1.114. (a) w' = co 2 R: (b) Fin = mco^2 r (2R/r)^2 — 1.1.115. F cf= in(0 2 R V 5/9=8 N, (^) V 5+8g/3co^2 R..,^
=17 N.
1.116. (a) F = 2mvco sin p = 3.8 kN, on the right rail; (b)
along the parallel from the east to the west with the velocity v =
= 2 oR cos cp 7e 420 km per hour. Here co is the angular rotation
velocity of the Earth about its axis, R is its radius.
1.117. Will deviate to the east by the distance x
2 -.
—coh 2h/g-=24 cm. Here co is the angular velocity of the 3 v
Earth's rotation about its axis.
1.118. A = F (r^2 — r^1 ) =-- —17 J.
1.119. A = ma 4 t 2 18.
1.120. F = 2as1/ 1 4- (sIR)^2.
1.121. A = mg (It + kl).
1.122. A = —kmgl/(1 — k cot a) --= —0.05 J.
1.123. Frain = (m 1 + m 2 /2) kg.
1.124. A = —(1 — 11) limg//2 = —1.3 3.
1.125. (P) = 0, P = mg (gt — v
0
sin a).
1.126. P = mRat, (P) = mRatI2.
1.127. (a) (P) = —kmgvo12 = —2 W; (b)
1.128. A = 11 zmco 2 (r: — r:) =
=0.20 J.^ ‘‘ F, (r)
1.129. Amen
where k = kik (^2) 1(lc1 (^) k2).
1.130. A = 3mg/4a, AU = U(r)\
= mg/2a.
1.131. (a) r 0 = 2a/b, steady;
(b) Finax = b 3 /27a 2 , see Fig. 7. t
1.132. (a) No; (b) ellipses
whose ratio of semiaxes is a/b =
yfl/cc; also ellipses, but with
alb =13/a.
1.133. The latter field is potential.
1.134. s = vV2g (sin a + k cos a), A = —mvpk/2(k -I- tan a).
1.135. h = H/2; Smax - -= H.
1.136. v = 2 / 3
1.137. vyril„=V5g1; T .3mg.
1.138. t=/V2v^0 R.
1.139. Al = (1 + V1 + 2klImg)mglk.
1.140. v. y 19g1 0 /32 =1.7 m/s.
1.141. A= km81°
1— cos 0
2 (sin 0+ k cos 0) cos 0 =
0.09 I.
1.142. A = x1 20 11(1 .4- 02(1 — 21)^2 , where it = mco^2 /x.
1.143. we = g (m 1 — m 2 ) 2 /(mi + m2) 2.
1.145. r = (g10) tan 0 = 0.8 cm, T = mg/cos 0 = 5 N.
= - 1 /2/na
Fig. 7.