920 Solutions Manual
Computation.
Substituting Eqs. (2)–(5) into Eq. (1), we obtain an equation in the only unknown
vA2
whose
solution is
Dynamics 2e 921
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.
922 Solutions Manual
Problem 5.52
Box
A
, which weighs
47 lb
, is released from rest in the position shown
in the top figure, where
hD3ft
. The box slides down the fixed incline
with negligible friction and it lands on a cart
B
, which is initially at
rest and weighs
12 lb
. When
A
reaches the bottom of the incline, the
velocity of
A
is completely horizontal and
A
starts sliding on the cart.
The coefficient of kinetic friction between Aand Bis kD0:6.
Determine the distance
d
from the right end of the cart at which
the box Astops relative to the cart.
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 923
Computation.
Substituting Eqs. (2)–(5) into Eq. (1), we obtain an equation in the only unknown
vA2
whose
solution is
924 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 925
Problem 5.53
Blocks
A
and
B
, with masses
mAD5kg
and
mBD3kg
, respectively, are
connected by a spring of stiffness
kD20 N=m
and unstretched length
L0D
0:75
m. The blocks are at rest and separated by the distance
L0
when block
B
is given a velocity to the right with magnitude
v0D15 m=s
. The friction
between the blocks and the horizontal surface on which they rest is negligible.
Determine the maximum value of the distance
d
between
A
and
B
that will
be achieved during the motion.
Solution
Referring to the figure at the right, we model
A
and
B
as particles subject
only to their weights
mAg
and
mBg
and the normal reactions
NA
and
926 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 927
Problem 5.54
Blocks
A
and
B
, with masses
mAD5kg
and
mBD3kg
, respectively, are
connected by a spring of stiffness
kD20 N=m
and unstretched length
L0D
0:75
m. The blocks are at rest and separated by the distance
L0
when block
B
is given a velocity to the right with magnitude
v0D15 m=s
. The friction
between the blocks and the horizontal surface on which they rest is negligible.
Assuming that the spring can be squeezed so that
dD0
, verify that
the blocks
A
and
B
will collide with one another in the ensuing motion by
computing the velocities of the blocks when dD0.
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.
928 Solutions Manual
Bv0˙qmAmB⇥mAmBv2
0.mACmB/kL2
0⇤
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 929
Problem 5.55
Energy storage devices that use spinning flywheels to store en-
ergy are starting to become available. To store as much energy
as possible, it is important that the flywheel spin as fast as pos-
sible. Unfortunately, if it spins too fast, internal stresses in the
flywheel cause it to come apart catastrophically. Therefore, it is
important to keep the speed at the edge of the flywheel below
about
1000 m=s
. It is also critical that the flywheel be almost
perfectly balanced to avoid the tremendous vibrations that would
otherwise result. With this in mind, let the flywheel
D
, whose
diameter is
0:3
m, rotate at
!D60;000 rpm
. Assume that the
cart
B
is constrained to move rectilinearly along the smooth guide
tracks. Given that the flywheel is not perfectly balanced, that the
unbalanced weight
A
has mass
mA
, and that the total mass of the
flywheel
D
, cart
B
, and electronics package
E
is
mB
, determine
the following as a function of
✓
, the masses, the diameter, and the
angular speed of the flywheel:
(a) the amplitude of the motion of the cart,
(b) the maximum speed achieved by the cart.
Neglect the mass of the wheels, assume that initially everything
is at rest, and assume that the unbalanced mass is at the edge of
the flywheel. Finally, evaluate your answers to Parts (a) and (b)
for
mAD1
g (about the mass of a paper clip) and
mBD70 kg
(the mass of the flywheel might be about 40 kg).
Solution