Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 12.6, Problem 82P
The roller coaster car travels down the helical path at constant speed such that the parametric equations that define its position are x = c sin kt, y = c cos kt, z = h – bt, where c, h, and b are constants. Determine the magnitudes of its velocity and acceleration.
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Chapter 12 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 12.2 - a. If s = (2t3) m, where t is in seconds,...Ch. 12.2 - Initially, the car travels along a straight road...Ch. 12.2 - A ball is thrown vertically upward with a speed of...Ch. 12.2 - A particle travels along a straight line with a...Ch. 12.2 - A particle travels along a straight line with a...Ch. 12.2 - The position of the particle is given by s = (2t2 ...Ch. 12.2 - A particle travels along a straight line with an...Ch. 12.2 - A particle moves along a straight line such that...Ch. 12.2 - A particle travels along a straight line with a...Ch. 12.2 - Starting from rest, a particle moving in a...
Ch. 12.2 - If a particle has an initial velocity of v0 = 12...Ch. 12.2 - A particle travels along a straight line with a...Ch. 12.2 - A particle travels along a straight line with a...Ch. 12.2 - Prob. 5PCh. 12.2 - Prob. 6PCh. 12.2 - Prob. 7PCh. 12.2 - A particle is moving along a straight line such...Ch. 12.2 - The acceleration of a particle as it moves along a...Ch. 12.2 - A particle moves along a straight line with an...Ch. 12.2 - A particle travels along a straight-line path such...Ch. 12.2 - Traveling with an initial speed of 70 km/h, a car...Ch. 12.2 - Tests reveal that a normal driver takes about 0.75...Ch. 12.2 - The position of a particle along a straight-line...Ch. 12.2 - A particle is moving with a velocity of v0 when s...Ch. 12.2 - A particle is moving along a straight line with an...Ch. 12.2 - Car B is traveling a distanced ahead of car A....Ch. 12.2 - The acceleration of a rocket traveling upward is...Ch. 12.2 - Prob. 19PCh. 12.2 - The velocity of a particle traveling along a...Ch. 12.2 - A freight train travels at v = 60(1 et) ft/s,...Ch. 12.2 - A sandbag is dropped from a balloon which is...Ch. 12.2 - A particle is moving along a straight line such...Ch. 12.2 - Prob. 24PCh. 12.2 - If the effects of atmospheric resistance are...Ch. 12.2 - The acceleration of a particle along a straight...Ch. 12.2 - When a particle falls through the air, its initial...Ch. 12.2 - Prob. 28PCh. 12.2 - Prob. 29PCh. 12.2 - A sphere is fired downwards into a medium with an...Ch. 12.2 - Prob. 31PCh. 12.2 - Prob. 32PCh. 12.2 - Prob. 33PCh. 12.2 - Prob. 34PCh. 12.3 - The particle travels along a straight track such...Ch. 12.3 - Prob. 10FPCh. 12.3 - Prob. 11FPCh. 12.3 - The sports car travels along a straight road such...Ch. 12.3 - The dragster starts from rest and has an...Ch. 12.3 - The dragster starts from rest and has a velocity...Ch. 12.3 - A freight train starts from rest and travels with...Ch. 12.3 - Prob. 36PCh. 12.3 - Prob. 37PCh. 12.3 - Prob. 38PCh. 12.3 - Prob. 39PCh. 12.3 - An airplane starts from rest, travels 5000 ft down...Ch. 12.3 - The elevator starts from rest at the first floor...Ch. 12.3 - The velocity of a car is plotted as shown....Ch. 12.3 - The motion of a jet plane just after landing on a...Ch. 12.3 - Prob. 44PCh. 12.3 - The vt graph for a particle moving through an...Ch. 12.3 - The a-s graph for a rocket moving along a straight...Ch. 12.3 - A two-stage rocket is fired vertically from rest...Ch. 12.3 - The race car starts from rest and travels along a...Ch. 12.3 - The jet car is originally traveling at a velocity...Ch. 12.3 - The car starts from rest at s = 0 and is subjected...Ch. 12.3 - The v-t graph for a train has been experimentally...Ch. 12.3 - A motorcycle starts from rest at s = 0 and travels...Ch. 12.3 - A motorcycle starts from rest at s = 0 and travels...Ch. 12.3 - The v-t graph for the motion of a car as it moves...Ch. 12.3 - An airplane lands on the straight runway,...Ch. 12.3 - Starting from rest at s = 0, a boat travels in a...Ch. 12.3 - Starting from rest at s = 0, a boat travels in a...Ch. 12.3 - A two-stage rocket is fired vertically from rest...Ch. 12.3 - The speed of a train during the first minute has...Ch. 12.3 - A man riding upward in a freight elevator...Ch. 12.3 - Two cars start from rest side by side and travel...Ch. 12.3 - If the position of a particle is defined as s =...Ch. 12.3 - From experimental data, the motion of a jet plane...Ch. 12.3 - The motion of a train is described by the as graph...Ch. 12.3 - The jet plane starts from rest at s = 0 and is...Ch. 12.3 - Prob. 66PCh. 12.3 - Prob. 67PCh. 12.3 - The v-s graph for a test vehicle is shown....Ch. 12.6 - Use the chain-rule and find and in terms of x, ...Ch. 12.6 - Prob. 4PPCh. 12.6 - Prob. 5PPCh. 12.6 - Prob. 6PPCh. 12.6 - Prob. 15FPCh. 12.6 - Prob. 16FPCh. 12.6 - A particle is constrained to travel along the...Ch. 12.6 - Prob. 18FPCh. 12.6 - A particle is traveling along the parabolic path y...Ch. 12.6 - Prob. 20FPCh. 12.6 - The ball is kicked from point A with the initial...Ch. 12.6 - The ball is kicked from point A with the initial...Ch. 12.6 - Prob. 23FPCh. 12.6 - Prob. 24FPCh. 12.6 - A ball is thrown from A. If it is required to...Ch. 12.6 - Prob. 26FPCh. 12.6 - If the velocity of a particle is defined as v(t) =...Ch. 12.6 - The velocity of a particle is v= {3i + (6 2t)j}...Ch. 12.6 - A particle, originally at rest and located at...Ch. 12.6 - The velocity of a particle is given by v ={16t2 i...Ch. 12.6 - The water sprinkler, positioned at the base of a...Ch. 12.6 - Prob. 74PCh. 12.6 - Prob. 75PCh. 12.6 - A particle travels along the curve from A to B in...Ch. 12.6 - The position of a crate sliding down a ramp is...Ch. 12.6 - A rocket is fired from rest at x = 0 and travels...Ch. 12.6 - The particle travels along the path defined by the...Ch. 12.6 - The motorcycle travels with constant speed v0...Ch. 12.6 - A particle travels along the curve from A to B in...Ch. 12.6 - The roller coaster car travels down the helical...Ch. 12.6 - Pegs A and B are restricted to move in the...Ch. 12.6 - The van travels over the hill described by y =...Ch. 12.6 - The flight path of the helicopter as it takes off...Ch. 12.6 - Determine the minimum initial velocity v0 and the...Ch. 12.6 - The catapult is used to launch a ball such that it...Ch. 12.6 - Neglecting the size of the ball, determine the...Ch. 12.6 - The girl at A can throw a ball at vA = 10 m/s....Ch. 12.6 - Show that the girl at A can throw the ball to the...Ch. 12.6 - The ball at A is kicked with a speed vA, = 80ft/s...Ch. 12.6 - The ball at A is kicked such that A = 30. If it...Ch. 12.6 - A golf ball is struck with a velocity of 80 ft/s...Ch. 12.6 - A golf ball is struck with a velocity of 80 ft/s...Ch. 12.6 - The basketball passed through the hoop even...Ch. 12.6 - It is observed that the skier leaves the ramp A at...Ch. 12.6 - It is observed that the skier leaves the ramp A at...Ch. 12.6 - Determine the horizontal velocity vA of a tennis...Ch. 12.6 - The missile at A takes off from rest and rises...Ch. 12.6 - The projectile is launched with a velocity v0....Ch. 12.6 - Prob. 101PCh. 12.6 - Prob. 102PCh. 12.6 - If the dart is thrown with a speed of 10 m/s,...Ch. 12.6 - Prob. 104PCh. 12.6 - Prob. 105PCh. 12.6 - Prob. 106PCh. 12.6 - Prob. 107PCh. 12.6 - Prob. 108PCh. 12.6 - The catapult is used to launch a ball such that it...Ch. 12.7 - a. Determine the acceleration at the instant...Ch. 12.7 - Prob. 27FPCh. 12.7 - Prob. 28FPCh. 12.7 - Prob. 29FPCh. 12.7 - Prob. 30FPCh. 12.7 - Prob. 31FPCh. 12.7 - Prob. 32FPCh. 12.7 - An automobile is traveling on a curve having a...Ch. 12.7 - Determine the maximum constant speed a race car...Ch. 12.7 - A boat has an initial speed of 16 ft/s. If it then...Ch. 12.7 - The position of a particle is defined by r = {4(t ...Ch. 12.7 - The automobile has a speed of 80 ft/s at point A...Ch. 12.7 - The automobile is originally at rest at s = 0. If...Ch. 12.7 - The automobile is originally at rest s = 0. If it...Ch. 12.7 - The two cars A and B travel along the circular...Ch. 12.7 - Prob. 118PCh. 12.7 - The satellite S travels around the earth in a...Ch. 12.7 - The car travels along the circular path such that...Ch. 12.7 - The car passes point A with a speed of 25 m/s...Ch. 12.7 - Prob. 122PCh. 12.7 - The motorcycle is traveling at 1 m/s when it is at...Ch. 12.7 - The box of negligible size is sliding down along a...Ch. 12.7 - The car travels around the circular track having a...Ch. 12.7 - The car travels around the portion of a circular...Ch. 12.7 - Prob. 127PCh. 12.7 - Prob. 128PCh. 12.7 - Prob. 129PCh. 12.7 - Prob. 130PCh. 12.7 - A boat is traveling along a circular path having a...Ch. 12.7 - Prob. 132PCh. 12.7 - Prob. 133PCh. 12.7 - Prob. 134PCh. 12.7 - When t = 0, the train has a speed of 8 m/s, which...Ch. 12.7 - At a given instant the jet plane has a speed of...Ch. 12.7 - The ball is ejected horizontally from the tube...Ch. 12.7 - The motorcycle is traveling at 40 m/s when it is...Ch. 12.7 - Prob. 139PCh. 12.7 - Cars move around the traffic circle which is in...Ch. 12.7 - A package is dropped from the plane which is...Ch. 12.7 - The race car has an initial speed vA = 15 m/s at...Ch. 12.7 - Prob. 143PCh. 12.7 - Prob. 144PCh. 12.7 - Particles A and B are traveling counter-clockwise...Ch. 12.7 - Prob. 146PCh. 12.7 - Prob. 147PCh. 12.7 - The jet plane is traveling with a constant speed...Ch. 12.7 - Prob. 149PCh. 12.7 - The train passes point A with a speed of 30 m/s...Ch. 12.7 - The particle travels with a constant speed of 300...Ch. 12.7 - Prob. 152PCh. 12.7 - Prob. 153PCh. 12.7 - If the speed of the crate at A is 15 ft/s, which...Ch. 12.8 - The car has a speed of 55 ft/s. Determine the...Ch. 12.8 - The platform is rotating about the vertical axis...Ch. 12.8 - Peg P is driven by the fork link OA along the...Ch. 12.8 - Prob. 36FPCh. 12.8 - Prob. 37FPCh. 12.8 - Prob. 38FPCh. 12.8 - A particle is moving along a circular path having...Ch. 12.8 - For a short time a rocket travels up and to the...Ch. 12.8 - A particle moves along a path defined by polar...Ch. 12.8 - An airplane is flying in a straight line with a...Ch. 12.8 - The small washer is sliding down the cord OA. When...Ch. 12.8 - A radar gun at O rotates with the angular velocity...Ch. 12.8 - If a particle moves along a path such that r = (2...Ch. 12.8 - Prob. 162PCh. 12.8 - Prob. 163PCh. 12.8 - The car travels along the circular curve of radius...Ch. 12.8 - The time rate of change of acceleration is...Ch. 12.8 - A particle is moving along a circular path having...Ch. 12.8 - The slotted link is pinned at O, and as a result...Ch. 12.8 - For a short time the bucket of the backhoe traces...Ch. 12.8 - Prob. 169PCh. 12.8 - A particle moves in the x y plane such that its...Ch. 12.8 - At the instant shown, the man is twirling a hose...Ch. 12.8 - The rod OA rotates clockwise with a constant...Ch. 12.8 - Determine the magnitude of the acceleration of the...Ch. 12.8 - A double collar C is pin connected together such...Ch. 12.8 - A block moves outward along the slot in the...Ch. 12.8 - The car travels around the circular track with a...Ch. 12.8 - The car travels around the circular track such...Ch. 12.8 - Prob. 178PCh. 12.8 - A horse on the merry-go-round moves according to...Ch. 12.8 - A horse on the merry-go-round moves according to...Ch. 12.8 - Prob. 181PCh. 12.8 - Prob. 182PCh. 12.8 - Prob. 183PCh. 12.8 - A truck is traveling along the horizontal circular...Ch. 12.8 - The rod OA rotates counterclockwise with a...Ch. 12.8 - Determine the magnitude of the acceleration of the...Ch. 12.8 - Prob. 187PCh. 12.8 - Prob. 188PCh. 12.8 - Prob. 189PCh. 12.8 - Prob. 190PCh. 12.8 - Prob. 191PCh. 12.8 - For a short time the arm of the robot is extending...Ch. 12.8 - The double collar C is pin connected together such...Ch. 12.8 - The double collar C is pin connected together such...Ch. 12.10 - Determine the velocity of block D if end A of the...Ch. 12.10 - Prob. 40FPCh. 12.10 - Prob. 41FPCh. 12.10 - Prob. 42FPCh. 12.10 - Prob. 43FPCh. 12.10 - Prob. 44FPCh. 12.10 - Prob. 45FPCh. 12.10 - Prob. 46FPCh. 12.10 - The boats A and B travel with constant speeds of...Ch. 12.10 - At the instant shown, cars A and B are traveling...Ch. 12.10 - If the end of the cable at A is pulled down with a...Ch. 12.10 - The motor at C pulls in the cable with an...Ch. 12.10 - The pulley arrangement shown is designed for...Ch. 12.10 - If the end of the cable at A is pulled down with a...Ch. 12.10 - Determine the displacement of the log if the truck...Ch. 12.10 - Determine the constant speed at which the cable at...Ch. 12.10 - Starting from rest, the cable can be wound onto...Ch. 12.10 - If the end A of the cable is moving at vA = 3 m/s,...Ch. 12.10 - Determine the time needed for the load at B to...Ch. 12.10 - The cable at A is being drawn toward the motor at...Ch. 12.10 - If block A of the pulley system is moving downward...Ch. 12.10 - Determine the speed of the block at B.Ch. 12.10 - Determine the speed of block A if the end of the...Ch. 12.10 - The motor draws in the cable at C with a constant...Ch. 12.10 - The cord is attached to the pm at C and passes...Ch. 12.10 - The 16-ft-long cord is attached to the pin at C...Ch. 12.10 - The roller at A is moving with a velocity of A = 4...Ch. 12.10 - The girl at C stands near the edge of the pier and...Ch. 12.10 - Prob. 213PCh. 12.10 - At the instant shown, the car at A is traveling at...Ch. 12.10 - The motor draws in the cord at B with an...Ch. 12.10 - If block B is moving down with a velocity vB and...Ch. 12.10 - The crate C is being lifted by moving the roller...Ch. 12.10 - Two planes, A and B, are flying at the same...Ch. 12.10 - Prob. 219PCh. 12.10 - The boat can travel with a speed of 16 km/h in...Ch. 12.10 - Two boats leave the pier P at the same time and...Ch. 12.10 - Prob. 222PCh. 12.10 - Prob. 223PCh. 12.10 - At the instant shown, car A has a speed of 20...Ch. 12.10 - Cars A and B are traveling around the circular...Ch. 12.10 - Prob. 226PCh. 12.10 - At the instant shown, cars A and B are traveling...Ch. 12.10 - Prob. 228PCh. 12.10 - Prob. 229PCh. 12.10 - Prob. 230PCh. 12.10 - Prob. 231PCh. 12.10 - Prob. 232PCh. 12.10 - The football player at A throws the ball in the...Ch. 12.10 - At a given instant the football player at A throws...Ch. 12.10 - Prob. 235PCh. 12.10 - Prob. 1CPCh. 12.10 - Prob. 1RPCh. 12.10 - Prob. 2RPCh. 12.10 - Prob. 3RPCh. 12.10 - Prob. 4RPCh. 12.10 - Prob. 5RPCh. 12.10 - Prob. 6RPCh. 12.10 - Prob. 7RPCh. 12.10 - Prob. 8RPCh. 12.10 - Prob. 9RPCh. 12.10 - Prob. 10RPCh. 12.10 - Prob. 11RP
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