Dynamics 2e 787
Problem 4.87
Consider the simple catapult shown in the figure with an
800 lb
counter–
weight
A
and a
150 lb
projectile
B
. If the system is released from rest as
shown, determine the speed of the projectile after the arm rotates (counter–
clockwise) through an angle of
110ı
. Model
A
and
B
as particles, neglect
the mass of the catapult’s arm, and assume that friction is negligible. The
catapult’s frame is fixed with respect to the ground, and the projectile does
not separate from the arm during the motion considered.
Solution
We model
A
and
B
as a system of two particles connected by a rigid arm
of negligible mass rotating about the fixed point
O
. The system is assumed
788 Solutions Manual
Problem 4.88
Two blocks Aand Bweighing 123 and 234 lb, respectively, are released
from rest as shown. At the moment of release the spring is unstretched. In
solving these problems, model
A
and
B
as particles, neglect air resistance,
and assume that the cord is inextensible.
Determine the maximum speed attained by block
B
and the distance
from the floor where the maximum speed is achieved if
˛D20ı
, the
contact between
A
and the incline is frictionless, and the spring constant
is kD30 lb=ft.
Solution
We model
A
and
B
as a system of two particles connected by an inextensible
cord that rolls over a fixed pulley with negligible inertia and no frictional
Dynamics 2e 789
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permission of McGraw-Hill, is prohibited.
790 Solutions Manual
Problem 4.89
Two blocks Aand Bweighing 123 and 234 lb, respectively, are released
from rest as shown. At the moment of release the spring is unstretched. In
solving these problems, model
A
and
B
as particles, neglect air resistance,
and assume that the cord is inextensible.
Determine the maximum displacement of block
B
if
˛D20ı
, the
contact between
A
and the incline is frictionless, and the spring constant
is kD300 lb=ft.
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 791
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.
792 Solutions Manual
Problem 4.90
Revisit Example 4.7 on p. 266 and determine the maximum height reached by the pole vaulter, but this
time include the mass of the pole in your analysis. To solve the problem, use the following data: the
maximum speed achieved by the pole vaulter and pole at the time the vault begins is
vmax D34:19 ft=s
;
the pole vaulter is
6ft
tall with mass center at
55
% of body height (as measured from the ground) and
weighs
190 lb
; the pole is uniform, has a weight of
5:8 lb
, and is
17:1 ft
long. In addition, assume that as
the pole vaulter sprints before the vault, the pole is carried horizontally at the same height as the vaulter’s
center of mass relative to the ground. Explain why the vault height you find when the pole is included is
higher than the vault height determined in Example 4.7, when the pole was not included.
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 793
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.
794 Solutions Manual
Problem 4.91
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
and
PD375
N, determine the speed of each crate
after Aslides 6m.
Solution
We model
A
and
B
as a system of two particles connected by an
inextensible cable. We include in the system the pulleys since
Dynamics 2e 795
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.
796 Solutions Manual
Problem 4.92
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
kD0:2
and
PD375
N, determine the speed of each crate
after Aslides 6m.
Solution
We model
A
and
B
as a system of two particles connected by an
inextensible cable. We include in the system the pulleys since