Dynamics 2e 797
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798 Solutions Manual
Problem 4.93
The two crates
A
and
B
of mass
mAD100 kg
and
mBD70 kg
,
respectively, are connected by a system of pulleys. The system is
initially at rest, when the man
C
starts pushing on
A
with a constant
force
P
. Neglect the mass of the cables and the pulleys and neglect
friction in the pulley bearings. Assume that cable segments are long
enough so that crate Adoes not hit any of the pulleys.
If
kD0:3
and
PD350
N, determine the distance the man
needs to push the crate Ato achieve a speed of 3m=s.
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 799
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.
800 Solutions Manual
Problem 4.94
The rope of mass
m
and length
l
is released from rest with a very small
amount of it hanging over the edge (i.e.,
s>0
, but it is very close to zero).
Determine the speed of the rope as a function of
s
. Assume the surface is
smooth.
Solution
Dynamics 2e 801
Problem 4.95
Consider a system of four identical particles
A
,
B
,
D
, and
E
, each with
a mass of
2:3 kg
. These particles are mounted on a wheel of negligible
mass whose hub is at
O
and whose radius is
RD0:75
m. The wheel
is mounted on a cart
H
of negligible mass. Suppose that the wheel is
spinning counterclockwise with an angular speed
!D3rad=s
and that
the cart is moving to the right with a speed of
vHD11 m=s
. Compute
the kinetic energy of the system, using
(a) Eq. (4.46) on p. 282,
(b) Eq. (4.50) on p. 283.
Show that the result is the same in both cases.
Solution
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permission of McGraw-Hill, is prohibited.
802 Solutions Manual
Problem 4.96
Reexamine Example 4.12 by choosing
¿
to be the same as that
in the example and
¡
to be an arbitrary position after release.
Determine the speed of
A
as a function of
yA
, and plot the kinetic
energy of
A
as a function of
yA
. Use this plot to argue that the
cord connecting
A
and
B
never goes slack between the instant of
release and the impact of
B
with the ground. Hint: To argue that
the cord remains taut between the positions of interest, you may
want to look at concept Prob. 4.29 on p. 256.
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.
804 Solutions Manual
Problem 4.97
Consider a battery that can power a machine whose operation requires
200
W of power.
If the battery can keep the machine operating for
8
h and supply energy at a constant
rate, determine the amount of energy initially stored in the battery pack.
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 805
Problem 4.98
A person takes
16
s to lift a
200 lb
crate to a height of
30 ft
. Determine the average
power supplied by the person.
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.
806 Solutions Manual
Problem 4.99
The weights
B
in the pulley systems shown are identical. Assume
that the two systems are released from rest, there are no energy losses
in the pulleys, and the same constant force
F
is applied. After
1
s,
will the power developed by the force
F
for system (a) be smaller
than, equal to, or greater than that of system (b)?
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.