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

180
ANSWERS AND SOLUTIONS
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0
9
2g
3g
4g
5g
Fig. 290 Fig. 29/
of air resistance is
f=F-(M -Jit) g-(M -~li) 0.8 g= 12,800 kgf
(3) Newton's equation for the weight gives mla=kx-m1g, where m 1 is
the mass of the weight at the end of the spring, a is the acceleration of
the rocket, k is the coefficient of elasticity of the spring, x is the elongation
of the spring. According to the condition, m1g=kl o • Therefore,
x=!JL (a+g). The scale of the device should be graduated uniformly
g
(Fig. 290). An acceleration of g corresponds to a division of one centimetre.
62. The only force acting on the bead is the reaction force of the rod N
directed at right angles to the rod. The absolute acceleration W a of the bead
(relative to a stationary observer) will be directed along the line of action
of the reaction force N. The relative acceleration w,. is directed along the
rod (Fig. 291)
wa=a+w r
It follows from the triangle of accelerations that W r =a cos Cl and
wa=asin Cl.
From Newton's second law, the reaction force is N = ma sin Cl.
The time 't' during which the bead moves along the rod can be found from
. a cos Cl·",2 (-2-[-
the equation [= 2 . Hence, '1'= --•
a cos a.
63. When the bead moves it is acted upon by the friction force kN and
the reaction force N.
The absolute acceleration will be directed along the resultant force F. It
follows from Fig. 292 that"
N =rna sin . a, and w,.=a cos ex--m=a kN ( cos k .
(X- SIn ex)