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
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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.