Transcript Class Problems

Examples and Problems
Problem 12-11
The acceleration of a particle as it moves along
a straight line is given by a = (2t-1) m/s2, where t
is in seconds. If s = 1 m and v = 2 m/s when t =
0, determine the particle’s velocity and position
when t = 6 s. Also, determine the total distance
the particle travels during this time period.
Problem 12-26
Ball A is released from rest at a height of 40 ft at
the same time that a second ball B is thrown
upward 5 ft from the ground. If the balls pass
one another at a height of 20 ft, determine the
speed at which ball B was thrown upward.
Problem 12-75
The path of a particle is defined by y2 = 4kx,
and the component of velocity along the y
axis is vy = ct, where both k and c are
constants. Determine the x and y
components of acceleration.
Problem 12-78
The particle travels along the path defined by
the parabola y = 0.5x2. If the component of
velocity along the x axis is vx = (5t) ft/s, where t
is in seconds, determine the particle’s distance
from the origin O and the magnitude of its
acceleration when t = 1 s. When t = 0, x = 0, and
y = 0.
(See diagram in the textbook.)
Problem 12-85
From a videotape, it was observed that a
pro football player kicked a football 126 ft
during a measured time of 3.6 seconds.
Determine the initial speed of the ball and
the angle θ at which it was kicked.
(See diagram in the textbook.)
Problem 12-95
Determine the horizontal velocity vA of a
tennis ball at A so that it just clears the net
at B. Also, find the distance s where the
ball strikes the ground.
(See diagram in the textbook.)
Problem 12-102
At a given instant the jet plane has a
speed of 400 ft/s and an acceleration of 70
ft/s2 acting in the direction shown.
Determine the rate of increase in the
plane’s speed and the radius of curvature
ρ of the path.
Problem 12-118
When the motorcyclist is at A, he
increases his speed along the vertical
circular path at the rate of v  0.3 t  ft/s2,
where t is in seconds. If he starts from rest
at A, determine the magnitudes of his
velocity and acceleration when he reaches
B.
Problem 12-150
A block moves outward along the slot in
the platform with a speed of r  4 t  m/s,
where t is in seconds. The platform rotates
at a constant rate of 6 rad/s. If the block
starts from rest at the center, determine
the magnitudes of its velocity and
acceleration when t = 1s.
Problem 12-172
If the end of the cable at A is pulled down
with a speed of 2 m/s, determine the
speed at which block B rises.
Problem 12-178
Determine the displacement of the block at
B if A is pulled down 4 ft.
Problem 12-150
A block moves outward along the slot in
the platform with a speed r  4t  of m/s,
where t is in seconds. The platform rotates
at a constant rate of 6 rad/s. If the block
starts from rest at the center, determine
the magnitudes of its velocity and
acceleration when t = 1 s.
Problem 13-2
The 10-Ib block has an initial velocity of 10
ft/s on the smooth plane. If a force F =
(2.5t) Ib, where t is in seconds, acts on the
block for 3 s, determine the final velocity of
the block and the distance the block
travels during this time.
Problem 13-14
Each of the two blocks has a mass m. The
coefficient of kinetic friction at all surfaces of
contact is µ. If a horizontal force P moves the
bottom block, determine the acceleration of the
bottom block in each case.
Problem 13-70
The package has a weight of 5Ib and slides down the
chute. When it reaches the curved portion AB, it is
traveling at 8 ft/s (θ = 0o). If the chute is smooth,
determine the speed of the package when it reaches the
intermediate point C (θ = 300) and when it reaches the
horizontal plane (θ = 450). Also, find the normal force on
the package at C.
Problem 13-90
The 0.5-Ib particle is guided along the circular
path using the slotted arm guide. If the arm has
an angular velocity   4 rad / s and an angular
acceleration   8 rad / s 2 at the instant   30 ,
determine the force of the guide on the particle.
Motion occurs in the horizontal plane.
Problem 14-2
The car having a mass of 2 Mg is originally
traveling at 2 m/s. Determine the distance
it must be towed by a force F = 4 kN in
order to attain a sped of 5 m/s. Neglect
friction and the mass of the wheels.
Problem 14-23
Packages having a weight of 50 Ib are delivered
to the chute at vA = 3 ft/s using a conveyor belt.
Determine their speeds when they reach points
B, C, and D. Also calculate the normal force of
the chute on the packages at B and C. Neglect
friction and the size of the packages.
Problem 14-56
The 50-kg crate is hoisted up the 30o incline by the
pulley system and motor M. If the crate starts from
rest and by constant acceleration attains a speed of
4 m/s after traveling 8 m along the plane, determine
the power that must be supplied to the motor at this
instant. Neglect friction along the plane. The motor
has an efficiency of e = 0.74.
Problem 14-72
The girl has a mass of
40 kg and center of
mass at G. If she is
swinging to a maximum
height defined by θ =
60o, determine the force
developed along each of
the
four
supporting
posts such as AB at the
instant θ = 0o. The
swing
is
centrally
located between the
posts.
Problem 14-89
The 2-kg ball of negligible size is fired from point
A with an initial velocity of 10 m/s up the smooth
inclined plane. Determine the distance from the
point C to where it hits the horizontal surface at
D. Also, what is its velocity when it strikes the
surface?
Problem 15-2
A 2-Ib ball is thrown in the direction shown
with an initial speed vA = 18 ft/s.
Determine the time needed for it to reach
its highest point B and the speed at which
it is traveling at B. Use the principle of
impulse and momentum for the solution.
(See diagram in the textbook.)
Problem 15-33
The car A has a weight of 4500 Ib and is
traveling to the right at 3 ft/s. Meanwhile a 3000Ib car B is traveling at 6 ft/s to the left. If the cars
crash head-on and become entangled,
determine their common velocity just after
collision. Assume that the brakes are not applied
during collision.
Problem 15-50
The 20-Ib cart B is supported on rollers of
negligible size. If a 10-Ib suitcase A is thrown
horizontally on it at 10 ft/s, determine the time t
and the distance B moves before A stops
relative to B. The coefficient of kinetic friction
between A and B is mk = 0.4.
Problem 15-61
The man A has a weight of 175 Ib
and jumps from rest h = 8 ft onto a
platform P that has a weight of 60
Ib. The platform is mounted on a
spring, which has a stiffness k =
200 Ib/ft. Determine (a) the
velocities of A and P just after
impact and (b) the maximum
compression imparted to the spring
by the impact. Assume the
coefficient of restitution between
the man and the platform is e =
0.6, and the man holds himself
rigid during the motion.
Problem 15-84
Two coins A and B have the initial velocities
shown just before they collide at point O. If they
have weights of WA = 13.2(10-3) Ib and WB =
6.60(10-3) Ib and the surface upon which they
slide is smooth, determine their speeds just after
impact. The coefficient of restitution is e = 0.65.
Problem 15-96
Determine the total angular momentum Ho
for the system of three particles about
point O. All the particles are moving in the
x-y plane.
Problem 15-107
An amusement park ride consists of a car which
is attached to the cable OA. The car rotates in a
horizontal circular path and is brought to a
speed v1 = 4 ft/s when r = 12 ft. The cable is
then pulled in at the constant rate of 0.5 ft/s.
Determine the speed of the car in 3 s.
Help Session
Problem 15-28
Block A weighs 10 Ib and block B weighs 3 Ib. If
B is moving downward with a velocity (vB)1 = 3
ft/s at t = 0, determine the velocity of A when t =
1 s. The coefficient of kinetic friction between the
horizontal plane and block A is mA = 0.15.
Problem 15-47
The 10-kg block is held at rest on the smooth
inclined plane by the stop block at A. If the 10-g
bullet is traveling at 300 m/s when it becomes
embedded in the 10-kg block, determine the
distance the block will slide up along the plane
before momentarily stopping.
Problem 15-64
If the girl throws the ball with a horizontal
velocity of 8 ft/s, determine the distance d so
that the ball bounces once on the smooth
surface and then lands in the cup at C. Take e =
0.8.
Problem 16-5
Due to an increase in power, the motor M rotates
the shaft A with an angular acceleration of a =
(0.06 2) rad/s2, where  is in radians. If the shaft
is initially turning at wo = 50 rad/s, determine the
angular velocity of gear B after the shaft
undergoes an angular displacement D = 10 rev.
Problem 16-19
Starting from rest when s = 0, pulley A is given a
constant angular acceleration ac = 6 rad/s2.
Determine the speed of block B when it has
risen s = 6 m. The pulley has an inner hub D
which is fixed to C and turns with it.
Problem 16-55
Determine the velocity of the slider block at C at
the instant  = 45o, if link AB is rotating at 4
rad/s.
Problem 16-87
The shaper mechanism
is designed to give a
slow cutting stroke and a
quick return to a blade
attached to the slider at
C. Determine the angular
velocity of the link CB at
the instant shown, if the
link AB is rotating at 4
rad/s.
Problem 16-119
The ends of the bar AB
are confined to move
along the paths shown.
At a given instant, A has
a velocity of 8 ft/s and an
acceleration of 3 ft/s2.
Determine the angular
velocity and angular
acceleration of AB at this
instant.
Problem 16-133
The man stands on the
platform at O and runs out
toward the edge such that
when he is at A, y = 5 ft, his
mass center has a velocity
of 2 ft/s and an acceleration
of 3 ft/s2, both measured
with respect to the platform
and directed along the y
axis. If the platform has the
angular motions shown,
determine the velocity and
acceleration of his mass
center at this instant.
Problem 16-141
Block
B
of
the
mechanism is confined
to move within the slot
member CD. If AB is
rotating at a constant
rate of wAB = 3 rad/s,
determine the angular
velocity and angular
acceleration of member
CD at the instant shown.
Problem 16-110
At a given instant the wheel is rotating with
the angular motions shown. Determine the
acceleration of the collar at A at this
instant.
Problem 17-20
The pendulum consists of two
slender rods AB and OC which
have a mass of 3 kg/m. The thin
plate has a mass of 12 kg/m2.
Determine the location y of the
center of mass G of the
pendulum, then calculate the
moment of inertia of the
pendulum
about
an
axis
perpendicular to the page and
passing through G.
Problem 17-28
The jet aircraft has a total mass of 22 Mg and a
center of mass at G. Initially at take-off the
engines provide a thrust 2T = 4 kN and T’ = 1.5
kN. Determine the acceleration of the plane and
the normal reactions on the nose wheel and
each of the two wing wheels located at B.
Neglect the mass of the wheels and, due to low
velocity, neglect any lift caused by the wings.
Problem 17-45 (modified)
The van has a weight of 4500 Ib and center of
gravity at Gv. It carries a fixed 800-Ib load which has
a center of gravity at Gl. If the van is travelling at 40
ft/s, determine the distance it skids before stopping.
The brakes cause all the wheels to lock or skid. The
coefficient of kinetic friction between the wheels and
the pavement is mk = 0.3. Also, determine the
reactions on the wheels. Neglect the mass of the
wheels.
Problem 17-57
The spool is supported on small
rollers at A and B. Determine the
constant force P that must be
applied to the cable in order to
unwind 8 m of cable in 4 s starting
from rest. Also calculate the
normal forces at A and B during
this time. The spool has a mass of
60 kg and a radius of gyration ko =
0.65 m. For the calculation neglect
the mass of the cable and the
mass of the rollers at A and B.
Problem 17-71
If the support at B is suddenly removed, determine
the initial downward acceleration of point C.
Segments AC and CB each have a weight of 10 Ib.
Problem 17-97
The spool has a mass of 100 kg and a radius of
gyration of kG = 0.3 m. If the coefficients of static and
kinetic friction at A are ms = 0.2 and mk = 0.15,
respectively, determine the angular acceleration of
the spool if P = 600 N.
Problem 18-14
A motor supplies a constant torque or twist M = 120
Ib.ft to the drum. If the drum has a weight of 30 Ib
and a radius of gyration of KO = 0.8 ft, determine the
speed of the 15-Ib crate A after it rises s = 4 ft
starting from rest. Neglect the mass of the cord.
Problem 18-43
The 50-Ib wheel has a radius of gyration about its
center of gravity G of kG = 0.7 ft. If it rolls without
slipping, determine its angular velocity when it has
rotated clockwise 90o from the position shown. The
spring AB has a stiffness k = 120 Ib/ft and an
unstreched length of 0.5 ft. The wheel is released
from rest.
Problem 18-50
The assembly consists of a 3-kg pulley A and 10-kg
pulley B. If a 2-kg block is suspended from the cord,
determine the block’s speed after it descends 0.5 m
starting from rest. Neglect the mass of the cord and
treat the pulleys as thin disks. No slipping occurs.
Problem 19-6
Solve Prob. 17-54 using the principle of impulse and
momentum.
Problem 17-54
The 10-kg wheel has a radius of gyration kA = 200
mm. If the wheel is subjected to a moment M = (5t)
N.m, where t is in seconds, determine its angular
velocity when t = 3 s starting from rest. Also,
compute the reactions which the fixed pin A exerts
on the wheel during the motion.
Problem 19-9
Solve Prob. 17-73 using the principle of impulse
and momentum.
Problem 17-73
The disk has a mass of 20 kg and is
originally spinning at the end of the
strut with an angular velocity of w =
60 rad/s. If it is then placed against
the wall, for which the coefficient of
kinetic friction is mk = 0.3 determine
the time required for the motion to
stop. What is the force in the strut
BC during this time?
Problem 19-51
The 4-Ib rod AB is hanging in the vertical position. A
2-Ib block, sliding on a smooth horizontal surface
with a velocity of 12 ft/s, strikes the rod at its end B.
Determine the velocity of the block immediately after
collision. The coefficient of restitution between the
block and the rod at B is e = 0.8.