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Dynamics 2e 827
Problem 4.117
Strength of materials tells us that if a load
P
is applied at the
free end of a cantilevered beam, then the tip displacement
ı
is
given by
ıDPL3=.3EIcs/
, where
L
is the length of the beam
and
E
and
Ics
are constants that depend on the material makeup
and the geometry of the cross section, respectively. Determine an
expression for the potential energy of a cantilevered beam loaded
as shown.
Solution
We are given that
PD3EIcs
828 Solutions Manual
Problem 4.118
Starting from the position shown, each horse moves to the right in such a way that the tension in the cord
is the same in cases (a) and (b) and remains constant. Knowing that
ˇ<
, and that in both cases (a) and
(b), the horse advances by an equal amount
L
, determine which of the following statements is true: (1) the
tension in the cord does more work in (a) than in (b); (2) the tension in the cord does exactly the same
amount of work in (a) as in (b); (3) the tension in the cord does less work in (a) than in (b).
Solution
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 829
Problem 4.119
A metal ball with mass
mD0:15 kg
is released from rest in a fluid. The
magnitude of the resistance due to the fluid is given by
Cdv
, where
Cd
is a
drag coefficient and
v
is the ball’s speed. If
CdD2:1 kg=s
, determine the total
work done on the ball from the moment of release until the ball achieves
99
% of
terminal velocity.
Solution
We model the ball as a particle subject to its weight
mg
and the drag force
Fd
. We by denote
¿
the
release position of the particle. We denote by
¡
the position of the particle when it reaches
99
%
830 Solutions Manual
Problem 4.120
A metal ball weighing
0:2 lb
is released from rest in a fluid. If the magnitude of
the resistance due to the fluid is given by
Cdv
, where
CdD0:5 lbs=ft
is a drag
coefficient and
v
is the ball’s speed, determine the work done by the drag force
during the first 2s of the ball’s motion.
Solution
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 831
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.
832 Solutions Manual
Problem 4.121
A
7lb
collar is constrained to travel along a frictionless vertical ring of radius
RD1ft
. The spring attached to the collar has a spring constant
kD20 lb=ft
.
Treating the collar as a particle, neglecting air resistance, and knowing that, while
at rest at
A
, the collar is displaced gently to the left, determine the spring’s
unstretched length if the collar is to reach point Bwith a speed of 15 ft=s.
Solution
We denote the positions of the collar at
A
and
B
by
and
, respectively. Between
Dynamics 2e 833
Problem 4.122
An
11 kg
collar is constrained to travel along a rectilinear and frictionless bar of
length
LD2
m that lies in the vertical plane. The springs attached to the collar
are identical, and they are unstretched when the collar is at
B
. Treating the
collar as a particle, neglecting air resistance, and knowing that at
A
the collar is
moving upward with a speed of
23 m=s
, determine the spring constant
k
so that
the collar reaches Dwith zero speed. Points Eand Fare fixed.
Solution
We denote the positions of the collar at
A
and
D
by
¿
and
¡
, respectively. Between
these two positions, we model the collar as a particle subject to its own weight
mg
, the
834 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 835
Problem 4.123
Consider the catapult shown in the figure with a
1200 kg
counterweight
A
and a
330 kg
projectile
B
. If the system is released from rest as shown,
determine the speed of the projectile after the arm rotates (counterclockwise)
through an angle of
110ı
. Model
A
and
B
as particles; assume that the
catapult’s arm has negligible mass and that friction is negligible. In addition,
assume that the cord has negligible mass, is inextensible, and is always
vertical. The catapult’s frame is fixed with respect to the ground, and the
projectile does not separate from the arm during the motion considered.
Solution
We model
A
and
B
as a system of two particles connected by a rigid arm
CB
and an inextensible cord. The arm has negligible mass and rotates
836 Solutions Manual
Problem 4.124
The crate
A
weighs
100 lb
and is attached to the springs with constants
k1D150 lb=ft
and
k2D300 lb=ft
. Both springs are unstretched
when
ıD0
and the box is centered between the two walls. The angle
of the incline is ✓D30ı.
If the crate is released from rest after being displaced a distance
ıD6ft
up the incline, and friction between the crate and the inclined
surface on which it slides is negligible, determine the speed of the
crate when it returns to ıD0.
Solution
We denote by
¿
and
¡
the release position of the crate and the position cor-
responding to
ıD0
, respectively. Between
¿
and
¡
, we model the crate as
Dynamics 2e 837
Problem 4.125
The crate
A
weighs
100 lb
and is attached to the springs with constants
k1D150 lb=ft
and
k2D300 lb=ft
. Both springs are unstretched
when
ıD0
and the box is centered between the two walls. The angle
of the incline is ✓D30ı.
If the crate is released from rest after being displaced a distance
ıD6ft
and the coefficient of kinetic friction between the crate and
the surface on which it slides is
kD0:2
, determine the speed of the
crate when ıD0.
Solution
We denote by
¿
and
¡
the release position of the crate and the position corre-
sponding to
ıD0
, respectively. Between
¿
and
¡
, we model the crate as a
