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physics
mechanics
Vector Mechanics for Engineers Statics and Dynamics 11th edition Ferdinand Beer, E. Russell Johnston Jr., David Mazurek, Phillip Cornwell, Brian Self - Solutions
For tests using a ballistocardiograph, a patient lies on a horizontal platform that is supported on jets of air. Because of the air jets, the friction impeding the horizontal motion of the platform is negligible. Each time the heart beats, blood is pushed out of the heart in a direction that is
The carbon monoxide molecule (CO) consists of a carbon atom and an oxygen atom separated by a distance of 1.13 × 10-10 m. The mass mC of the carbon atom is 0.750 times the mass mO of the oxygen atom, or mC = 0.750 mO. Determine the location of the center of mass of this molecule relative to the
Two arrows are fired horizontally with the same speed of 30.0 m/s. Each arrow has a mass of 0.100 kg. One is fired due east and the other due south. Find the magnitude and direction of the total momentum of this two-arrow system. Specify the direction with respect to due east.
A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon is holding a rock. The total mass of the wagon, rider, and rock is 95.0 kg. The mass of the rock is 0.300 kg. Initially the wagon is rolling forward at a speed of 0.500 m/s. Then the person throws
Three guns are aimed at the center of a circle, and each fires a bullet simultaneously. The directions in which they fire are 1208 apart. Two of the bullets have the same mass of 4.50 × 1023 kg and the same speed of 324 m/s. The other bullet has an unknown mass and a speed of 575 m/s. The bullets
A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities 1 and 2, as shown in the drawing. What are the magnitudes of?(a) 1(b) 2?
Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another, as in Figure 7.9, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces acting on their skates can
The drawing shows a human figure in a sitting position. For purposes of this problem, there are three parts to the figure, and the center of mass of each one is shown in the drawing. These parts are: (1) the torso, neck, and head (total mass 5 41 kg) with a center of mass located on the y axis at a
For the situation depicted in the figure, use momentum conservation to determine the magnitude and direction of the final velocity of ball 1 after the collision.(a) Top view of two balls colliding on a horizontal surface.(b) This part of the drawing shows the x and y components of the velocity of
Two joggers, Jim and Tom, are both running at a speed of 4.00 m/s (see the figure). Jim has a mass of 90.0 kg, and Tom has a mass of 55.0 kg. Concepts: (i) Does the total kinetic energy of the two jogger system have a smaller value in part a or b of the figure, or is it the same in both cases? (ii)
The table gives mass and speed data for the two objects in the figure. Concepts: (i) Is it possible for two objects to have different speeds when their momenta have the same amplitude? Explain your answer. (ii) If two objects have the same momenta do they necessarily have the same kinetic energy?
When jumping straight down, you can be seriously injured if you land stiff -legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 75-kg man just before contact with the ground has a speed of 6.4 m/s. (a) In a stiff-legged landing he comes to a halt
A space probe is traveling in outer space with a momentum that has a magnitude of 7.5 × 107 kg ∙ m/s. A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of 2.0 × 106 N and a direction opposite to the probe's motion. It fires for a period of 12s.
A merry-go-round at a playground is a circular platform that is mounted parallel to the ground and can rotate about an axis that is perpendicular to the platform at its center. The angular speed of the merry-go-round is constant, and a child at a distance of 1.4 m from the axis has a tangential
A wheel rotates with a constant angular speed v. Which one of the following is true concerning the angular acceleration a of the wheel, the tangential acceleration aT of a point on the rim of the wheel, and the centripetal acceleration ac of a point on the rim? (a) α = 0 rad/s2, αT = 0 m/s2, and
A rotating object has an angular acceleration of α = 0 rad/s2. Which one or more of the following three statements is consistent with a zero angular acceleration? A. The angular velocity is w = 0 rad/s at all times. B. The angular velocity is w = 10 rad/s at all times. C. The angular displacement
A floor polisher has a rotating disk that has a 15-cm radius. The disk rotates at a constant angular velocity of 1.4 rev/s and is covered with a soft material that does the polishing. An operator holds the polisher in one place for 45 s, in order to buff an especially scuffed area of the floor. How
The sun appears to move across the sky, because the earth spins on its axis. To a person standing on the earth, the sun subtends an angle of θsun = 9.28 × 10-3 rad (see Conceptual Example 2). How much time (in seconds) does it take for the sun to move a distance equal to its own diameter?
A propeller is rotating about an axis perpendicular to its center, as the drawing shows. The axis is parallel to the ground. An arrow is fired at the propeller, travels parallel to the axis, and passes through one of the open spaces between the propeller blades. The angular open spaces between the
Two people start at the same place and walk around a circular lake in opposite directions. One walks with an angular speed of 1.7 × 10-3 rad/s, while the other has an angular speed of 3.4 × 10-3 rad/s. How long will it be before they meet?
A space station consists of two donut-shaped living chambers, A and B that have the radii shown in the drawing. As the station rotates, an astronaut in chamber A is moved 2.40 × 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?
The drawing shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.850 m, and rotating with an angular speed of 95.0 rad/s. The bullet first passes through the left disk and then through the right disk. It is
An automatic dryer spins wet clothes at an angular speed of 5.2 rad/s. Starting from rest, the dryer reaches its operating speed with an average angular acceleration of 4.0 rad/s2. How long does it take the dryer to come up to speed?
The drawing shows a golf ball passing through a windmill at a miniature golf course. The windmill has 8 blades and rotates at an angular speed of 1.25 rad/s. The opening between successive blades is equal to the width of a blade. A golf ball (diameter 4.50 × 10-2 m) has just reached the edge of
The table that follows lists four pairs of initial and final angles of a wheel on a moving car. The elapsed time for each pair of angles is 2.0 s. For each of the four pairs, determine the average angular velocity (magnitude and direction as given by the algebraic sign of your answer). Initial
A figure skater is spinning with an angular velocity of +15 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is +5.1 rad. Determine (a) Her average angular acceleration (b) The time during which she comes to rest.
The angular speed of the rotor in a centrifuge increases from 420 to 1420 rad/s in a time of 5.00 s. (a) Obtain the angle through which the rotor turns. (b) What is the magnitude of the angular acceleration?
A car is traveling along a road, and its engine is turning over with an angular velocity of +220 rad/s. The driver steps on the accelerator, and in a time of 10.0 s the angular velocity increases to +280 rad/s. (a) What would have been the angular displacement of the engine if its angular velocity
A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.05 × 104 rad/s to an angular speed of 3.14 × 104 rad/s. In the process, the bit turns through 1.88 × 104 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum
A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 64 cm and is wound around the top at a spot where its radius is 2.0 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls
The drive propeller of a ship starts from rest and accelerates at 2.90 × 10-3 rad/s2 for 2.10 × 103 s. For the next 1.40 × 103 s the propeller rotates at a constant angular speed. Then it decelerates at 2.30 × 10-3 rad/s2 until it slows (without reversing direction) to an angular speed of 4.00
The earth spins on its axis once a day and orbits the sun once a year (365 ¼ days). Determine the average angular velocity (in rad/s) of the earth as it (a) Spins on its axis (b) Orbits the sun. In each case, take the positive direction for the angular displacement to be the direction of the
The drawing shows a graph of the angular velocity of a rotating wheel as a function of time. Although not shown in the graph, the angular velocity continues to increase at the same rate until t = 8.0 s. What is the angular displacement of the wheel from 0 to 8.0 s?
At the local swimming hole, a favorite trick is to run horizontally off a cliff that is 8.3 m above the water. One diver runs off the edge of the cliff, tucks into a "ball," and rotates on the way down with an average angular speed of 1.6 rev/s. Ignore air resistance and determine the number of
A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.00 rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -25.0 rad/s. While this change
A fan blade is rotating with a constant angular acceleration of + 12.0 rad/s2. At what point on the blade, as measured from the axis of rotation, does the magnitude of the tangential acceleration equal that of the acceleration due to gravity?
Some bacteria are propelled by biological motors that spin hairlike flagella. A typical bacterial motor turning at a constant angular velocity has a radius of 1.5 × 10-8 m, and a tangential speed at the rim of 2.3 × 10-5 m/s. (a) What is the angular speed (the magnitude of the angular velocity)
An auto race takes place on a circular track. A car completes one lap in a time of 18.9 s, with an average tangential speed of 42.6 m/s. Find (a) The average angular speed (b) The radius of the track.
In 9.5 s a fisherman winds 2.6 m of fishing line onto a reel whose radius is 3.0 cm (assumed to be constant as an approximation). The line is being reeled in at a constant speed. Determine the angular speed of the reel.
The take-up reel of a cassette tape has an average radius of 1.4 cm. Find the length of tape (in meters) that passes around the reel in 13 s when the reel rotates at an average angular speed of 3.4 rad/s.
Our sun rotates in a circular orbit about the center of the Milky Way galaxy. The radius of the orbit is 2.2 × 1020 m, and the angular speed of the sun is 1.1 × 10-15 rad/s. How long (in years) does it take for the sun to make one revolution around the center?
The earth has a radius of 6.38 × 106 m and turns on its axis once every 23.9 h.(a) What is the tangential speed (in m/s) of a person living in Ecuador, a country that lies on the equator?(b) At what latitude (i.e., the angle u in the drawing) is the tangential speed one-third that of a
A person lowers a bucket into a well by turning the hand crank, as the drawing illustrates. The crank handle moves with a constant tangential speed of 1.20 m/s on its circular path. The rope holding the bucket unwinds without slipping on the barrel of the crank. Find the linear speed with which the
A thin rod (length = 1.50 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge. The mass of the rod may be ignored, compared to the mass of an object fixed to the top of the rod. The rod, starting from rest, tips over and rotates downward. (a) What
One type of slingshot can be made from a length of rope and a leather pocket for holding the stone. The stone can be thrown by whirling it rapidly in a horizontal circle and releasing it at the right moment. Such a slingshot is used to throw a stone from the edge of a cliff, the point of release
Two Formula One racing cars are negotiating a circular turn, and they have the same centripetal acceleration. However, the path of car A has a radius of 48 m, while that of car B is 36 m. Determine the ratio of the angular speed of car A to the angular speed of car B.
Review Multiple-Concept Example 7 in this chapter as an aid in solving this problem. In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves on a circle. In one instance, the radius of the circle
A rectangular plate is rotating with a constant angular speed about an axis that passes perpendicularly through one corner, as the drawing shows. The centripetal acceleration measured at corner A is n times as great as that measured at corner B. What is the ratio L1/L2 of the lengths of the sides
Multiple-Concept Example 7 explores the approach taken in problems such as this one. The blades of a ceiling fan have a radius of 0.380 m and are rotating about a fixed axis with an angular velocity of 11.50 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an
An electric drill starts from rest and rotates with a constant angular acceleration. After the drill has rotated through a certain angle, the magnitude of the centripetal acceleration of a point on the drill is twice the magnitude of the tangential acceleration. What is the angle?
An automobile tire has a radius of 0.330 m, and its center moves forward with a linear speed of v = 15.0 m/s. (a) Determine the angular speed of the wheel. (b) Relative to the axle, what is the tangential speed of a point located 0.175 m from the axle?
A car is traveling with a speed of 20.0 m/s along a straight horizontal road. The wheels have a radius of 0.300 m. If the car speeds up with a linear acceleration of 1.50 m/s2 for 8.00 s, fi nd the angular displacement of each wheel during this period.
Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 9.1 rad/s. The wheel has a radius of 0.45 m. If you ride the bike for 35 min, how far would you have gone if the bike could move?
A motorcycle, which has an initial linear speed of 6.6 m/s, decelerates to a speed of 2.1 m/s in 5.0 s. Each wheel has a radius of 0.65 m and is rotating in a counterclockwise (positive) direction. What are (a) The constant angular acceleration (in rad/s2) (b) The angular displacement (in rad) of
A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 384 m, the angular speed of the wheels is 288 rad/s. Determine (a) The linear speed of the dragster (b) The magnitude of the angular acceleration of its wheels.
Over the course of a multi-stage 4520-km bicycle race, the front wheel of an athlete's bicycle makes 2.18 × 106 revolutions. How many revolutions would the wheel have made during the race if its radius had been 1.2 cm larger?
The initial angular velocity and the angular acceleration of four rotating objects at the same instant in time are listed in the table that follows. For each of the objects (a), (b), (c), and (d), determine the final angular speed after an elapsed time of 2.0 s. Initial angular velocity v0
A bicycle is rolling down a circular portion of a path; this portion of the path has a radius of 9.00 m. As the drawing illustrates, the angular displacement of the bicycle is 0.960 rad. What is the angle (in radians) through which each bicycle wheel (radius = 0.400 m) rotates?
The differential gear of a car axle allows the wheel on the left side of a car to rotate at a different angular speed than the wheel on the right side. A car is driving at a constant speed around a circular track on level ground, completing each lap in 19.5 s. The distance between the tires on the
The trap-jaw ant can snap its mandibles shut in as little as 1.3 × 10-4 s. In order to shut, each mandible rotates through a 908 angle. What is the average angular velocity of one of the mandibles of the trap-jaw ant when the mandibles snap shut?
A flywheel has a constant angular deceleration of 2.0 rad/s2. (a) Find the angle through which the flywheel turns as it comes to rest from an angular speed of 220 rad/s. (b) Find the time for the flywheel to come to rest.
Refer to Multiple-Concept Example 7 for insight into this problem. During a tennis serve, a racket is given an angular acceleration of magnitude 160 rad/s2. At the top of the serve, the racket has an angular speed of 14 rad/s. If the distance between the top of the racket and the shoulder is 1.5 m,
The drawing shows a chain-saw blade. The rotating sprocket tip at the end of the guide bar has a radius of 4.0 × 1022 m. The linear speed of a chain link at point A is 5.6 m/s. Find the angular speed of the sprocket tip in rev/s.
The table that follows lists four pairs of initial and final angular velocities for a rotating fan blade. The elapsed time for each of the four pairs of angular velocities is 4.0 s. For each of the four pairs, find the average angular acceleration (magnitude and direction as given by the algebraic
In a large centrifuge used for training pilots and astronauts, a small chamber is fixed at the end of a rigid arm that rotates in a horizontal circle. A trainee riding in the chamber of a centrifuge rotating with a constant angular speed of 2.5 rad/s experiences a centripetal acceleration of 3.2
After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of + 1.88 rad/s. During this time, the wheel has an angular acceleration of - 5.04 rad/s2. Determine the angular displacement of the wheel.
At a county fair there is a betting game that involves a spinning wheel. As the drawing shows, the wheel is set into rotational motion with the beginning of the angular section labeled "1" at the marker at the top of the wheel. The wheel then decelerates and eventually comes to a halt on one of the
A racing car, starting from rest, travels around a circular turn of radius 23.5 m. At a certain instant, the car is still accelerating, and its angular speed is 0.571 rad/s. At this time, the total acceleration (centripetal plus tangential) makes an angle of 35.0o with respect to the radius. (The
A quarterback throws a pass that is a perfect spiral. In other words, the football does not wobble, but spins smoothly about an axis passing through each end of the ball. Suppose the ball spins at 7.7rev/s. In addition, the ball is thrown with a linear speed of 19 m/s at an angle of 55o with
Take two quarters and lay them on a table. Press down on one quarter so it cannot move. Then, starting at the 12:00 position, roll the other quarter along the edge of the stationary quarter, as the drawing suggests. How many revolutions does the rolling quarter make when it travels once around the
An automobile, starting from rest, has a linear acceleration to the right whose magnitude is 0.800m/s2 (see the figure). During the next 20.0 s, the tires roll and do not slip. The radius of each wheel is 0.330 m. At the end of this time, what is the angle through which each wheel has rotated?
A rider on a mountain bike is traveling to the left in the figure. Each wheel has an angular velocity of + 21.7 rad/s, where, as usual, the plus sign indicates that the wheel is rotating in the counterclockwise direction. (a) To pass another cyclist, the rider pumps harder, and the angular velocity
Suppose you are driving a car in a counterclockwise direction on a circular road whose radius is r = 390 m (see the figure). You look at the speedometer and it reads a steady 32 m/s (about 72 mi/h). Concepts: (i) Does an object traveling at a constant tangential speed (for example, vT = 32 m/s)
Conceptual Example 2 provides some relevant background for this problem. A jet is circling an airport control tower at a distance of 18.0 km. An observer in the tower watches the jet cross in front of the moon. As seen from the tower, the moon subtends an angle of 9.04 × 10-3 radians. Find the
Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using(a) The parallelogram law,(b) The triangle rule.
Two forces are applied as shown to a hook support. Knowing that the magnitude of P is 35 N, determine by trigonometry (a) The required angle α if the resultant R of the two forces applied to the support is to be horizontal, (b) The corresponding magnitude of R.
Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in cable AD is 481 N.
Three cables are used to tether a balloon as shown. Knowing that the balloon exerts an 800-N vertical force at A, determine the tension in each cable.
A 36-lb triangular plate is supported by three wires as shown. Determine the tension in each wire, knowing that a = 6 in.
Solve Prob. 2.103, assuming that a = 8 in.PROBLEM 2.103A 36-lb triangular plate is supported by three wires as shown. Determine the tension in each wire, knowing that a = 6 in.
A crate is supported by three cables as shown. Determine the weight of the crate knowing that the tension in cable AC is 544 lb.
A 1600-lb crate is supported by three cables as shown. Determine the tension in each cable.
Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that 0, Q = find the value of P for which the tension in cable AD is 305 N.
Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that 1200 N, P = determine the values of Q for which cable AD is taut.
A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AC is 60 N, determine the weight of the plate.
A steel tank is to be positioned in an excavation. Knowing that α = 20°, determine by trigonometry (a) The required magnitude of the force P if the resultant R of the two forces applied at A is to be vertical, (b) The corresponding magnitude of R.
A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AD is 520 N, determine the weight of the plate.
A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 840 lb, determine the vertical force P exerted by the tower on the pin at A.
For the rectangular plate of Problems 2.109 and 2.110, determine the tension in each of the three cables knowing that the weight of the plate is 792 N.
For the cable system of Problems 2.107 and 2.108, determine the tension in each cable knowing that P = 2880 N= and Q = 0
For the cable system of Problems 2.107 and 2.108, determine the tension in each cable knowing that P = 2880 N and Q = 576 N.
For the cable system of Problems 2.107 and 2.108, determine the tension in each cable knowing that P = 2880 N and Q = -576N. (Q is directed downward).
For the transmission tower of Probs. 2.111 and 2.112, determine the tension in each guy wire knowing that the tower exerts on the pin at A an upward vertical force of 1800 lb.PROBLEM 2.111A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If
A steel tank is to be positioned in an excavation. Knowing that the magnitude of P is 500 lb, determine by trigonometry (a) The required angle α if the resultant R of the two forces applied at A is to be vertical, (b) The corresponding magnitude of R.
Three wires are connected at point D, which is located 18 in. below the T-shaped pipe support ABC. Determine the tension in each wire when a 180-lb cylinder is suspended from point D as shown.
Cable BAC passes through a frictionless ring A and is attached to fixed supports at B and C, while cables AD and AE are both tied to the ring and are attached, respectively, to supports at D and E. Knowing that a 200-lb vertical load P is applied to ring A, determine the tension in each of the
Knowing that the tension in cable AE of Prob. 2.123 is 75 lb, determine (a) the magnitude of the load P, (b) the tension in cables BAC and AD.PROBLEM 2.123Cable BAC passes through a frictionless ring A and is attached to fixed supports at B and C, while cables AD and AE are both tied to the ring
Collars A and B are connected by a 525-mm-long wire and can slide freely on frictionless rods. If a force P = (341 N)j is applied to collar A, determine(a) The tension in the wire when y = 155 mm,(b) The magnitude of the force Q required to maintain the equilibrium of the system.
Solve Problem 2.125 assuming that y = 275 mm.PROBLEM 2.125Collars A and B are connected by a 525-mm-long wire and can slide freely on frictionless rods. If a force P = (341 N)j is applied to collar A, determine(a) The tension in the wire when y155 mm,(b) The magnitude of the force Q required to
Two structural members A and B are bolted to a bracket as shown. Knowing that both members are in compression and that the force is 15 kN in member A and 10 kN in member B, determine by trigonometry the magnitude and direction of the resultant of the forces applied to the bracket by members A and B.
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