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646 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 647
Problem 3.148
Referring to Example 3.9 on p. 200, let
RD1:25 ft
and let the angle
at which the sphere separates from the cylinder be
✓sD34ı
. If the
sphere were placed in motion at the very top of the cylinder, determine
the sphere’s initial speed.
Solution
We model the sphere as a particle subject only to its own weight
mg
and the normal reaction
N
with the cylinder. We use a polar coordinate
648 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 649
Problem 3.149
Referring to Example 3.8 on p. 198, show that, for ✓D33ıand under the
assumption that
s> 1= tan ✓
, the no-slip solution in Eqs. (15) and (16)
satisfies the no-slip condition
jFjsjNj
for any value of the car’s speed.
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.
650 Solutions Manual
Problem 3.150
Revisit Example 3.7 and assume that the drag force acting on the ball has the form
E
FdD⌘Ev
, where
Ev
is
the velocity of the ball and
⌘
is a drag coefficient. Determine the trajectory of the ball, expressing it in the
form yDy.x/.
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 651
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.
652 Solutions Manual
Problem 3.151
Revisit Example 3.7 and assume that the drag force acting on the ball has the form
E
FdD⌘Ev
, where
Ev
is
the velocity of the ball and
⌘
is a drag coefficient. Determine the value of
⌘
such that a
1:61 oz
ball has
a range
RD270 yd
when put in motion with an initial velocity of magnitude
v0D186 mph
and initial
direction ˇD11:2ı.
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 653
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.
654 Solutions Manual
Problem 3.152
The load
B
has a mass
mBD250 kg
, and the load
A
has a mass
mAD120 kg
.
Let the system be released from rest, and neglecting any source of friction, as
well as the inertia of the ropes and the pulleys, determine the acceleration of
Aand the tension in the cord to which Ais attached.
Solution
We model
A
and
B
as particles subject to their own weights,
mAg
and
mBg
respectively, and the tension in the cords connected to them,
T
(for
Dynamics 2e 655
Problem 3.153
The load
B
weighs
300 lb
. Neglecting any source of friction, as well as
the inertia of the ropes and the pulleys, determine the weight of
A
if, after
the system is released from rest,
B
moves upward with an acceleration of
0:75 ft=s2.
Solution
We model
A
and
B
as particles subject to their own weights,
mAg
and
mBg
respectively, and the tension in the cords connected to them,
T
(for
656 Solutions Manual
Problem 3.154
A crate of mass
m
is gently placed with zero initial velocity on an inextensible
conveyor belt that is moving to the right at a constant speed
v0
. Treating the
crate as a particle and assuming that the coefficients of static and kinetic friction
between the crate and conveyor are sand k, respectively, determine:
(a)
the distance the crate slides before it stops slipping relative to the belt, and
(b) the time it takes for the crate to stop sliding.
Solution
We model the crate as a particle subject to its own weight
mg
, the normal reaction
N
with the conveyor, and the friction force
F
due to the belt. The direction of
F
