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physics
mechanics
Physics 10th edition David Young, Shane Stadler - Solutions
A square plate of side 2r is welded to a vertical shaft that rotates with a constant angular velocity ω1. At the same time, rod AB of length r rotates about the center of the plate with a constant angular velocity ω2 with respect to the plate. For the position of the plate shown, determine
Two disks, each of 130-mm radius, are welded to the 500-mm rod CD. The rod-and-disks unit rotates at the constant rate ω2 = 3rad/s with respect to arm AB. Knowing that at the instant shown ω1 = 4rad/s,determine the velocity and acceleration of (a) Point E, (b) Point F.
The position of the stylus tip A is controlled by the robot shown. In the position shown the stylus moves at a constant speed u = 180mm/s relative to the solenoid BC. At the same time, arm CD rotates at the constant rate ω2 = 1.6rad/s with respect to component DEG. Knowing that the entire robot
A wheel moves in the xy plane in such a way that the location of its center is given by the equations x0 = 12????3 and ???????? = ???? = 2, where xO and yO are measured in feet and t is measured in seconds. The angular displacement of a radial line measured from a vertical
Two blocks and a pulley are connected by inextensible cords as shown. The relative velocity of block A with respect to block B is 2.5 ft/s to the left at time t = 0 and 1.25 ft/s to the left when t = 0.25 s. Knowing that the angular acceleration of the pulley is constant, find (a) the relative
A belt is pulled to the right between cylinders A and B. Knowing that the speed of the belt is a constant 5 ft/s and no slippage occurs, determine (a) the angular velocities of A and B, (b) the accelerations of the points which are in contact with the belt.
A baseball pitching machine is designed to deliver a baseball with a ball speed of 70 mph and a ball rotation of 300 rpm clockwise. Knowing that there is no slipping between the wheels and the baseball during the ball launch, determine the angular velocities of wheels A and B.
Knowing that inner gear A is stationary and outer gear C starts from rest and has a constant angular acceleration of 4 rad/s2 clockwise, determine at t = 5 s (a) the angular velocity of arm AB, (b) the angular velocity of gear B, (c) the acceleration of the point on gear B that is in contact with
Knowing that at the instant shown bar AB has an angular velocity of 10 rad/s clockwise and it is slowing down at a rate of 2 rad/s2, determine the angular accelerations of bar BD and bar DE.
Water flows through a curved pipe AB that rotates with a constant clockwise angular velocity of 90 rpm. If the velocity of the water relative to the pipe is 8 m/s, determine the total acceleration of a particle of water at Point P.
A disk of 0.15-m radius rotates at the constant rate ω2 with respect to plate BC, which itself rotates at the constant rate ω1 about the y axis. Knowing that ω1 = ω2= determine, for the position shown, the velocity and acceleration (a) of Point D, (b) of Point F.
Two rods AE and BD pass through holes drilled into a hexagonal block. (The holes are drilled in different planes so that the rods will not touch each other.) Knowing that rod AE has an angular velocity of 20 rad/s clockwise and an angular acceleration of 4 rad/s2 counterclockwise when θ =
Rod BC of length 24 in. is connected by ball-and-socket joints to a rotating arm AB and to a collar C that slides on the fixed rod DE. Knowing that the length of arm AB is 4 in. and that it rotates at the constant rate ω1= 110 rad/s,determine the velocity of collar C when θ =0.
Ring C has an inside radius of 55 mm and an outside radius of 60 mm and is positioned between two wheels A and B, each of 24-mm outside radius. Knowing that wheel A rotates with a constant angular velocity of 300 rpm and that no slipping occurs, determine (a) The angular velocity of the ring C
Ring B has an inside radius r2 and hangs from the horizontal shaft A as shown. Shaft A rotates with a constant angular velocity of 25 rad/s and no slipping occurs. Knowing that r1 = 12 mm, r2 = 30 mm, and r3 = 40 mm, determine (a) The angular velocity of ring B, (b) The accelerations of
A plastic film moves over two drums. During a 4-s interval the speed of the tape is increased uniformly from v0 = 2 ft/s to v1 = 4 ft/s. Knowing that the tape does not slip on the drums, determine (a) The angular acceleration of drum B, (b) The number of revolutions executed by drum B
Cylinder A is moving downward with a velocity of 3 m/s when the brake is suddenly applied to the drum. Knowing that the cylinder moves 6 m downward before coming to rest and assuming uniformly accelerated motion, determine (a) The angular acceleration of the drum, (b) The time required
The system shown is held at rest by the brake-and-drum system shown. After the brake is partially released at 0,t= it is observed that the cylinder moves 5 m in 4.5 s. Assuming uniformly accelerated motion, determine (a) The angular acceleration of the drum, (b) The angular velocity of
A load is to be raised 20 ft by the hoisting system shown. Assuming gear A is initially at rest, accelerates uniformly to a speed of 120 rpm in 5 s, and then maintains a constant speed of 120 rpm, determine (a) The number of revolutions executed by gear A in raising the load, (b) The time
Steel tape is being wound onto a spool that rotates with a constant angular velocity ω0. Denoting by r the radius of the spool and tape at any given time and by b the thickness of the tape, derive an expression for the acceleration of the tape as it approaches the spool.
An automobile travels to the right at a constant speed of 48 mi/h. If the diameter of a wheel is 22 in., determine the velocities of Points B, C, D, and E on the rim of the wheel.
The rotor of a gas turbine is rotating at a speed of 6900 rpm when the turbine is shut down. It is observed that 4 min is required for the rotor to coast to rest. Assuming uniformly accelerated motion, determine (a) The angular acceleration, (b) The number of revolutions that the rotor
A painter is halfway up a 10-m ladder when the bottom starts sliding out from under him. Knowing that point A has a velocity vA = 2 m/s directed to the left when θ = 60°, determine (a) The angular velocity of the ladder, (b) The velocity of the painter.
The plate shown moves in the xy plane. Knowing that (vA)x = 250mm/s, (vB)x = −450mm/s, and (vC)x = −500mm/s, determine (a) The angular velocity of the plate, (b) The velocity of Point A.
Velocity sensors are placed on a satellite that is moving only in the xy plane. Knowing that at the instant shown the uni-directional sensors measure (vA)x = 2 ft/s, (vB)x = −0.333 ft/s, and (vC)y = −2 ft/s, determine (a) The angular velocity of the satellite, (b) The velocity
In the planetary gear system shown, the radius of gears A, B, C, and D is 30 mm and the radius of the outer gear E is 90 mm. Knowing that gear E has an angular velocity of 180 rpm clockwise and that the central gear A has an angular velocity of 240 rpm clockwise, determine (a) The angular
A small grinding wheel is attached to the shaft of an electric motor which has a rated speed of 3600 rpm. When the power is turned on, the unit reaches its rated speed in 5 s, and when the power is turned off, the unit coasts to rest in 70 s. Assuming uniformly accelerated motion, determine the
Arm AB rotates with an angular velocity of 20 rad/s counter-clockwise. Knowing that the outer gear C is stationary, determine (a) the angular velocity of gear B, (b) the velocity of the gear tooth located at Point D.
In the simplified sketch of a ball bearing shown, the diameter of the inner race A is 60 mm and the diameter of each ball is 12 mm. The outer race B is stationary while the inner race has an angular velocity of 3600 rpm. Determine (a) The speed of the center of each ball, (b) The angular
A simplified gear system for a mechanical watch is shown. Knowing that gear A has a constant angular velocity of 1 rev/h and gear C has a constant angular velocity of 1 rpm, determine (a) The radius r, (b) The magnitudes of the accelerations of the points on gear B that are in contact
Knowing that at the instant shown the velocity of collar A is 900 mm/s to the left, determine (a) The angular velocity of rod ADB, (b) The velocity of Point B.
Knowing that at the instant shown the angular velocity of rod DE is 2.4 rad/s clockwise, determine (a) The velocity A, (b) The velocity of Point B.
Knowing that the disk has a constant angular velocity of 15 rad/s clockwise, determine the angular velocity of bar BD and the velocity of collar D when (a) θ = 0, (b) θ = 90°, (c) θ = 180°.
The test rig shown was developed to perform fatigue testing on fitness trampolines. A motor drives the 9-in radius flywheel AB, which is pinned at its center point A, in a counterclockwise direction. The flywheel is attached to slider CD by the 18-in connecting rod BC. Knowing that the "feet" at D
A connecting rod is supported by a knife-edge at Point A. For small oscillations the angular acceleration of the connecting rod is governed by the relation α = −6θ where α is expressed in rad/s2 and θ in radians. Knowing that the connecting rod is released from rest when θ =
In the eccentric shown, a disk of 2-in.-radius revolves about shaft O that is located 0.5 in. from the center A of the disk. The distance between the center A of the disk and the pin at B is 8 in. Knowing that the angular velocity of the disk is 900 rpm clockwise, determine the velocity of the
In the engine system shown, l = 160 mm and b = 60 mm. Knowing that the crank AB rotates with a constant angular velocity of 1000 rpm clockwise, determine the velocity of the piston P and the angular velocity of the connecting rod when (a) θ = 0, (b) θ = 90°.
In the engine system shown l = 160mm and b = 60mm. Knowing that crank AB rotates with a constant angular velocity of 1000 rpm clockwise, determine the velocity of the piston P and the angular velocity of the connecting rod when θ = 60°.
Linkage DBEF is part of a windshield wiper mechanism, where points O, F and D are fixed pinned connections. At the position shown, θ = 60° and link EB is horizontal. Knowing that link EF has a counterclockwise angular velocity of 4 rad/s at the instant shown, determine the angular velocity of
Robert's linkage is named after Richard Robert (1789-1864) and can be used to draw a close approximation to a straight line by locating a pen at Point F. The distance AB is the same as BF, DF and DE. Knowing that the angular velocity of bar AB is 5 rad/s clockwise in the position shown,
Robert's linkage is named after Richard Robert (1789-1864) and can be used to draw a close approximation to a straight line by locating a pen at Point F. The distance AB is the same as BF, DF and DE. Knowing that the angular velocity of plate BDF is 2 rad/s counterclockwise when θ = 90°,
In the position shown, bar DE has a constant angular velocity of 10 rad/s clockwise. Knowing that h = 500 mm, determine (a) The angular velocity of bar FBD, (b) The velocity of Point F.
In the position shown, bar DE has a constant angular velocity of 10 rad/s clockwise. Determine (a) The distance h for which the velocity of Point F is vertical, (b) The corresponding velocity of Point F.
When studying whiplash resulting from rear end collisions, the rotation of the head is of primary interest. An impact test was performed, and it was found that the angular acceleration of the head is defined by the relation α = 700cosθ + 70sinθ where α is expressed in rad/s2 and θ in
Both 6-in.-radius wheels roll without slipping on the horizontal surface. Knowing that the distance AD is 5 in., the distance BE is 4 in. and D has a velocity of 6 in./s to the right, determine the velocity of Point E.
The 80-mm-radius wheel shown rolls to the left with a velocity of 900 mm/s. Knowing that the distance AD is 50 mm, determine the velocity of the collar and the angular velocity of rod AB when (a) β = 0, (b) β = 90°.
For the gearing shown, derive an expression for the angular velocity ωC of gear C and show that ωC is independent of the radius of gear B. Assume that Point A is fixed and denote the angular velocities of rod ABC and gear A by ωABC and ωA respectively.
A juggling club is thrown vertically into the air. The center of gravity G of the 20 in. club is located 12 in. from the knob. Knowing that at the instant shown G has a velocity of 4 ft/s upwards and the club has an angular velocity of 30 rad/s counterclockwise, determine (a) the speeds of Point A
At the instant shown during deceleration, the velocity of an automobile is 40 ft/s to the right. Knowing that the velocity of the contact point A of the wheel with the ground is 5 ft/s to the right, determine (a) The instantaneous center of rotation of the wheel, (b) The velocity of point
A helicopter moves horizontally in the x direction at a speed of 120 mi/h. Knowing that the main blades rotate clockwise with an angular velocity of 180 rpm, determine the instantaneous axis of rotation of the main blades.
The spool of tape shown and its frame assembly are pulled upward at a speed vA = 750 mm/s. Knowing that the 80-mm-radius spool has an angular velocity of 15 rad/s clockwise and that at the instant shown the total thickness of the tape on the spool is 20 mm, determine (a) The instantaneous
The spool of tape shown and its frame assembly are pulled upward at a speed vA = 100mm/s. Knowing that end B of the tape is pulled downward with a velocity of 300 mm/s and that at the instant shown the total thickness of the tape on the spool is 20 mm, determine (a) The instantaneous center of
The double gear rolls on the stationary left rack R. Knowing that the rack on the right has a constant velocity of 2 ft/s, determine (a) The angular velocity of the gear, (b) The velocities of Points A and D.
An overhead door is guided by wheels at A and B that roll in horizontal and vertical tracks. Knowing that when θ = 40° the velocity of wheel B is 1.5 ft/s upward, determine (a) The angular velocity of the door, (b) The velocity of end D of the door.
Rod BDE is partially guided by a roller at D that moves in a vertical track. Knowing that at the instant shown the angular velocity of crank AB is 5 rad/s clockwise and that β = 25°, determine (a) The angular velocity of the rod, (b) The velocity of Point E.
Rod BDE is partially guided by a roller at D which moves in a vertical track. Knowing that at the instant shown β = 30°, Point E has a velocity of 2 m/s down and to the right, determine the angular velocities of rod BDE and crank AB.
A motor at O drives the windshield wiper mechanism so that OA has a constant angular velocity of 15 rpm. Knowing that at the instant shown linkage OA is vertical, θ = 30°, and β = 15°, determine (a) the angular velocity of bar AB, (b) the velocity of the center of the center of bar AB.
A motor at O drives the windshield wiper mechanism so that point B has a speed of 20 mm/s. Knowing that at the instant shown linkage OA is vertical, θ = 40°, and β = 15°, determine (a) The angular velocity of bar OA, (b) The velocity of the center of the center of bar AB.
Two slots have been cut in plate FG and the plate has been placed so that the slots fit two fixed pins A and B. Knowing that at the instant shown the angular velocity of crank DE is 6 rad/s clockwise, determine (a) The velocity of Point F, (b) The velocity of Point G.
The disk is released from rest and rolls down the incline. Knowing that the speed of A is 1.2 m/s when θ = 0°, determine at that instant (a) The angular velocity of the rod, (b) The velocity of B. Only portions of the two tracks are shown.
Two 25-in. rods are pin-connected at D as shown. Knowing that B moves to the left with a constant velocity of 24 in./s, determine at the instant shown (a) The angular velocity of each rod, (b) The velocity of E.
A rectangular plate swings from arms of equal length as shown below. What is the magnitude of the angular velocity of the plate?(a) 0 rad/s(b) 1 rad/s(c) 2 rad/s(d) 3 rad/s(e) Need to know the location of the center of gravity
Knowing that wheel A rotates with a constant angular velocity and that no slipping occurs between ring C and wheel A and wheel B, which of the following statements concerning the angular speeds are true?(a) ωa = ωb(b) ωa > ωb(c) ωa (d) ωa = ωc(e) The contact points
The ball rolls without slipping on the fixed surface as shown. What is the direction of the velocity of Point A?
Three uniform rods, ABC, DCE and FGH are connected as shown. Which of the following statements are true?(a) ωABC = ωDCE = ωFGH(b) ωDCE > ωABC > ωFGH(c) ωDCE (d) ωABC > ωDCE > ωFGH(e) ωFGH = ωDCE
The disk rolls without sliding on the fixed horizontal surface. At the instant shown, the instantaneous center of zero velocity for rod AB would be located in which region?(a) Region 1(b) Region 2(c) Region 3(d) Region 4(e) Region 5(f) Region 6
Bar BDE is pinned to two links, AB and CD. At the instant shown the angular velocities of link AB, link CD and bar BDE are ωAB, ωCD, and ωBDE, respectively. Which of the following statements concerning the angular speeds of the three objects is true at this instant?(a) ωAB = ωCD
Briefly, what is science?
Why do we say that force is a vector quantity?
Consider these measurements: 10 m, 10 m/s, and 10 m/s2. Which is a measure of speed, which of distance, and which of acceleration?
What is ultrasound?
Why does a struck tuning fork sound louder when it is held against a table?
Give at least two factors that determine the natural frequency of an object?
How do forced vibrations relate to resonance?
When you listen to a radio, why do you hear only one station at a time rather than hearing all stations at once?
How did wind-generated resonance affect the Tacoma Narrows Bridge in Washington in 1940?
When is it possible for one wave to cancel another?
What kind of waves can exhibit interference?
What is the result of a mirror image of a sound signal combining with the sound itself?
What physical phenomenon underlies the production of beats?
What is the speed over the ground of an airplane flying at 100 km/h relative to the air caught in a 100-km/h right-angle crosswind?
What beat frequency will occur when a 370-Hz and a 374-Hz sound source are sounded together?
How does a radio wave differ from a sound wave?
In the bathtub, submerge your head and listen to the sound you make when you click your fingernails together or tap the tub beneath the water surface. Compare the sound you make when both the source and your ears are above the water. At the risk of getting the floor wet, slide back and forth in the
Stretch a piece of balloon rubber not too tightly over a radio loudspeaker. Glue a small, very lightweight piece of mirror, aluminum foil, or polished metal near one edge. Project a narrow beam of light on the mirror while your favorite music is playing and observe the beautiful patterns that are
For years, marine scientists were mystified by sound waves detected by underwater microphones in the Pacific Ocean. These so-called T-waves were among the purest sounds in nature. Eventually the scientists traced the source to underwater volcanoes, whose rising columns of bubbles resonated like
Why don't you hear the sound of distant fireworks until after you see them?
If the Moon blew up, why wouldn't we hear it?
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If you toss a stone in still water, concentric circles are formed. What form will waves have if a stone is tossed into smoothly flowing water?
Why do flying bees buzz?
Grandma is interested in your educational progress. Text Grandma and, without using equations, explain to her the difference between velocity and acceleration.
A cat can hear sound frequencies up to 70,000 Hz. Bats send and receive ultra-high-frequency squeaks up to 120,000 Hz. Which hears sound of shorter wavelengths: cats or bats?
What does it mean to say that a radio station is "at 101.1 on your FM dial"?
Sound from source A has twice the frequency of sound from source B. Compare the wavelengths of sound from the two sources?
What happens to the wavelength of sound as the frequency increases?
In the stands of a racetrack, you notice smoke from the starter's gun before you hear the gun fire. Explain.
In Olympic competition, a microphone detects the sound of the starter's gun and sends it electrically to speakers at every runner's starting block. Why?
Why is the Moon described as a "silent planet"?
What two physics mistakes occur in a science fiction movie that shows a distant explosion in outer space and you see and hear the explosion at the same time?
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