Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 12.2, Problem 33P
To determine
The minimum initial velocity (escape velocity) of the body so that the body don’t fall back to earth.
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Students have asked these similar questions
2. Express the following complex numbers in rectangular form.
(a) z₁ = 2еjл/6
(b) Z2=-3e-jπ/4
(c) Z3 =
√√√3e-j³/4
(d) z4 = − j³
A prismatic beam is built into a structure. You can consider the boundary conditions at A and B to be
fixed supports. The beam was originally designed to withstand a triangular distributed load, however,
the loading condition has been revised and can be approximated by a cosine function as shown in the
figure below. You have been tasked with analysing the structure. As the beam is prismatic, you can
assume that the bending rigidity (El) is constant.
wwo cos
2L
x
A
B
Figure 3: Built in beam with a varying distributed load
In order to do this, you will:
a. Solve the reaction forces and moments at point A and B.
Hint: you may find it convenient to use the principal of superposition.
(2%)
b. Plot the shear force and bending moment diagrams and identify the maximum shear force
and bending moment.
(2%)
c. Develop an expression for the vertical deflection. Clearly state your expression in terms of x.
(1%)
Question 1: Beam Analysis
Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts
as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces
can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a
roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied
to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB
and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these
moments is PL.
Moment Release
A
B
с
°
MB = PL
Mc=
= PL
-L/2-
-L/2-
→
P
D
Figure 1: Two beam arrangement for question 1.
To analyse this structure, you will:
a) Construct the free body diagrams for the structure shown above. When constructing your
FBD's you must make section cuts at point B and C. You can represent the structure as three
separate beams. Following this, construct the…
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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