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

MECHANICS 19
Fig. 20
56. A heavy sphere with a mass m is suspended on a thin
rope. Another rope as strong as the first one is attached to the
bottom of the sphere. When the lower rope is sharply pulled
it breaks. What accelera tion will be imparted to the sphere?
57. Two weights with masses m 1 and m, are connected by
a string passing over a pulley. The surfaces on which they rest
form angles a and ~ with the horizontal (Fig. 20). The righthand
weight is h metres below the left-hand one. Both weights
will be at the same height in 't seconds after motion begins.
The coefficients of friction between the weights and the surfaces
are k. Determine the relation between the masses of the
weights.
58. A slide forms an angle of a = 30° with the horizon.
A stone is thrown upward along it and covers a di-t.iuco of
1= 16 metres in t, == 2 seconds, after which it slides down. Wha t
time t 2
is required for the return motion? What is the coefficient
of friction between the slide and the stone?
59. A cart with a mass of M = 500 g is connected by a string
to a weight having a mass m = 200 g. At the initial moment
the cart moves to the left along a horizontal plane at a speed
of V o = 7 m/s (Fig. 21). Find the magni tude and direction of
I{,
~
Fig. 21
Fig. 22
.) .a-