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

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180 ANSWERS AND SOLUTIONS --+- 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)
MECHANICS 181 Hence (see Problem 62). .r 2l 't= V a (cos a.-k sin a) If k ~ cot a, the bead will not move with respect to the rod, and of friction is rna cos a.. the force 64. The equations of motion of the block and the body have the form: ma=f (1) Mb::xF-f (2) where f Is the force of friction; a and b are accelerations. Let us assume that there is no sliding, then a=b. The acceleration and the force of friction can be found from the equations of motion. The force of friction is f=m M:m' For the body not to slide, the force of friction should satisfy the inequality f
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B. B. 6yX08I4e8. B. JI. KpU8IleHIC0
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First published 1971 Second printin
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6 Chapter 5. Geometrical Optics •
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a Fig. 41 Fig. 42 for the rotating
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a 0' Fig. 80 Fig- 8/ ces '1 and " f
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--- --r-- - Fig. 114 ~--l---I"" Fig
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CHAPTER 2 HEAT. MOLECULAR PHYSICS 2
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CHAPTER 2 HEAT. MOLECULAR PHYSICS 2
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CHAPTER 3 ELECTRICITY AND MAGNETISM
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A ~-..----4-----r--------r-- Fig. 4
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CHAPTER 5 GEOMETRICAL OPTICS 5-1. P
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