Consider the arrangement depicted in the figure. Determine the tension in the string connecting the 1.0 kg blocks. (Assume g = 10 m/s ^2 )

Step-by-step solution

Let the masses be m₁ = 1.0 kg (left), m₂ = 1.0 kg (middle), and m₃ = 0.5 kg (hanging). The maximum friction force on the two blocks on the horizontal surface is: f_ max = m₁ g + m₂ g = 0.2 1.0 10 + 0.2 1.0 10 = 2 + 2 = 4 N The driving force due to the hanging block is: F_ drive = m₃ g = 0.5 10 = 5 N Since F_ drive > f_ max , the system will accelerate. Let the common acceleration be a . The equation of motion for the entire system is: m₃ g - f_ max = (m₁ + m₂ + m₃) a 5 - 4 = (1.0 + 1.0 + 0.5) a 1 = 2.5 a a = 0.4 m/