Engineering Mechanics Dynamics RC Hibbeler 6th edition

Engineering Mechanics
Dynamics
R.C. Hibbeler
6th edition
Solution manual; manual & mathcad
December 2015. V0.1
Made by A.J.P. Schalkwijk
12.1 Rectilinear Kinematics: Continuous Motion
Page 7, example 12-1: The car in fig. 12-2 moves in a straight line such
that for a short time it's velocity is defined by v=(9t^2 + 2t) ft/s, where t is in
seconds. Determine its position and acceleration when t=3s. When t=0,
s=0.
Page 8, example 12-2: A small particle is fired vertically downward into a
fluid medium with an initial velocity of 60m/s. If the projectile experiences
a deceleration which is equal to a=(-0.4v^3) m/s^2, where v is measured
in m/s, determine the projectile's velocity and position 4s after it is fired.
Page 9, example 12-3: A boy tosses a ball in the vertical direction of the
side of a cliff, as shown in fig. 12-4. If the initial velocity of the ball is 15m/s
upward, and the ball is released 40m from the bottom of the cliff,
determine the maximum height Sb reached by the ball and the speed of
the ball just before it hits the ground. During the entire time the ball is in
motion, it is subjected to a constant downward acceleration of 9.81m/s^2
due to gravity. Neglect the effect of air resistance.
Page 10, example 12-4: A metallic particle is subjected to the influence of
a magnetic field such that it travels downward through a fluid that extends
from plate A to plate B, fig 12-5. If the particle is released from rest at the
midpoint C, s=100mm, and the acceleration is measured as a=(4s)m/s^2,
where s is in meters, determine the velocity of the particle when it reaches
plate B, s=200mm, and the time it needs to travel van C to B.
Page 11, example 12-5: A particle moves along a horizontal line such that it's
velocity is given by v=(3t^2-6t)m/s, where t is the time in seconds. If it is
initially located at the origin O, determine the distance traveled by the particle
during the time interval t=0 to t=3.5, and the particle's average velocity and
average speed during this time interval.
Page12, problem 12-1: If a particle has an initial velocity of V0=12ft/sec to right,
determine its position when t=10s, if a=2ft/sec^2 to the left. Originally s0=0.
Page 12, problem 12-2: From approximately what floor of a building must
a car be dropped from an at-rest position so that it reaches a speed of
80.7 ft/sec (55 mi/hr) when it hits the ground? Each floor 12ft higher than
the one below it.
Page 12, problem 12-3: A particle is moving along a straight line such that
its position is given by s=(4t-t^2) ft., where t is in seconds. Determine the
distance travelled from t=0 to t=5s, the average velocity, and the average
speed of the particle during this time interval.
Page 12, problem 12-5: A particle is moving along a straight line path such
that it's position is defined by s=(10t^2+20)mm, where t is in seconds.
Determine (a) the displacement of the particle during the time interval from
t=1 s to t=5 s, (b) the average velocity of the particle during this time
interval, and (c) the acceleration at t=1 s.
Page 12, problem 12-6: A ball is thrown vertically upward from the top of a
ledge with an initial velocity of Va=35ft/sec. Determine (a) how high above
the top of the cliff the ball will go before its stops at B, (b) the time Ta-b it
takes to reach its maximum height, and (c) the total time Ta-c needed for it
to reach the ground at C from the instant it is released.
Page 12, problem 12-7: A car, initially at rest, moves along a straight road
with constant acceleration such that it attains a velocity of V=60ft/s when
s=150ft. Then after being subjected to another constant acceleration, it
attains a final velocity of V=100ft/s when s=325ft. Determine the average
velocity and average acceleration of the car for the entire 325ft
displacement.
Page 12, problem 12-9: When a train is travelling along a straight track at
2m/s, it begins to accelerate at a=(60V^-4)m/s^2, where V is in m/s.
Determine the velocity V and the position of the train 3sec. after the
acceleration.
Page 12, problem 12-10: A race car uniformly accelerates at 10ft/s^2 from
rest, reaches a maximum speed of 60mi/h, and then decelerates uniformly
to a stop. Determine the total elapsed time if the distance travelled was
1500ft.
Page 13, problem 12-11: A small metal particle passes through a fluid
medium under the influence of magnetic attraction. The position of the
particle is defined by s=(0.5t^3+4t)inch., where t is in seconds. Determine
the position, velocity, and acceleration of the particle when t=3s.
Page 13, problem 12-13: A particle travels to the right along a straight path
with a velocity v=[5/(4+s)]m/s, where s is in meters. Determine its position
when t=6s if s=5m when t=0.
Page 13, problem 12-14: The velocity of a particle traveling along a
straight line is v=(6t-3t^2)m/s, where t is in seconds. If s=0 when t=0,
determine the particle's deceleration and position when t=3s. How far has
the particle traveled during the 3-s time interval, and what is the average
speed?
Page 13, problem 12-17: At the same instant, two cars A and B start from
rest at a stop line. Car A has a constant acceleration of aA=8m/s^2, while
car B has an acceleration of aB=(2t(3/2))m/s^2, where t is in seconds.
Determine the distance between the cars when A reaches a velocity of
Va=120km/h.
Page 13, problem 12-18: A particle moves along a straight path with an
acceleration of a=(5/s)m/s^2, where s is in meters. Determine the
particle's velocity when s=2m if it is released from rest when s=1m.
Page 13, problem 12-19: A particle moves with accelerated motion such
that a=-k*s, where s is the distance from the starting point and k is a
proportionality constant which is to be determined. When s=2ft the velocity
is 4ft/s, and when s=3.5ft the velocity is 8ft/s. What is s when v=0?
Page 13, problem 12-21: A particle moving along a straight line is
subjected to a deceleration a=(-2v^3)m/s^2, where v is in m/s. If it has a
velocity v=8m/s and a position s=10m when t=0, determine its velocity and
position when t=4s.
Page 14, problem 12-22: The acceleration of a rocket travelling upward is
given by a=(6+0.02s) m/s^2, where s in meters. Determine the rocket's
velocity when s=2km and the time needed to reach this elevation. Initially,
v=0 and s=0 when t=0.
Page 14, problem 12-23: Two trains are traveling in opposite directions on
parallel tracks. Train A is 150m long and has a speed which is twice as
fast as train B, which is 250m long. Determine the speed of each train if a
passenger in train A observes that train B passes in 4s.
Page 14, problem 12-25: The juggler maintains the motion of three balls,
such that each rises to a height of 4ft. If two balls are in the air at any one
time, determine the time the third ball must remain in her hand after the
first ball is thrown.
Page 14, problem 12-26: The juggler throws a ball into the air 4ft above
her hand. How much time will elapse before she must catch it at the same
elevation from which she threw it? What would be the elapsed time if she
threw it 8 ft into the air?
Page 14, problem 12-27: When two cars A and B are next to one another,
they are traveling in the same direction with speeds Va and Vb,
respectively. If B maintains its constant speed, while A begins to
decelerate at aA, determine the distance between the cars at the instant A
stops.
Page 14, problem 12-29: When a particle falls through the air, it's initial
acceleration a=g diminishes until it is zero, and thereafter it falls at a
constant velocity Vf. If this variation of the acceleration can expressed as
a=(g/Vf^2)(Vf^2-V^2), determine the time needed for the velocity to
become V<Vf. Initially the particle falls from rest.
12.2 Rectilinear Kinematics: Erratic Motion
Page 17, example 12-6: A car moves along a straight line path such that
its position is described by the graph shown in fig. 12-9a. Construct the v-t
and a-t graphs for the time period 0<t<30s.
Page 19, example 12-7: A rocket sled starts from rest and travels along a
straight track such that it accelerates at a constant rate for 10s and then
decelerates at a constant rate. Draw the v-t and s-t graphs and determine the
time t' needed to stop the sled. How far has the sled traveled?
Page 21, problem 12-8: The v-s graph describing the motion of a motorcycle
is shown in fig. 12-15a. Construct the a-s graph of the motion and determine
the time needed for the motorcycle to reach the position s=400ft.
Page 22, problem 12-31: If the position of a particle is defined as
s=(5t-3t^2) ft, where t is in seconds, construct the s-t, v-t and a-t graph for
0 < t < 10 s.
Page 22, problem 12-33: The speed of a train during the first minute of its
motion has been recorded as follows:
Plot the v-t graph, approximating the curve as straight line segments between
the given points. Determine the total distance traveled.
Page 22, problem 12-34: The s-t graph for a train has been determined
experimentally. From the data, construct the v-t and a-t graphs for the
motion.
Page 22, problem 12-35: Two cars start from rest side by side at the same
time and position and race along a straight track. Car A accelerates at 4 ft/
s^2 for 35 s and then maintains a constant speed. Car B accelerates at 10
ft/s^2 until reaching a speed of 45mi/h and then maintains a constant
speed. Determine the time at which the cars will again be side by side.
How far has each car traveled? Construct the v-t graphs for each car.
Page 22, problem 12-37: From experimental data, the motion of a jet plane
while traveling along a runway is defined by the v-t graph. Construct the s-t
and a-t graphs for the motion.
Page 23, problem12-38: The car travels along a straight road according to the
v-t graph. Determine the total distance the car travels until it stops when
t=48sec. Also plot the s-t and a-t graphs.
Page 23, problem 12-39: The snowmobile moves along a straight course
according to the v-t graph. Construct the s-t and a-t graphs for the same 50 s
time interval. When t=0, s=0.
Page 23, problem 12-41: The v-t graph for the motion of a car as it moves
along a straight road is shown. Construct the s-t graph and determine the
average speed and the distance traveled for the 30 s time interval. The car
starts from rest at s=0.
Page 23, problem 12-42: A particle starts from rest and is subjected to the
acceleration shown. Construct the v-t graph for the motion, and determine
the distance traveled during the time interval 2s < t < 6s.
Page 24, problem 12-43: An airplane lands on the straight runway, originally
traveling at 110ft/s when s=0. If it is subjected to the decalerations shown,
determine the time t' needed to stop the plane and construct the s-t graph
for the motion:
Page 24, problem 12-45: The a-t graph for a car is shown. Construct the vt graph if the car starts from rest at t=0. At what time t' does the car stop?
Page 24, problem 12-46: A race car starting from rest travels along a
straight road and for 10s has the acceleration shown. Construct the v-t
graph that describes the motion and find the distance traveled in 10s.
Page 25, problem 12-47: The boat is originally traveling at a speed of 8 m/s
when it is subjected to the acceleration shown in the graph. Determine the
boat's maximum speed and the time t when it stops.
Page 25, problem 12-49: The a-s graph for a race car moving along a
straight track has been experimentally determined. If the car starts from rest,
determine its speed when s=50 ft, 150ft and 200ft, respectively.
Page 25, problem 12-51: The jet plane starts from rest at s=0 and is
subjected to the acceleration shown. Construct the v-t graph and determine
the time needed to travel 500ft.
Page 26, problem 12-53: The v-s graph for the car is given for the first 500ft
of its motion. Construct the a-s graph for 0<s<500ft. How long does it take to
travel the 500ft distance? The car starts at s=0 when t=0.
Page 26, problem 12-54: The a-s graph for a boat moving along a straight
path is given. If the boat starts at s=0 when v=0, determine its speed when it
is at s=75ft and 125ft respectively. Use Simpson's rule with n=100 to evaluate
v at s=125ft.
12.3 General Curvilinear motion
Page 32, example 12-9: At any instant the position of the kite in fig. 12-18a
is defined by the coordinates x=30t and y=9t^2 ft, where t is given in
seconds. Determine (a) the equation which describes the path and the
distance of the kite from the boy when t=2s, (b) the magnitude and
direction of the velocity when t=2, and (c) the magnitude and direction of
the acceleration when t=2sec.
Page 33, example 12-10: The motion of a bead B sliding down along the
spiral path shown in fig. 12-19 is defined by the position vector
r={0.5sin(2t)i + 0.5cos(2t)j - 0.2tk}m, where t is given in seconds and the
arguments for sine and cosine are given in radians (pi rad = 180deg).
Determine the location of the bead when t=0.75s and the magnitude of the
bead's velocity and acceleration at this instant.
Page 36, example 12-11: A ball is ejected from the tube, shown in fig
12-21 with a horizontal velocity of 12 m/s. If the height of the tube is 6m,
determine the time needed for the ball to strike the floor and the range R.
Page 37, example 12-12: A ball is thrown from a position 5 ft above the
ground to the roof of a 40ft high building, as shown in fig 12-22. If the
initial velocity of the ball is 70ft/s, inclined at an angle of 60deg from the
horizontal, determine the range or horizontal distance R from the point
where the ball is thrown to where it strikes the roof.
Page 38, example 12-13: When a ball is kicked from A as shown in fig. 12-23,
it just clears the top of the wall at B as it reaches its maximum height.
Knowing that the distance from A to the wall is 20m and the wall is 4m heigh,
determine the initial speed at which the ball was kicked. Neglect the size of
the ball.
Page 39, problem 12-55: If x=1-t and y=t^2, where x and y are in meters
and t is in seconds, determine the x and y components of velocity and
acceleration and construct the path y=f(x).
Page 39, problem 12-57: If the position of a particle is defined by its
coordinates x=4t^2 and y=3t^3, where x and y are in meters and t is in
seconds, determine the x and y components of velocity and acceleration and
construct the path y=f(x).
Page 39, problem 12-58: The position of a particle is defined by
If
, where t is in seconds, determine the particles velocity v
and acceleration a at the instant t=1 sec. Express v and a as Cartesian
vectors.
Page 39, problem 12-59: If the velocity of a particle is v(t)={0.8t^2i + 12t^0.5j
+ 5k}m/s, determine the magnitude and coordinate direction angles a,b and c
of the particle's acceleration when t=2s.
Page 39, problem 12-61: A particle travels along the curve from A to B in
2s. It takes 4s for it to go from B to C and then 3s to go from C to D.
Determine its average velocity when it goes from A to D.
Page 39, problem 12-62: A particle moves with curvilinear motion in the
positive x-y plane such that the y component of motion is described by
y=7t^3, where y is in feet and t is in seconds. When t=1s, the particle's speed
is 60ft/s. If the acceleration of the particle in the x direction is zero, determine
the velocity of the particle when t=2s.
Page 39, problem 12-63: A car traveling along the road has the velocities
indicated in the figure when it arrives at it points A, B and C. If it takes 10s
to go from A to B, and then 15s to go from B to C, determine the average
acceleration between points A and B and between points A and C.
Page 40, problem 12-66: The flight path of the helicopter as it takes off
from A is defined by the parametric equations x=(2t^2)m and
y=(0.04t^3)m, where t is the time in seconds after takeoff. Determine the
distance the helicopter is from point A and the magnitude of its velocity
and acceleration when t=10s.
Page 40, problem 12-67: A particle is moving along the curve y=x-(x^2/400).
If the velocity component in the x direction is Vx=2ft/s, determine the
magnitude of the particle's velocity and acceleration when x=20ft.
Page 40, problem 12-69: A particle moves along a hyperbolic path
X^2/16 - y^2=28. If the x component of its velocity is always Vx=4m/s,
determine the magnitude of its velocity and acceleration when it is at point
(32m,6m).
Page 41, problem 12-74: A basketball is tossed from A at angle of 30deg
from the horizontal. Determine the speed Va at which the ball is released
in order to make the basket B. With what speed does the ball pass
through the hoop?. Neglect the size of the ball in the calculation.
Page 41, problem 12-78: The centre of the wheel is traveling at 60ft/s. If it
encounters the transitions of two rails, such that there is a drop of
0.25inch. at the joint between the rails, determine the distance s to point A
where the wheel strikes the next rail.
Page 42, problem 12-82: A boy at A throw's a ball 45deg from the
horizontal such that it strikes the slope at B. Determine the speed at which
the ball is thrown and the time of flight.
Page 42, problem 12-83: A frog jumps upward, perpendicular to the
incline, with a velocity of Va=10ft/sec. Determine the distance R where it
strikes the plate at B.
12.6: Curvilinear motion: normal and tangential components
Page 51, problem 12-93: A particle is moving along a curved path at a
constant speed of 60ft/s. The radii of curvature of the path at points P and
P' are 20 and 50 ft, respectively. If it takes the particle 20 sec to go from P
to P', determine the acceleration of the particle at P and P'.
Page 51, 12-94: A car travels along a horizontal curved road that has a
radius of 600m. If the speed is uniformly increased at a rate of 2000km/
h^2, determine the magnitude of the acceleration at the instant the speed
of the car is 60km/h.
Page 51, problem 12-95: A boat is traveling along a circular path having a
radius of 20m. Determine the magnitude of the boat's acceleration if at a
given instant the boat's speed is v=5 m/s and the rate of increase in the
speed is dv/dt =2 m/s^2.
Page 51, problem 12-97: A car moves along a circular track of radius 100ft
such that it's speed for a short period of time 0 <= t <= 4s is v=3(t+t^2) ft/s,
where t is in seconds. Determine the magnitude of its acceleration when t=
2s. How far has the car traveled in 2s ?
Page 51, problem 12-99: A race car has an initial speed of V0=15m/s when
s=0. If it increases its speed along the circular track at the rate of at=(0.4s)
m/s^2, where s is in meters, determine the normal and tangential
components of the car's acceleration when s=100m.