Question

... Instead of two blocks and one pulley, let

Answer 1

(a) Draw a complete free-body diagrams as shown in figure 2 below ::

(b) equation(s) that come from the free-body diagrams is given as ::

1. First, for mass m₁ :               F_{Net, 1} = T₁ - F_f1 = m₁ a

2. tensions at T₁ and T₂ :          _net = R T₂ - R T₁ = I

3. forces on m₂, the mass on the incline :         F_net = w₂ sin 30^o - F_f2 - T₂ = m₂ a

4. equations with three unknowns, T₁, T₂, and a : T₁ - m₁ g = m₁ a

5. T₂ - T₁ = ( I / R) = ( I / R ) ( a / R ) = ( I / R² ) a

6. T₁ - (0.36) (2.0 kg) (9.8 m/s²) = (2.0 kg) a

7. T₂ - T₁ = [ 0.3125 kg m² / (0.25 m)² ] a = 5 kg a

(c) equations that relate the various accelerations to each other is given as ::

1. F_{Net, 1} = T₁ - F_f1 = m₁ a

2. linear acceleration of the blocks is closely related to angular acceleration of the pulley : a = r

3. T₁ - m₁ g = m₁ a

4. angular acceleration is related with acceleration :       = a /r