A 13 kg block and a 27 kg block are attached to opposite end

A 1.3 kg block and a 2.7 kg block are attached to opposite ends of a light rope. The rope hangs over a solid, frictionless pulley that is 25 cm in diameter and has a mass of 0.80 kg. When the blocks are released, what is the acceleration of the lighter block? Express your answer using two significant figures.

Solution

From newton\'s 2nd law for the net forces on each block, and one for the net torque on the pulley.

sigma F = m₁ a = T₁ - m₁ g ------------- (1)

sigma F = m₂ a = m₂ g - T₂   -------------- (2)

sigma T = r F = I * alpha = r (T₂ - T₁)

I a / r = r (T₂ - T₁)

I a / r² = (T₂ - T₁) ----------- (3)

Add (1) (2) and (3)

a = [ g (m₂ - m₁) ] / ( m₁ + m₁+ I/r² )

= [g (m₂ - m₁)] / ( m₁ + m ₂ + 0.5 M r²/r²)

= [g (m₂ - m₁)] / ( m₁ + m₁ + 0.5 M)

a = [ 9.8 (2.7 - 1.3) ] / [1.3+ 2.7 + 0.5(0.80)]

a = 3.12 m/s²