940 Solutions Manual
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 941
Problem 5.61
In the ride shown, a person Asits in a seat that is attached by a cable of
length
L
to a freely moving trolley
B
of mass
mB
. The total mass of
the person and the seat is
mA
. The trolley is constrained by the beam
to move only in the horizontal direction. The system is released from
rest at the angle
✓D✓0
, and it is allowed to swing in the vertical plane.
Neglect the mass of the cable and treat the person and the seat as a single
particle.
Determine the equations needed to find the velocity of the trolley and
the rider for any arbitrary value of
✓
. Clearly label all equations and list
the corresponding unknowns, showing that you have as many equations
as you have unknowns. Solve the equations for the unknowns, and then
plot the velocity of the trolley and the speed of the rider as a function of
the angle
✓
for both halves of a full swing of the rider. Use
WAD100 lb
,
WBD20 lb, LD15 ft, and ✓0D70ı.
Solution
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942 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.
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.
944 Solutions Manual
Problem 5.62
A tower crane is lifting a
10;000 lb
object
B
at a constant rate of
7ft=s
while rotating at a constant rate of
P
✓D0:15 rad=s
.
B
is also
moving outward with a radial velocity of
1:5 ft=s
. Assume that the
object
B
does not swing relative to the crane (i.e., it always hangs
vertically) and that the crane is fixed to the ground at O.
(a)
Determine the radial velocity required of the
20 ton
counter-
weight
A
to prevent the horizontal motion of the system’s
center of mass.
(b) Find the total force acting on Aand on B.
(c)
Determine the velocity and acceleration of the mass center of
the system when Amoves as determined in Part (a).
Solution
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Dynamics 2e 945
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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.
Dynamics 2e 947
Problem 5.63
If an impact is an event spanning an infinitesimally small time interval, is the total potential energy of two
colliding objects conserved through the impact? What about the potential energy of each individual object?
Solution
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948 Solutions Manual
Problem 5.64
If an impact is an event spanning an infinitesimally small time interval, is the total kinetic energy of two
colliding objects conserved through an impact? What about the kinetic energy of each individual object?
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Dynamics 2e 949
Problem 5.65
Although competition rules prohibit significant difference in size, typical
coin-operated pool tables may present players with a significant difference
in diameter between the typical object ball (i.e., a colored ball) and the
cue ball (i.e., the white ball). In fact, once an object ball goes into a
pocket, it is captured by the table, whereas a cue ball must always be
returned to the player; and it is not uncommon for the return mechanism
to use the difference in ball diameter to separate the cue ball from the rest.
Given this, suppose we want to hit a ball resting against the bumper in
such a way that, after the collision, it moves along the bumper. Modeling
the contact between balls as frictionless, establish whether or not it is
possible to execute the shot in question with (a) an undersized cue ball
and (b) an oversized cue ball.
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