1.146. (al Fir = mg [sin a + (w211 g) ccs al= 6 N.
(b) co<
1.147. (a) V = (mivi
m2v2)/(m1 + m2); (b) T = µ (v1 —
— v2)212, where p, = m1m2 (ml -h m2).
1.148. E
E
mV2/2.
1.149. E =
-I- v2 2)/2, where p. = mi.m2/(m1
m2).
1.150. p = Po mgt, where pc, = mvi m 2v2, m =
m2;
re = vot
gt2/2, where v0 = (m1v1
m2v2)/(ml
m2)•
1.151. ve = xV xm2/(mi. ± m 2).
1.152. (a) /max = /0
Flx,
can = lo;
(b) /max = to +
2m1 F/x (m1 + m2), /min = 4,•
1.153. (a) Al > 3mg/x; (b) h = (1 + xAl/mg)2 mg/8x = 8mg/x.
1.154. v1 = —mv/(M — m), v2 = Mv/(M —
, mM
1.155. vrear vo —
u; vform = vo -t-
+no, U.
2m
1.156. (1) vi— — m+2m u;
m 2M + 3m)
(2) v2 —
(m+
(
m)(m+ 2m) u,
V2k, = 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 = Mv2/2g (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 (v1 — v2)212, where p, = m1m2/(m1
m2).
1.168. (a) 11 = 2m1 1
(m1
-I - m2); (b) = 4m1m2/(m1 + m2)21.169. (a) m1/m2 = 1/3; (b) m1/m2 = 1 + 2 cos e = 2.0.
1.170. 11 = 1/2cos2 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 '/211(v -Fv:).
Here p.=
= mim2/(mi+ m2)1.175. Sin 0max
1.176. v' = —v (2 — r12)/(6 — r12). 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"
(b) co<
1.147. (a) V = (mivi
m2v2)/(m1 + m2); (b) T = µ (v1 —
— v2)212, where p, = m1m2 (ml -h m2).
1.148. E
E
mV2/2.
1.149. E =
-I- v2 2)/2, where p. = mi.m2/(m1
m2).
1.150. p = Po mgt, where pc, = mvi m 2v2, m =
m2;
re = vot
gt2/2, where v0 = (m1v1
m2v2)/(ml
m2)•
1.151. ve = xV xm2/(mi. ± m 2).
1.152. (a) /max = /0
Flx,
can = lo;
(b) /max = to +
2m1 F/x (m1 + m2), /min = 4,•
1.153. (a) Al > 3mg/x; (b) h = (1 + xAl/mg)2 mg/8x = 8mg/x.
1.154. v1 = —mv/(M — m), v2 = Mv/(M —
, mM
1.155. vrear vo —
u; vform = vo -t-
+no, U.
2m
1.156. (1) vi— — m+2m u;
m 2M + 3m)
(2) v2 —
(m+
(
m)(m+ 2m) u,
V2k, = 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 = Mv2/2g (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 (v1 — v2)212, where p, = m1m2/(m1
m2).
1.168. (a) 11 = 2m1 1
(m1
-I - m2); (b) = 4m1m2/(m1 + m2)21.169. (a) m1/m2 = 1/3; (b) m1/m2 = 1 + 2 cos e = 2.0.
1.170. 11 = 1/2cos2 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 '/211(v -Fv:).
Here p.=
= mim2/(mi+ m2)1.175. Sin 0max
1.176. v' = —v (2 — r12)/(6 — r12). 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"