2M and radius r = R/4 is released as shown, the system rocks back and forth until it
A 63-kg canoeist stands in the middle of her 22-kg canoe. The canoe is 3.0 m long, and the end that is closest to land is 2.5 m from the shore. The canoeist now walks toward the shore until she comes to the end of the canoe.(a) When the canoeist stops at the end of her canoe, is her distance from
A honeybee with a mass of 0.150 g lands on one end of a floating 4.75-g popsicle stick, as shown in FIGURE 9-42. After sitting at rest for a moment, it runs toward the other end with a velocity v(vector)brelative to the still water. The stick moves in the opposite direction with a speed of 0.120
A young hockey player stands at rest on the ice holding a 1.3-kg helmet. The player tosses the helmet with a speed of 6.5 m/s in a direction 11° above the horizontal, and recoils with a speed of 0.25 m/s. Find the mass of the hockey player.
A 0.341-kg block of wood hangs from the ceiling by a string, and a 0.0567-kg wad of putty is thrown straight upward, striking the bottom of the block with a speed of 8.05 m/s. The wad of putty sticks to the block.(a) Is the mechanical energy of this system conserved?(b) How high does the
A 0.454-kg block is attached to a horizontal spring that is at its equilibrium length, and whose force constant is 25.0 N/m. The block rests on a frictionless surface. A 0.0500-kg wad of putty is thrown horizontally at the block, hitting it with a speed of 8.94 m/s and sticking. How far does the
The giant Pacific octopus (Enteroctopus dofleini) has a typical mass of 15 kg and can propel itself by means of a water jet when frightened.(a) If it expels water at a mass rate of 2.4 kg/s and with a speed of 27 m/s, what thrust can it generate?(b) If the seawater exerts a resistive force of 18 N
Object 1 has a mass m1 and a velocity v(vector)1 = (2.80 m/s)x̂. Object 2 has a mass m2 and a velocity v(vector)2 = (3.10 m/s)ŷ. The total momentum of these two objects has a magnitude of 17.6 kg ∙ m/s and points in a direction 66.5° above the positive x axis. Find m1 and m2.
Find the center of mass of a water molecule, referring to FIGURE 9-43 for the relevant angles and distances. The mass of a hydrogen atom is 1.0 u, and the mass of an oxygen atom is 16 u, where u is the atomic mass unit (see Problem 39). Use the center of the oxygen atom as the origin of your
The three air carts shown in FIGURE 9-44 have masses, reading from left to right, of m, 2m, and 4m, respectively. Initially, the cart on the right is at rest, whereas the other two carts are moving to the right with a speed v0. All carts are equipped with putty bumpers that give completely
Four identical textbooks, each of length L, are stacked near the edge of a table, as shown in FIGURE 9-45. The books are stacked in such a way that the distance they overhang the edge of the table, d, is maximized. Find the maximum overhang distance d in terms of L. In particular, show that d > L;
Consider a one-dimensional, head-on elastic collision. One object has a mass m1 and an initial velocity v1; the other has a mass m2 and an initial velocity v2. Use momentum conservation and energy conservation to show that the final velocities of the two masses are
Two air carts of mass m1 = 0.84 kg and m2 = 0.42 kg are placed on a frictionless track. Cart 1 is at rest initially, and has a spring bumper with a force constant of 690 N/m. Cart 2 has a flat metal surface for a bumper, and moves toward the bumper of the stationary cart with an initial speed v =
A popular earring design features a circular piece of gold of diameter D with a circular cutout of diameter d, as shown in FIGURE 9-46. If this earring is to balance at the point P, show that the diameters must satisfy the condition D = ϕd, where ϕ = (1 + √5)/2 = 1.61803 is the famous
Two small rubber balls are dropped from rest at a height h above a hard floor. When the balls are released, the lighter ball (with mass m) is directly above the heavier ball (with mass M). Assume the heavier ball reaches the floor first and bounces elastically; thus, when the balls collide, the
A wedge of mass m1 is firmly attached to the top of a scale, as shown in FIGURE 9-47. The inclined surface of the wedge makes an angle θ with the horizontal. Now, a block of mass m2 is placed on the inclined surface of the wedge and allowed to accelerate without friction down the slope.(a) Show
A uniform rope of length L and mass M rests on a table.(a) If you lift one end of the rope upward with a constant speed, v, show that the rope's center of mass moves upward with constant acceleration.(b) Next, suppose you hold the rope suspended in air, with its lower end just touching the table.
The lightest ship that's subject to the mandatory reporting regulations, traveling at 5.0 knots, collides with a large stationary adult right whale of maximum size. As sometimes happens, the whale remains stuck on the prow of the ship after the collision. By how much does the speed of the ship
Your car rolls slowly in a parking lot and bangs into the metal base of a light pole. In terms of safety, is it better for your collision with the light pole to be elastic, inelastic, or is the safety risk the same for either case? Explain.
By how much does the whale's speeds change (in knots) as a result of this collision?A. 0.95B. 1.1C. 2.5D. 4.1
What is the magnitude of the average force (in kN) the ship exerts on the whale during the collision?A. 62B. 270C. 520D. 620
If the ship was traveling at 5.0 knots but was 10 times more massive, how would the force of the collision on the whale compare?A. It would be 100 times larger.B. It would be 10 times larger.C. It would be larger, but not as much as 10 times larger.D. It would be the same.
Suppose a bullet of mass m = 6.75 g is fired into a ballistic pendulum whose bob has a mass of M = 0.675 kg.(a) If the bob rises to a height of 0.128 m, what was the initial speed of the bullet?(b) What was the speed of the bullet- bob combination immediately after the collision took place?
A bullet with a mass m = 8.10 g and an initial speed vi = 320 m/s is fired into a ballistic pendulum. What mass must the bob have if the bullet-bob combination is to rise to a maximum height of 0.125 m after the collision?
Suppose that cart 1 has a mass of 3.00 kg and an initial speed of 0.250 m/s. Cart 2 has a mass of 1.00 kg and is at rest initially.(a) What is the final speed of the carts?(b) How much kinetic energy is lost as a result of the collision?
Suppose the two carts have equal masses and are both moving to the right before the collision. The initial speed of cart 1 (on the left) is v0, and the initial speed of cart 2 (on the right) is v0/2.(a) What is the speed of the center of mass of this system?(b) What percentage of the initial
Suppose we change the race shown in Conceptual Example 10-17 so that a hoop of radius R and mass M races a hoop of radius R and mass 2M.(a) Does the hoop with mass M finish before, after, or at the same time as the hoop with mass 2M? Explain.(b) How would your answer to part (a) change if the hoops
Why should changing the axis of rotation of an object change its moment of inertia, given that its shape and mass remain the same?
Two spheres have identical radii and masses. How might you tell which of these spheres is hollow and which is solid?
The following angles are given in degrees. Convert them to radians: 30°, 45°, 90°, 180°.
A 3.5-inch floppy disk in a computer rotates with a period of 2.00 × 10-1 s. What are(a) The angular speed of the disk(b) The linear speed of a point on the rim of the disk?(c) Does a point near the center of the disk have an angular speed that is greater than, less than, or the same as the
The angle an airplane propeller makes with the horizontal as a function of time is given by θ = (125 rad/s)t + (42.5 rad/s2)t2.(a) Estimate the instantaneous angular velocity at t = 0.00 by calculating the average angular velocity from t = 0.00 to t = 0.010 s.(b) Estimate the instantaneous angular
An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle u in the time t, through what angle did it rotate in the time t/2?
An object at rest begins to rotate with a constant angular acceleration. If the angular speed of the object is v after the time t, what was its angular speed at the time t/2?
The angular speed of a propeller on a boat increases with constant acceleration from 11 rad/s to 39 rad/s in 3.0 revolutions. What is the angular acceleration of the propeller?
After fixing a flat tire on a bicycle you give the wheel a spin.(a) If its initial angular speed was 6.35 rad/s and it rotated 14.2 revolutions before coming to rest, what was its average angular acceleration?(b) For what length of time did the wheel rotate?
A ceiling fan is rotating at 0.96 rev/s. When turned off, it slows uniformly to a stop in 2.4 min.(a) How many revolutions does the fan make in this time?(b) Using the result from part (a), find the number of revolutions the fan must make for its speed to decrease from 0.96 rev/s to 0.48 rev/s.
A discus thrower starts from rest and begins to rotate with a constant angular acceleration of 2.2 rad/s2.(a) How many revolutions does it take for the discus throwers angular speed to reach 6.3 rad/s?(b) How much time does this take?
At 3:00 the hour hand and the minute hand of a clock point in directions that are 90.0° apart. What is the first time after 3:00 that the angle between the two hands has decreased by half to 45.0°?
A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a
The following angles are given in radians. Convert them to degrees: π/6, 0.70π, 1.5π, 5π.
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