Question

1 Review (Figure 1) Part A If P = 200 N and the 21 kg uniform slender rod starts from rest at @= 0, determine the rod's angular velocity at the instant just before 0 = 45 Express your answer to three significant figures and include the appropriate units. Figure < 1 of 1 HÅ Value Units 600 mm Submit Request Answer P= 200 N < Return to Assignment Provide Feedback

Answer 1

Referring to Fig. a,

r_{​​​​​​A/IC} = 0.6*tan 45° = 0.6 m

TAVIY INC 0.3m 0.3m (a)

- - mass center is Then; MalTC = No. 3² + 0.62 = 0.6700m Thus; (vada - We Matic = W2 (0.6700) The Mass moment of Inertia of the rod about its Iga Ime (As m= 2119) = 5 * 2144 0.65 = 0.63 kg m ² Thes, finae Kinesie Fanergy it; T2 = 1 m(vada + I IG Wz

= 4(21) [ W, (0.6700)] ++ (0.63) wz2 - = L wa [ 9,44 9 42544 + 0,63] T2 - 5.039 w2² z = 5.04 w2

Since the rod is initially at rest, . Referring to Fig. b

W=2119.81) N P=200N (b)

And do no work,while does positive work and does negative work. When , displaces
through a horizontal distance and displaces vertically upwards
through a distance of , Fig. c.

0.3m (C)

Thus, the work done by P and W and is :-

U_{​​​​​​P} = Ps_{​​​​​P} = 200(0.6) = 120 J

U_{​​​​​​W} = -Wh = - 21(9.81)(0.3 sin 45°) = - 43.7 J

T1 + $\sum U$ _1-2 = T2

0 + [120 - 43.7] = 5.04 (w​​​​​​₂)²

w_{​​​​​​2} = 3.89 rad/sec. Ans