Question

B D 0.8 ft 45° C30° F А UA

vA = 4.6 ft/s

vB = 9.2 ft/s

Solve for vD using relative motion scalar method. (NO CROSS PRODUCT)

Thank you!

Answer 1

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Soln- Ve= -9.2 ft/ B Rw A VA = 4.6 ft/s as the superposition of transodational Rolling motion can be considered as shown below. motion and rotational motion VB=Rw B B C VCM A A VA'= Rw Translational Motion Rotational Motion

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in translational motion, every point on the body will bave transla tional velocity equal to the translational velocity of the contre of mass ( point c), het Vem Ivanslational velocity of the Then, point A and a will also have Ivans lational relocity Vem direction that of a be certre of mass in the Sam as 13 In rotational motion, each point the body will have longential veloilty Raw, which is perpendicular to the live joining that point to the centre af mass So, point and B cuill have tingential velocities Rw as shown in the the figure Now, 4.6 ft/s is taken as positive because it is in positive x - direction · VAE -9.2 ft/s is taken as negative because it is in negative x-direction. Now, Vo - VCM Rw C VA RO - VCM (2) (2) – (1) =) VA - VB 2 RW. VA-VB 2R 4.6 -- (-9.22 2x 0.8 8.625 kads

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VB = -Ven Ru Vem a RwVB - 0.8x8.625 - (1962) - 2.3 ft/s. To find velocity of point D Voc Rw 0.88 8.625 6.9 ft/s . ( Direction is perpe- ndicular to the line Now , co). see figure Voc Vorve =) V Voctva wicas s Wiose who 16 >> Vio Rw + VCM (3) From first figure, vema and Rw are two velocity vectors with angle b/w them as 0 = 45° There fore , (3) =) LVI = (Rw)+(Ven) + 2 (Rus) (v cm) cos 45º 629?+ 2.3*+ 2x6.9x2.3 * hu 75- 34 36 8.68 ft/s. Therefore, resultant velocity of point D is Vo = 8.68 ft/s.

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