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PROBLEM 17.27
Greek engineers had the unenviable task of moving large
columns from the quarries to the city. One engineer,
Chersiphron, tried several different techniques to do this. One
method was to cut pivot holes into the ends of the stone and
then use oxen to pull the column. The 4-ft diameter column
weighs 12,000 lbs, and the team of oxen generates a constant
pull force of 1500 lbs on the center of the cylinder G. Knowing
that the column starts from rest and rolls without slipping,
determine (a) the velocity of its center G after it has moved
5 ft, (b) the minimum static coefficient of friction that will keep
it from slipping.
PROBLEM 17.27 (Continued)
PROBLEM 17.28
A small sphere of mass m and radius r is released from rest at A
and rolls without sliding on the curved surface to Point B where
it leaves the surface with a horizontal velocity. Knowing that
a 1.5 m and b 1.2 m, determine (a) the speed of the sphere as
it strikes the ground at C, (b) the corresponding distance c.
PROBLEM 17.28 (Continued)
PROBLEM 17.29
The mass center G of a 3-kg wheel of radius
180 mmR
is located at a distance
r 60 mm from its geometric center C. The centroidal radius of gyration of the wheel
is 90 mm.k As the wheel rolls without sliding, its angular velocity is observed to
vary. Knowing that 8 rad/s
in the position shown, determine (a) the angular
velocity of the wheel when the mass center G is directly above the geometric center C,
(b) the reaction at the horizontal surface at the same instant.
22
22 2
222
22
2
2
(3)(9.81)(0.06)
1.7658 J
11
22
11
(3)(0.24 ) (3)(0.09)
22
0.09855
mgh
Tmv I
PROBLEM 17.29 (Continued)
PROBLEM 17.30
A half-cylinder of mass m and radius r is released from rest in the position shown.
Knowing that the half-cylinder rolls without sliding, determine (a) its angular velocity
after it has rolled through 90 , (b) the reaction at the horizontal surface at the same
instant. [Hint: Note that 4/3GO r
and that, by the parallel-axis theorem,
22
1().
2
I
mr m GO ]
PROBLEM 17.30 (Continued)
PROBLEM 17.31
A sphere of mass m and radius r rolls without slipping inside a curved
surface of radius R. Knowing that the sphere is released from rest in the
position shown, derive an expression (a) for the linear velocity of the sphere
as it passes through B, (b) for the magnitude of the vertical reaction at that
instant.
PROBLEM 17.31 (Continued)
