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.
778 Solutions Manual
Problem 4.81
Blocks
A
and
B
are released from rest when the spring is unstretched. Block
A
has a mass
mAD2kg
, and the linear spring has stiffness
kD7N=m
. If
all sources of friction are negligible, determine the mass of block
B
such that
B
has a speed
vBD1:5 m=s
after moving
1:2
m downward, assuming that
A
never leaves the horizontal surface shown and the cord connecting
A
and
B
is
inextensible.
Solution
Referring to the FBD at the right, we models blocks
A
and
B
as a system of
particles subject to their respective weights
mAg
and
mBg
, the force of the spring
Dynamics 2e 779
Problem 4.82
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. In
your solution, note that most scales read zero when no mass
m
has been placed on
them; that is, they are calibrated so that the weight reading neglects 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
We denote by
¿
the equilibrium position of the platform when
780 Solutions Manual
Problem 4.83
Two small spheres
A
and
B
, each of mass
m
, are attached at either
end of a stiff light rod of length
d
. The system is released from rest in
the position shown. Determine the speed of the spheres when
A
has
reached point
D
, and determine the normal force between sphere
A
and the surface on which it is sliding immediately before it reaches
point
D
. Neglect friction, treat the spheres as particles (assume that
their diameter is negligible), and neglect the mass of the rod.
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.
782 Solutions Manual
Problem 4.84
Solve Example 4.14 by applying the work-energy principle to each
block individually, and show that the net work done by the cord on
the two blocks is zero.
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 783
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.
784 Solutions Manual
Problem 4.85
Consider a simple elevator design in which a
15;000 kg
car
A
is con-
nected to a
12;000 kg
counterweight
B
. Suppose that a failure of the
drive system occurs (the failure does not affect the rope connecting
A
and
B
) when the car is at rest and
50
m above its buffer, causing the
elevator car to fall. Model the car and the counterweight as particles
and the cord as massless and inextensible, and model the action of
the emergency brakes using a Coulomb friction model with kinetic
friction coefficient
kD0:5
and a normal force equal to 35% of the
car’s weight. Determine the speed with which the car impacts the
buffer.
Solution
Dynamics 2e 785
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.
786 Solutions Manual
Problem 4.86
Two identical balls, each of mass
m
, are connected by a string of
negligible mass and length
2l
. A short string is attached to the first
at its middle and is pulled vertically with a constant force
P
(exerted
by the hand). If the system starts at rest when
✓D✓0
, determine the
speed of the two balls as
✓
approaches 90
ı
. Neglect the size of the
balls as well as friction between the balls and the surface on which
they slide.
Solution
We denote the left and right balls by
A
and
B
, respectively. We