Leaning pole with friction Two identical masses M are pivoted at each end of a massless pole of length L. The pole is held leaning against frictionless surfaces at angle 6, as shown, and then released. Find the initial acceleration of each mass.
Leaning pole with friction Two identical masses M are pivoted at each end of a massless pole of length L. The pole is held leaning against frictionless surfaces at angle 6, as shown, and then released. Find the initial acceleration of each mass.
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Transcribed Image Text:110
FORCES AND EQUATIONS OF MOTION
However, the integral is simply the total mass of the sphere, and we find
that for r > R, the force between m and the sphere is identical to the
force between two particles m and M separated a distance r.
Problems
For problems marked *, refer to page 520 for a hint, clue, or
answer.
3.1 Leaning pole with friction
Two identical masses M are pivoted at each end of a massless pole
of length L. The pole is held leaning against frictionless surfaces at
angle 6, as shown, and then released. Find the initial acceleration
of each mass.
3.2 Sliding blocks with friction*
Mass MA = 4 kg rests on top of mass Mg = 5 kg that rests on a fric-
tionless table. The coefficient of friction between the two blocks is
4 kg
5 kg
such that the blocks just start to slip when the horizontal force F
applied to the lower block is 27 N. Suppose that now a horizontal
force is applied to the upper block. What is its maximum value for
the blocks to slide without slipping relative to each other?
3.3 Stacked blocks and pulley
Mass Ma lies on top of mass M, as shown. Assume M > Ma.
The two blocks are pulled from rest by a massless rope passing
over a pulley. The pulley is accelerated at rate A. Block M, slides
on the table without friction, but there is a constant friction force f
between M, and M, due to their relative motion. Find the tension
in the rope.
M.
3.4 Synchronous orbit
Find the radius of the orbit of a synchronous satellite that circles
the Earth. (A synchronous satellite goes around the Earth once ev-
ery 24 h, so that its position appears stationary with respect to a
ground station.) The simplest way to find the answer and give your
results is by expressing all distances in terms of the Earth's radius
Re.
45
3.5 Mass and axle
A mass m is connected to a vertical revolving axle by two strings of
length I, each making an angle of 45 with the axle, as shown. Both
the axle and mass are revolving with angular velocity w. Gravity
is directed downward.
(a) Draw a clear force diagram for m.
(b) Find the tension in the upper string, Tup, and lower string,
45"
Tow.
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