Irodov – Problems in General Physics

less spring to a point B. The spring stiffness is equal to x. The whole

system rotates with a constant angular velocity co about a vertical

axis passing through the point 0. Find the elongation of the spring.

How is the result affected by the rotation direction?

1.89. A cyclist rides along the circumference of a circular horizontal

plane of radius R, the friction coefficient being dependent only on

Fig. 1.26.

distance r from the centre 0 of the plane as k= ko (1—rIR), where
k, is a constant. Find the radius of the circle with the centre at the
point along which the cyclist can ride with the maximum velocity.
What is this velocity?
1.90. A car moves with a constant tangential acceleration wti =
= 0.62 m/s 2 along a horizontal surface circumscribing a circle of
radius R = 40 m. The coefficient of sliding friction between the
wheels of the car and the surface is k = 0.20. What distance will
the car ride without sliding if at the initial moment of time its veloc-
ity is equal to zero?
1.91. A car moves uniformly along a horizontal sine curve y
= a sin (xla), where a and a are certain constants. The coefficient of
friction between the wheels and the road is equal to k. At what veloc-
ity will the car ride without sliding?
1.92. A chain of mass m forming a circle of radius R is slipped on a
smooth round cone with half-angle 0. Find the tension of the chain
if it rotates with a constant angular velocity co about a vertical axis
coinciding with the symmetry axis of the cone.
1.93. A fixed pulley carries a weightless thread with masses m 1
and m 2 at its ends. There is friction between the thread and the pul-
ley. It is such that the thread starts slipping when the ratio m^2 im^1 =
= rya. Find:
(a) the friction coefficient;
(b) the acceleration of the masses when m^2 1m^1 = >
1.94. A particle of mass m moves along the internal smooth sur-
face of a vertical cylinder of radius R. Find the force with which the
particle acts on the cylinder wall if at the initial moment of time
its velocity equals vo and forms an angle a with the horizontal.

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