The three objects in the figure are connected by a light cord.A triangular structure is oriented such that its base rests upon a horizontal surface, its right side is perpendicular to its base, and its left side forms an incline of anglewith the base. A pulley is attached to the structure's apex. Three objects (massesm, 2m, andM) are connected by two cords (tensionsT₁andT₂) and arranged as follows

• Masses 2mandmare, respectively, attached to the left and right ends of cordT₁such that massmis nearest to the structure's apex.
• MassesmandMare, respectively, attached to the left and right ends of cordT₂such that cordT₂passes over the pulley and massMhangs freely.

(a)If the inclined plane is frictionless, find the following, assuming the system is in equilibrium. (Use the following as necessary:m,g, and.)massM=

tensionT₁=

tensionT₂=

(b)If the value ofMis double that from part (a), find the following. Note that the system will no longer be in equilibrium. (Use the following as necessary:m,g, and.)accelerationa=

tensionT₁=

tensionT₂=

(c)If the coefficient of static friction between the blocks and the inclined plane is_s, and the system is in equilibrium, find the following. (Use the following as necessary:_s,m,g, and.)M_max=

3.8407

M_min=

(d)Compare the values ofT₂whenMhas its minimum and maximum values. (Use the following as necessary:_s,,m, andg.)T_{2, max}T_{2, min}