Determine the accelerations a₁ , a₂ , and a₃ of the three blocks illustrated in the figure when a horizontal force of 10 N is applied to the 2 kg block. Take g = 10 m/s ^2 .

Step-by-step solution

First, we find the maximum possible friction forces at each interface. Between the 2 kg and 3 kg blocks: f_ 1, max = ₁ m₁ g = 0.2 2 10 = 4 N Between the 3 kg and 7 kg blocks: f_ 2, max = ₂ (m₁ + m₂) g = 0.3 (2 + 3) 10 = 15 N Between the 7 kg block and the ground: f_ 3, max = ₃ (m₁ + m₂ + m₃) g = 0 12 10 = 0 N Let us assume all three blocks move together with a common acceleration a . a = F m₁ + m₂ + m₃ = 10 2 + 3 + 7 = 10 12 = 5 6 m/s ^2 The required friction force f₁ to keep the 2 kg block moving with this acceler