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physics
mechanics
Questions and Answers of
Mechanics
(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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 =
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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?
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
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
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
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
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
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
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
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
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
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
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 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
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,
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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.
The following angles are given in radians. Convert them to degrees: π/6, 0.70π, 1.5π, 5π.
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