Solid Marble
Friday, July 29th, 2011
Marble 1.5 kg and 2.7 kg of marble attached to opposite ends of a rope light?
The rope hangs over a solid pulley Frictionless is 31cm in diameter and has a mass of 0.76 kg. What is the acceleration of the lighter ball?
Lighter marble mass M1 = Mass of 1.5 kg heavier marble m2 = 2.7 kg block radius R = 31 / 2 cm = 15.5 cm = 0.155 m Weight 0.76 kg block Let M = T1 = tension of the string between M1 and M, T2 = tension in the chain between M1 and M2 M2 M falls and rises with an acceleration of the same magnitude. Let the magnitude of acceleration = the M1, T1 – m1 = m1 * g * a —————— (1) For m2, m2 * g – T2 = m2 * a ——– ———- (2) the pulley moment of inertia I = (1 / 2) MR ^ 2 angular acceleration the pulley alpha = R / in the pair of pulleys = (T2 – T1) R = I * alpha pair after (T2 – T1) = R (1 / 2) MR ^ 2 * R / (T2 – T1) R = (1 / 2) divided by the right arm, T2 – T1 = (1 / 2) My ———— (3) Addition (1) and (2), (T1 – T2) + (M2 – M1) g = (M1 + M2) or T2 – T1 = (m2 – m1) g – (M1 + M2) to —– – (4) (3) and (4), (1 / 2) Ma = (M2 – M1) g – (M1 + M2) aa (M / 2 + M1 + M2) = (M2 – M1) ga (0.76 / 2 + 1.5 + 2.7) = (2.7 – 1.5) * 9.8 (4.58) = 11.76 11.76/4.58 = a = 2.57 m / s ^ 2 Answer: 2.57 m / s ^ 2 to the top
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