Question: Find velocity of c and point D at the instant shown $\omega_{AB}=3 rad/sec$ clockwise.
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$AB = 400 mm.$

Mumbai University > FE > Sem 1 > Engineering Mechanics

Marks : 06

Years : DEC 2015

 modified 14 months ago by Yashbeer ★ 170 written 2.9 years ago by Aksh_31 • 680
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$$V_c= ?,V_D= ?,W_{AB}=3rad/sec$$

$AB = 400 mm. \\ V_B=r.w \\ =AB.ω_{AB } \\ =100×3=300 mm/s$

$IC = 100 mm \\ IB=\sqrt{125^2-100^2} =75mm\\ ∠ IBC = \tan^{-1} (\dfrac {100}{75})=53.13^0 \\ ω_{CD} = \dfrac {V_B}{IB} = \dfrac {300}{75} =4 rad/s \\ V_C = I_C.ω_{CD}=100×4=400 mm/s \\ In\space \space ΔDBI \\ ∠DBI=180-53.13=126.87^0$

By cosine Rule,

$I_D=\sqrt{IB^2+BD^2-2IBBD×\cos ∠DBI} \\ =\sqrt{75^2+125^2-2×75×125×\cos⁡126.87 } \\ = 180.3 m \\ V_D = ID.ω_{CD} = 180.3×400=721.2 mm/s$

By sine rule

$\dfrac {I_D}{\sin ∠DBI} = \dfrac {BD}{\sin ∠DIB} = \dfrac {180.3}{\sin 126.87} = \dfrac {125}{\sin ∠DIB} \\ ∴∠DIB=33.69^0$

In Δ DMI

$∠ DMI=180-90-33.69=56.31^0$

Instantaneous velocity of $C = 400mm/s (→)$

Instantaneous velocity of $D = 721.2mm/s (56.31^0 )$