526 Solutions Manual
Problem 3.77
The wedge-shaped cart
B
is moving up and to the left with accel-
eration
aB
. The coefficient of static friction between the crate and
the cart is insufficient to prevent slipping between the two. If the
mass of
A
is
m
and the coefficient of kinetic friction between the
crate and the cart is
k
, determine the acceleration of the crate in the
component system shown.
Solution
Dynamics 2e 527
Problem 3.78
The pendulum is released from rest when
✓D0ı
. If the string holding the pendulum bob breaks when
the tension is twice the weight of the bob, at what angle does the string break? Treat the pendulum as a
particle, ignore air resistance, and let the string be inextensible and massless.
Solution
Referring to the FBD at the right, we model the pendulum bob as a particle subject only
to its own weight
mg
and the tension in the string
T
. The component system is polar
528 Solutions Manual
Problem 3.79
The trolley
T
moves along rails on the horizontal truss of the
tower crane. The trolley and the load of mass
m
are both initially
at rest (with
✓D0
) when the trolley starts moving to the right
with constant acceleration aTDg. Determine
(a) The maximum angle ✓max achieved by the load m.
(b) The tension in the supporting cable as a function of ✓.
Treat the load
m
as a particle, and ignore the mass of the support-
ing cable.
Solution
Dynamics 2e 529
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.
530 Solutions Manual
Problem 3.80
If the particle is constrained to only move back and forth in the plane of the center of the bowl, how many
degrees of freedom must it have? Recall that this will also be the number of equations of motion of the
particle.
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 531
Problem 3.81
Derive the equation(s) of motion for a particle moving on the inner surface of the smooth parabolic bowl
shown. Assume that the particle only moves in the vertical
xy
plane that goes through the center of the
bowl, that the equation of the parabola is
y.x/D1C0:5x2
, and that gravity is acting in the
y
direction.
The bowl’s cross section is shown on the right side of the figure.
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.
532 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 533
Problem 3.82
A satellite orbits the Earth as shown. Model the satellite as a
particle, and assume that the center of the Earth can be chosen as
the origin of an inertial frame of reference.
Using a polar coordinate system and letting
me
be the mass
of the Earth, determine the equations of motion of the satellite.
Solution
As shown on the right, we adopt a polar coordinate system with origin
O
at the
center of the Earth.
534 Solutions Manual
Problem 3.83
A satellite orbits the Earth as shown. Model the satellite as a
particle, and assume that the center of the Earth can be chosen as
the origin of an inertial frame of reference.
The minimum and maximum distances from the center of
the Earth are
RPD4:5 ⇥107
m and
RAD6:163⇥107
m, re-
spectively, where the subscripts
P
and
A
stand for perigee (the
point on the orbit closest to Earth) and apogee (the point on
the orbit farthest from Earth), respectively. If the satellite’s speed
at Pis vPD3:2⇥103m=s, determine the satellite’s speed at A.
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 535
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.