Determine the acceleration of the 500 g block as shown in the figure.

Step-by-step solution

Let a be the common acceleration of the system and T₁, T₂ be the tensions in the strings. Assuming the 500 g block moves downward, the equations of motion for the three masses are: For the 500 g block: 500g - T₂ = 500a For the 100 g block on the incline: T₂ - T₁ - 100g 30^ = 100a For the 50 g block: T₁ - 50g = 50a Adding the three equations, we get: (500g - T₂) + (T₂ - T₁ - 100g 30^ ) + (T₁ - 50g) = (500 + 100 + 50)a 500g - 100g 1 2 - 50g = 650a 500g - 50g - 50g = 650a 400g = 650a a = 400g 650 = 8g 13 Since a is po