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As shown in the figure, a block of mass m is at rest on a ramp inclined 30∘ to the horizontal, and another block of mass 2 3 m at rest on a ramp inclined 60∘. Two blocks are connected by a light, inextensible cord, and the cord passes on a light, frictionless pulley. The other end of the block of mass m is connected to an spring with a force constant k. The spring is neither compressed nor extended. (a) What is the maximum distance the blocks will move when the inclines are frictionless? Express the answer in terms of m, k, and the gravitational acceleration g. (b) Repeat (a) when the coefficients of kinetic friction are 1/3 for both blocks. (c) What is the change in the internal energy of the system composed of the blocks, the inclines, and the spring?

As shown in the figure, a block of mass m is at rest on a ramp inclined 30∘ to the horizontal, and another block of mass 2 3 m at rest on a ramp inclined 60∘. Two blocks are connected by a light, inextensible cord, and the cord passes on a light, frictionless pulley. The other end of the block of mass m is connected to an spring with a force constant k. The spring is neither compressed nor extended. (a) What is the maximum distance the blocks will move when the inclines are frictionless? Express the answer in terms of m, k, and the gravitational acceleration g. (b) Repeat (a) when the coefficients of kinetic friction are 1/3 for both blocks. (c) What is the change in the internal energy of the system composed of the blocks, the inclines, and the spring?

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  1. [25 pts.] As shown in the figure, a block of mass m is at rest on a ramp inclined 30 ∘ to the horizontal, and another block of mass 2 3 m at rest on a ramp inclined 60 ∘ . Two blocks are connected by a light, inextensible cord, and the cord passes on a light, frictionless pulley. The other end of the block of mass m is connected to an spring with a force constant k . The spring is neither compressed nor extended. (a) What is the maximum distance the blocks will move when the inclines are frictionless? Express the answer in terms of m , k , and the gravitational acceleration g . (b) Repeat (a) when the coefficients of kinetic friction are 1 / 3 for both blocks. (c) What is the change in the internal energy of the system composed of the blocks, the inclines, and the spring?

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