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

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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 angle with the base. A pulley is attached to the structure’s apex. Three objects (masses m, 2m, and M) are connected by two cords (tensions T1 and T2) and arranged as follows

Masses 2m and m are, respectively, attached to the left and right ends of cord T1 such that mass m is nearest to the structure’s apex.

Masses m and M are, respectively, attached to the left and right ends of cord T2 such that cord T2 passes over the pulley and mass M hangs 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 .)

mass M =

tension T1 =

tension T2 =

(b)

If the value of M is 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 .)

acceleration a =

tension T1 =

tension T2 =

(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 .)

Mmax =

Mmin =

(d)

Compare the values of T2 when M has its minimum and maximum values. (Use the following as necessary: s, , m, and g.)

T2, max − T2, min =

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