Question

Am7 = 14.3 kg mass and a m2 = 11.9 kg mass are suspended by a pulley that has a radius of R = 11.0 cm and a mass of M = 2.98 kg, as seen in the figure below. m2 The cord has a negligible mass and causes the pulley to rotate without slipping. The pulley rotates without friction. The masses start from rest d = 3.13 m apart. Treating the pulley as a uniform disk, determine the speeds of the two masses as they pass each other.

Answer 1

to solve this let us choose the zerogravitational potential energy at the level where the masses

   pass

   KE_f + PE_gf =KE_i + PE_gi + ΔE

   (1 / 2) m₁ v² + (1 / 2)m₂ v² + (1 / 2) I ω² =0 + m₁ g h_1i +  m₂ gh_2i + 0

0.5*14.3*v^2 +0.5*11.9*v^2 + 1/4*2.98*v^2 = 14.3*9.8*3.13/2 + -11.9*9.8*3.13/2

3.13 3.13 0.5x 14.3 v 0.5x 11.9 v 2.98 v - 11.9 x9.8 x 2 14.3x9.8x 2

v≈1.63053 m/s answer

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