586 Solutions Manual
Problem 3.117
Two identical balls, each of mass
m
, are connected by a string of neg-
ligible mass and length
2l
. A short string is attached to the middle
of the string connecting the two balls and is pulled vertically with a
constant force
P
. If the system starts from rest at
✓D✓0
and assum-
ing that the balls only move in the horizontal direction, determine
the expression for the speed of the two balls as
✓
approaches
90ı
.
Neglect the size of the balls as well as friction between the balls and
the surface on which they slide.
Solution
The symmetry of the problem allows us to consider only one of
the balls (we chose to consider the left ball), which we model as a
Dynamics 2e 587
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588 Solutions Manual
Problem 3.118
The two sliders
A
and
B
of mass
mAD4kg
and
mBD3kg
, respec-
tively, move with negligible friction in the slots shown, which lie in
the vertical plane. They are connected by a rigid bar of negligible
mass and length
LD0:5
m. If, for
yBD0:3
m, the system is initially
at rest, determine the acceleration of each slider and the force in the
bar immediately after release. Hint: The force that the bar exerts on
each slider has the same direction as the bar itself.
Solution
We model the sliders as particles. Both
A
and
B
are subject to their
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590 Solutions Manual
Problem 3.119
The two sliders
A
and
B
of weight
WAD8lb
and
WBD6lb
,
respectively, move with negligible friction in the slots shown, which
lie in the vertical plane. They are connected by a rigid bar of
negligible weight and length
LD1:75 ft
. Slider
A
is also subject
to the force
PD15 lb
. If, for
yBD1:0 ft
, the system is initially at
rest, determine the acceleration of each slider and the force in the
bar immediately after release. Hint: The force that the bar exerts
on each slider has the same direction as the bar itself.
Solution
We model the sliders as particles. Slider
A
is subject to the applied
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592 Solutions Manual
Problem 3.120
Spring scales work by measuring the displacement of a spring that supports both the
platform of mass
mp
and the object, of mass
m
, whose weight is being measured.
Most scales read zero when no mass
m
has been placed on them; that is, they are
calibrated so that the weight reading accounts for the mass of the platform
mp
.
Assume that the spring is linear elastic with spring constant k.
If the mass
m
is gently placed on the spring scale (i.e., it is released from zero
height above the scale), determine the maximum reading on the scale after the mass
is released.
Solution
Dynamics 2e 593
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594 Solutions Manual
Problem 3.121
Spring scales work by measuring the displacement of a spring that supports both the
platform of mass
mp
and the object, of mass
m
, whose weight is being measured.
Most scales read zero when no mass
m
has been placed on them; that is, they are
calibrated so that the weight reading accounts for the mass of the platform
mp
.
Assume that the spring is linear elastic with spring constant k.
If the mass
m
is gently placed on the spring scale (i.e., it is released from zero
height above the scale), determine the expression for maximum speed attained by
the mass mas the spring compresses.
Solution
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 595
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