Please report your answer to 2 significant figures. Ac shown below, three blocks

Question

Please report your answer to 2 significant figures. Ac shown below, three blocks are connected by a cord which passes over two frictionless, massless pulleys Two of the blocks are hanging, while the third is on a frictionless horizontal surface. A spring of constant k = 317 N/m is attached to the block of muss m,. The masses of the blocks are: m_1 = 217 kg m_2 = 390 kg, and m_3 = 50kg. The system is released from rest with the spring initially neither compressed nor stretched. Please find the speed v of block 2 when it has fallen a distance h = 2.83 m. Note that U_g = mgh, U_s = 1/2 kx^2, and K = 1/2 mv^2.

Explanation / Answer

By energy conservation,

decrease in gravitational potential energy = increase in KE + increase in spring potential energy

m2gh - m1gh = 0.5 (m1+m2+m3) v^2 + 0.5k h^2...............because all blocks move with same speed

(390-217)*9.8*2.83 = 0.5(390+217+50) v^2 +0.5*317*2.83*2.83

4797.982 = 328.5 v^2 + 1269.41

v^2 = (4797.982 - 1269.41)/328.5 =10.74

v = sqrt 10.74

v = 3.277 m/s

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