Question

Find the linear momentum of the system below. Model the pulleys as particles. Assume that hy movent of the system only occurs in the vertical direction. Also assume that all of the blocks are identical in size, shape and material. Use the inertial reference point given in the figure, and define any other quantities you need to solve the problem. Z А B

Answer 1

sol? Assume all Pulleys are mass less and fichon less. . 2 // , / since all blocks are same size, shape and misernical MA=mba meam N T Led, T- Tension in string. X 2Т TX Хэт Хат с 1 Led system starts from ress & Assume XA, XB & Xe are displacemena of Block A, B & C respectively. Xe А Х4-Т р 8, E work done by session forces acting on blocks to Тk Xa + 4 + Хе 2 Т% к. со XA=4&B + 2 Xc Differentiating twiie word "t" Од . АМО + rac — 1 for Block 1) T न Laa ng -T=maa \\ mg 11, АТ for Лоси 4T-mg = mab р. КО my

от рок ч 2 W ac 2т - 4 = m и from egn & hu тя - Te m (44) +24) (- 4р - 4cAg+2) my -T= ama tamu add egn 110 kV 6T -2mg = mag + mac 1 ет" у 2 4 (V)) с _12т Tra - T 4mag tama Amy = _2map + 2 mac 1ът с 2-м ба + 5 mg ТО 15}e cm + 4% е с v1 52T 13 mg = 13 mar frelor 8 mars Б) Т able in = hub ar (1. VII 1 from ean w 4t-my = maab mat 8 Ат-т" = Rule

(с 4T = 1 / 1 mg ting - 2-3 28 mg AT= 28 mg IT - S foue' from eys mg - T - maa You=hu % E Shwe = bulk hul e СА: 48 from regn 2t - my = mac = mac 24 my - my -Yong mac aca - 48 a= - 49 (-ve sign indicates dirn is opposite to assume direction ) S., ac = 1 Он - 9 ср = 8 -%9 Since system start from rest-so, vel.as time "' V = ut ad Vk - Ha) * V. - 98 V - 48 so, Linear mongendum of systems are Linear moment of Block 'À LLAF mna= m*2596 LA = 2 ngt I down word) Linear momentum of Block "B" (LB) =mVB = may of LB= 2 ngt lupward) Lineun momentum of Block "C" (Le) = m Ve=m*ggd Les xmat (Downwoord