Fig. 3.
1.41. R = a312bs, w = all1+ (4bs21a3) 2.
1.42. (a) w = 2av2, R = I/2a; (b) w = bv2/a2, R = a2/b.
1.43. v = 2Rco = 0.40 m/s, w = 4Ro.i2 = 0.32 m/s2.
1.44. w= (v/t) 1/1 4a2t4 = 0.7 m/s2.
1.45. co = 231nvil = 2.0.103 rad/s.
1.46. (a) (cD). 2a/3 = 4 rad/s, (A) = j/- 3ab = 6 rad/s2; (b)
= 21/3ab =12 rad/s2.
1.47. t= ir(4/a) tan a = 7 s.
1.48. (o.)) = o.)0/3.
1.49. (a) cp = (1 - e') coda; (b) 6.)
1.50. coz = f li2130 sin cp, see Fig. 3.
1.51. (a) y = v2/(32; (hyperbola); (b) y = 1/2wx/o.)
1.52. (a) W A = v2/R = 2.0 m/s2, the
vector WA is permanently directed to the
centre of the wheel; (b) s = 8./1 = 4.0 m.
1.53. (a) vA -=---2wt =10.0 cm/s,
wt = 7.1 cm/s, vo = 0; (b)
=2w 1/1
(wt2/2R)2 =5.6 cm/s2,
= will+ (1-wt2/R)2 ---- 2.5 cm/s2,
= w2t 2/R = 2.5 cm/s2.
1.54. RA= 4r, Rg= 2 1/2 -r.
1.55. co= Vo4-1-, co: =5 rad/s, j3= 0)0)2 = 12
1.56. (a) w = at 1/1
(btla)2=8 rad/s,
=1.3 rad/s2; (b) 17°.
1.57. (a) (.6-= vIR cos a = 2.3 rad/s,
=2.3 rad/s2.
1.58. o.)= coo yi + cootiwor 0.6 rad/s,
(3= [30111 Oot2 =
= 0.2 rad/s2.
1.59. t1m = 2mwl(g
w).
1.60. ar =
(nit+ , m2) g, T - (1, ±k) m ° m2g.
nto-rmi-rm2
'1.61. (a)
(k1- k2) mi ,m2g
Cosa . (b) tan a
= kinii+ k2m2
m1 ms
min
mi +77,2 •
1.62. k = [(12 - 1)1(12 + 1)1 tan a = 0.16.
1.63. (a) m2/m1 > sin a
k cos a; (b) m2/m1 < sin a - k cos a;
(c) sin a - k cos a
1.65. When t G to, the accelerations w1 = w2 = at/(m1 + m2);
when t > to w 1 = kgm2/m1, w2 = (at - km2g)Im2. Here to
= kgm2 (m1 + m2)1am. See Fig. 4.
1.66. tan 2a = -1/k, a = 49°; tmin = 1.0 s.
1.67. tan3= k; T = mg (sin a k cos cc)11/ 1+k2.
= woe -at.
(parabola).
Vg=WA =
rad/s2.
p = all1+ (2bt/a)2
60°; (b) 1= (v/R)2 tan a =
2 3 c
1.68. (a) v=
mg2 cos a
(b)
s=
m g os a
2a sin 2 a '
6az sina a •
1.69. v =11(2g/3a) sin a.
1.41. R = a312bs, w = all1+ (4bs21a3) 2.
1.42. (a) w = 2av2, R = I/2a; (b) w = bv2/a2, R = a2/b.
1.43. v = 2Rco = 0.40 m/s, w = 4Ro.i2 = 0.32 m/s2.
1.44. w= (v/t) 1/1 4a2t4 = 0.7 m/s2.
1.45. co = 231nvil = 2.0.103 rad/s.
1.46. (a) (cD). 2a/3 = 4 rad/s, (A) = j/- 3ab = 6 rad/s2; (b)
= 21/3ab =12 rad/s2.
1.47. t= ir(4/a) tan a = 7 s.
1.48. (o.)) = o.)0/3.
1.49. (a) cp = (1 - e') coda; (b) 6.)
1.50. coz = f li2130 sin cp, see Fig. 3.
1.51. (a) y = v2/(32; (hyperbola); (b) y = 1/2wx/o.)
1.52. (a) W A = v2/R = 2.0 m/s2, the
vector WA is permanently directed to the
centre of the wheel; (b) s = 8./1 = 4.0 m.
1.53. (a) vA -=---2wt =10.0 cm/s,
wt = 7.1 cm/s, vo = 0; (b)
=2w 1/1
(wt2/2R)2 =5.6 cm/s2,
= will+ (1-wt2/R)2 ---- 2.5 cm/s2,
= w2t 2/R = 2.5 cm/s2.
1.54. RA= 4r, Rg= 2 1/2 -r.
1.55. co= Vo4-1-, co: =5 rad/s, j3= 0)0)2 = 12
1.56. (a) w = at 1/1
(btla)2=8 rad/s,
=1.3 rad/s2; (b) 17°.
1.57. (a) (.6-= vIR cos a = 2.3 rad/s,
=2.3 rad/s2.
1.58. o.)= coo yi + cootiwor 0.6 rad/s,
(3= [30111 Oot2 =
= 0.2 rad/s2.
1.59. t1m = 2mwl(g
w).
1.60. ar =
(nit+ , m2) g, T - (1, ±k) m ° m2g.
nto-rmi-rm2
'1.61. (a)
(k1- k2) mi ,m2g
Cosa . (b) tan a
= kinii+ k2m2
m1 ms
min
mi +77,2 •
1.62. k = [(12 - 1)1(12 + 1)1 tan a = 0.16.
1.63. (a) m2/m1 > sin a
k cos a; (b) m2/m1 < sin a - k cos a;
(c) sin a - k cos a
1.65. When t G to, the accelerations w1 = w2 = at/(m1 + m2);
when t > to w 1 = kgm2/m1, w2 = (at - km2g)Im2. Here to
= kgm2 (m1 + m2)1am. See Fig. 4.
1.66. tan 2a = -1/k, a = 49°; tmin = 1.0 s.
1.67. tan3= k; T = mg (sin a k cos cc)11/ 1+k2.
= woe -at.
(parabola).
Vg=WA =
rad/s2.
p = all1+ (2bt/a)2
60°; (b) 1= (v/R)2 tan a =
2 3 c
1.68. (a) v=
mg2 cos a
(b)
s=
m g os a
2a sin 2 a '
6az sina a •
1.69. v =11(2g/3a) sin a.