Irodov – Problems in General Physics

1.232. A ym (M 1 /R 1 M 2 /R 2 ) = 1.3.10 8 kJ, where M and
R are the mass and the radius of the Earth and the Moon.

1.233. v 3 V 2v: + - 1)2 V;, x 17 km/s. Here i4
TME IR, ME and R are the mass and the radius of the Earth;
Vi = yMslr, Ms is the mass of the Sun, r is the radius of the
Earth's orbit.
1.234. 1 = 2aF 2 /mw = 1.0 m.
1.235. N = (aB—bA)k, where k is the unit vector of the z

axis; l= I aB — bA^ + B^2.
1.236. 1= I aA—bB A^2 + B^2.
1.237. F„ = 2F. This force is parallel to the diagonal AC and
is applied at the midpoint of the side BC.
1.238. (a) I = 1 / 3 m1^2 ; (b) I = 'ism (a^2 b^2 ).
1.239. (a) I = iJ 2 rtpbR^4 = 2.8 g•m^2 ; (b) I =^8 /^10 mR^2.
1.240. I = il 4 mR 2.
1.241. I = (37/72) mR 2 = 0.15 kg•m^2.
1.242. I =^213 mR^2.
1.243. (a) co = gt1R (1 + M/2m); (b) T = mg 2 t 2 /2(1 M12m).
1.244. T = 112 mg, Ivo = gmr^2 1I.
1.245. co =176F sin (/ml.
1.246. R

1,71 2 — rnilg Ti

—

(m+4m2)

(mi - I- m 2 m/2) R '^ T2^ MI (M+ 4171 1)

1.247. A- (^7712 — kini) kntig^2 t^2

rad/s2;

m+2(mi-Fm2) •

1.248. n = (1 + k 2 ) co:R/8ak (k 1) g.

1.249. t = 314 coRlkg.

1.250. (w) = 1 / 3 ceo•

1.251. 13 = 2mgx1R1(M + 2m).

1.252. (a) k > 2 /7 tan a; (b) T = 5114 mg^2 t^2 sins a.

1.253. (a) T = 116 mg = 13 N, t3 =^2 /3 g/R = 5.10^2

(b) P = 213 mg^2 t.

1.254. w' = 2 / 3 (g — w 0 ), F =^1 /^3 m (g — wo).

1.255. w= g sin a/(1^ I/mr^2 ) = 1.6 m/s^2.

1.256. Finax = 3kmg1(2 — 3k); wmax = 2kg1(2 — 3k).

1.257. (a) wx— F (cos m (1+7) cc— r I R)^ (b) A — F^2 t^2 (cos a, —r/R)^2

2m (1+7)

1.258. T = 1110 mg.

1.259. w = 3g (M + 3m)1(M + 9m ± I1R^2 ).

1.260. (a) w =

F (3m 1 -1-2m 2 )F^2 t^2 (3m^2 -1-2m^2 )

m1

(b)

(m1M2) 2m1(m1+ ms)

1.261. w

1

(^) F/(m (^1 2) 17m2); w 2 2 /7
1.262. (a) t = co 0 R1kg; (b) A = —^1 /ontw:R^2.
1.263. a) =1710g (R+r)/17r^2.
1.264. vo = V 113 gR (7 cos a — 4) =1.0 m/s.
1.265. v
°
=1/ 8gR.
1.266. T = mv 2.
1.267. T = 7110 mv^2 (1 +^217 r^2 1R^2 ).
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