1.146. (al Fir= mg [sin a + (w 2 11 g) ccs al= 6 N. (b) co<
<V g (k— tan a)// (1^ k tan cz) = 2 rad/s.
1.147. (a) V = (mivi m 2 v 2 )/(m 1 + m 2 ); (b) T = μ (v 1 —
— v 2 ) 2 12, where p, = m 1 m^2 (ml -h m^2 ).
1.148. E E mV 2 /2.
1.149. E = -I- v 22 )/2, where p. = mi.m2/(m1 m 2 ).
1.150. p = Po mgt, where pc, = mvi m 2 v 2 , m = m2;re = vot gt 2 /2, where v (^0) = (m1v1 m2v2)/(ml (^) m2)•
1.151. ve = xV xm2/(mi. ± m^2 ).
1.152. (a) /max = / 0 Flx, (^) can = lo; (b) /max = to +
2m (^1) F/x (m1 + m2), /min = 4,•
1.153. (a) Al > 3mg/x; (b) h = (1 + xAl/mg) 2 mg/8x = 8mg/x.
1.154. v 1 = —mv/(M — m), v 2 = Mv/(M —
, mM
1.155. vrear vo —^ u; vform = vo -t- +no, U.
1.156. (1) vi— —m+2m u;2m^ (2) v 2 — (m+m 2M + 3m) (m)(m+ 2m) u,
V 2 k, = 1 -^1 - m/2 (M -1- m) > 1.
1.158. Ap = m y 2gh 1)/(71— 1) = 0.2 kg -m/s.
1.159. (a) I—
m
jw+m I'; (b) F—
mM dv'
M m dt •
1.160. 1 = m1'12M.
1.161. -c= (p cos a— M 17 - 2g1 sin a)/Mg sin a.
1.162. (a) v = (2M/m) Vir sin (0/2); (b) 1— m/M.
1.163. h = Mv 2 /2g (M m).
1.164. (1) A = —Rgh, where p, = mM/(m M); (2) Yes.
1.166. v = 1.0i + 2.0j — 4.0k, v 4.6 m/s.
1.167. AT = --p (v 1 — v^2 )^2 12, where p, = m1m 2 /(m1 m^2 ).
1.168. (a) 11 = 2 m1 1
(m1
- I- m2); (b) = 4m^1 m^2 /(m^1 + m2)^2 -
1.169. (a) m 1 /m 2 = 1/3; (b) m 1 /m 2 = 1 + 2 cos e = 2.0.
1.170. 11 = 1 / 2 cos 2 a = 0.25.
1.171. max = v (1 + -I/2 (1-1)) =1.0 km per second.
1.172. Will continue moving in the same direction, although
this time with the velocity v' = (1— V1 — 2i) v/2. For 11< 1 the
velocity v' Tiv/2 = 5 cm/s.
1.173. AT IT = (1 ml M) tang 0 m/M — 1 = —40%.
1.174. (a) p = IAA / 14. v:; (b) T '/ 2 11(v -Fv:).^ Here p.=
= mim2/(mi+ m2)-
1.175. Sin 0max
1.176. v' = —v (2 — r1 2 )/(6 — r1^2 ). Respectively at smaller 11,equal, or greater than V T.
1.178. Suppose that at a certain moment t the rocket has the
mass m and the velocity v relative to the reference frame employed.
Consider the inertial reference frame moving with the same velocity
as the rocket has at a given moment. In this reference frame the
momentum increment that the system "rocket-ejected portion of gas"