Bukhovtsev-et-al-Problems-in-Elementary-Physics

MECHANICS
61
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Fig. 88 Fig. 89
ving with a speed v. The distance between the centres of the
wheels which the crawler is placed onto is I. The radius of the
wheels is r. A unit of crawler length weighs G.
209. Two cylinders of equal mass and size are made of unknown
materials of different density. How is it possible to tell which
of the two is hollow?
210. A flexible cable is wound in one row around a drum
with a radius R (Fig. 87). The weight of a unit of cable length
is p. The entire cable weighs G. The drum moves by inertia
without slipping along a horizontal surface, and the cable is
wound otT onto it.
At the initial moment, when the cable was completely wound
on the drum, the velocity of the drum centre was v.
Appraise the velocity of the drum centre at the moment of
time when a part of the cable with a length x lies on the surface,
neglecting the radius of the cable cross section (in comparison
with R) and the mass of the drum.
What force changes the momentum of the cable?
211. A friction force f is applied to a pulley with a radius r
rotating around a stationary axis (Fig. 88). Determine the change
in the angular velocity of the pulley with time if this velocity
is W o at the initial moment. The mass of the pulley is m and
the mass of the spokes can be neglected.
212. A hoop of radius, rotating with an angular velocity 6).
is placed on a rough horizontal surface. Determine the velocity v
of the centre of the hoop when the hoop ceases to slip. At the
initial moment the velocity of the centre of the hoop is zero.
213. A translational velocity V o is imparted in a 1iorizontal
direction to a hoop with a radius r placed on a rough horizontal
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