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626 Solutions Manual
Problem 3.137
In the ride shown, a person
A
sits in a seat that is attached by
a cable of length
L
to a freely moving trolley
B
of mass
mB
.
The total mass of the person and the seat is
mA
. The trolley is
constrained by the beam to move in only the horizontal direction.
The system is released from rest at the angle
✓D✓0
and is allowed
to swing in the vertical plane. Neglect the mass of the cable, and
treat the person and the seat as a single particle.
Derive the system’s equations of motion, using the position
of the trolley and the angle
✓
as dependent variables, and then
use a computer to solve these equations for one full period/cycle
of the motion. Plot the speed of the trolley and the speed of the
person vs. the angle
✓
for
mAD45 kg
,
mBD10 kg
,
LD3
m,
and ✓0D70ı.
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.
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.
628 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 629
Problem 3.138
A constant force
P
is applied at
A
to the rope running behind the load
G
, which
has a mass of
300 kg
. Assuming that any source of friction and the inertia of the
pulleys can be neglected, determine
P
such that
G
has an upward acceleration of
1m=s2.
Solution
Neglecting the inertia of the ropes and the friction in the pulleys, the tension
in the cord going around
D
is
P
. We denote by
T2
the tension in the cord
630 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 631
Problem 3.139
A constant force
PD300 lb
is applied at
A
to the rope running behind the load
G
, which weighs
1000 lb
. If each of the pulleys weighs
7lb
, and assuming that
any source of friction and the rotational inertia of the pulleys can be neglected,
determine the acceleration of
G
and the tension in the rope connecting pulleys
B
and C.
Solution
Neglecting the inertia of the ropes and the friction in the pulleys,
the tension in the cord going around
D
is
P
. We denote by
T2
632 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 633
Problem 3.140
A metal ball weighing
0:2 lb
is dropped 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 depth at which the ball will have
sunk when the ball achieves a speed of 0:3 ft=s.
Solution
We model the ball as a particle subject only to its own weight
mg
and to the drag resitance
Fd
due to the water. We consider only the motion in the vertical direction.
634 Solutions Manual
Problem 3.141
A metal ball weighing
0:2 lb
is dropped from rest in a fluid. After falling
1ft
, the
ball has a speed of
2:25 ft=s
. If 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, determine
the value of Cd.
Solution
We model the ball as a particle subject only to its own weight
mg
and to the drag resitance
Fd
due to the water. We consider only the motion in the vertical direction.
Dynamics 2e 635
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.
