In the arrangement shown in the figure, the tension in the string is 16 N and the acceleration of each block is 0.5 m/s ^2 . Determine the friction coefficients ₁ and ₂ at the two contacts with the blocks.

Step-by-step solution

Taking g = 10 m/s ^2 . For the 2 kg block, the equation of motion is: T - ₁ m₁ g = m₁ a Substituting the given values ( T = 16 N , m₁ = 2 kg , a = 0.5 m/s ^2 ): 16 - ₁ (2)(10) = 2(0.5) 16 - 20 ₁ = 1 20 ₁ = 15 ₁ = 0.75 For the 4 kg block, the component of weight along the incline is m₂ g 30^ = 4 10 0.5 = 20 N . Since 20 N > 16 N , the block moves down the incline. The equation of motion for the 4 kg block is: m₂ g 30^ - T - ₂ m₂ g 30^ = m₂ a Substituting the given values ( m₂ = 4 kg , a = 0.5 m/s ^2 ): 4(10) 30^ - 1