486 Solutions Manual
Problem 3.54
A partial cross section of an amusement park ride is shown. While the
ride spins up to the angular speed
!c
, there is a small platform at
F
on
which the person
P
stands. Once the ride reaches the desired angular
speed, the platform falls away and only friction keeps the person from
sliding to the floor of the ride. The wall, against which the person lies,
is inclined at the angle
✓D15ı
with respect to the vertical. Model the
person as a particle that is a distance
dD20 ft
from the spin axis
AB
and let the coefficient of static friction between the person and the wall
be sD0:7.
Determine whether or not the person can slide up the wall and out of
the ride. If yes, determine the value of
!c
at which the person begins to
slide.
Solution
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488 Solutions Manual
Problem 3.55
A person is swinging a ball of mass
m
above their head in a horizontal plane. When the ball is moving at a
constant speed, the string forms an angle
✓
with respect to the horizontal. Assuming that the motion of
point
O
is negligible and that the distance between the point
O
and the mass
m
is
L
, determine the speed
of the ball.
Solution
Dynamics 2e 489
Problem 3.56
Initially, the wrecking ball
A
of mass
m
is held stationary by the
horizontal cable
AB
. The cable
AB
is then released so that the
wrecking ball
A
starts swinging about the fixed point
O
. Determine
the tension in the cable
OA
before the cable
AB
is released and
immediately after it is released. What is the percent change in
cable tension if ✓D30ı?
Solution
In this problem we consider two situations. Referring to the FBD
before release, we first model the wrecking ball
A
as a particle in
490 Solutions Manual
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 491
Problem 3.57
A car traveling over a hill starts to lose contact with the ground at the top of the hill at O. If the radius of
curvature of the hill is 282 ft, determine the speed of the car at O.
Solution
Referring to the FBD at the right, when the car is at
O
, we model the car as a particle subject
only to its own weight
mg
, the reaction
N
from the ground, and the propelling force
F
due
492 Solutions Manual
Problem 3.58
A
950 kg
aerobatics plane initiates the basic loop maneuver at the bottom of a loop with radius
⇢D110
m
and a constant speed of
225 km=h
. At this instant, determine the magnitude of the plane’s acceleration,
expressed in terms of
g
, the acceleration due to gravity, and the magnitude of the lift provided by the
wings.
Solution
Referring to the FBD on the right, at the bottom of the loop we model the airplane as
a particle subject only to its own weight
mg
, the lift force
FL
, and the thrust force
Dynamics 2e 493
Problem 3.59
The ball of mass
m
is guided along the vertical circular path of radius
RD1
m using the arm
OA
. If the
arm starts from
D90ı
and rotates clockwise with a constant angular velocity
!D0:87 rad=s
, determine
the angle
at which the particle starts to leave the surface of the semicylinder. Neglect all friction forces
acting on the ball, neglect the thickness of the arm OA, and treat the ball as a particle.
Solution
The FBD at the right follows the modeling directives in the problem
statement.
N
is the normal force between the ball and the semicylin-
494 Solutions Manual
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 495
Problem 3.60
Referring to Example 3.10, instead of using polar coordinates as was done in that example, work the
problem using a Cartesian coordinate system with origin at
O
(cf. Fig. 1 of Example 3.10) and derive the
problem’s equations of motion.
Solution