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An block of mass m , starting from rest, slides down an inclined plane of length L and angle θ with respect to the horizontal. The coefficient of kinetic friction between the block and the inclined surface is μ1 . At the bottom of the incline, the block slides along a horizontal and rough surface with a coefficient of kinetic friction μ2. The goal of this problem is to find out how far the block slides along the rough surface.

1)after leaving the incline, the block slides along the rough surface until it comes to rest. How far has it traveled? Express your answer in terms of g, m, L, θ, μ1, and μ2 (enter theta for θ, mu_1 for μ1, and mu_2 for μ2).

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  1. (m*g*sin(theta)*L-mu_1*m*g*cos(theta)*L)/(mu_2*m*g)

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  2. (a) What is the work done by the friction force on the block while it is sliding down the inclined plane? Express your answer in terms of g, m, L, θ, μ1, and μ2 (enter theta for θ, mu_1 for μ1, and mu_2 for μ2).

    Wf=

    (b) What is the work done by the gravitational force on the block while it is sliding down the inclined plane? Express your answer in terms of g, m, L, θ, μ1, and μ2 (enter theta for θ, mu_1 for μ1, and mu_2 for μ2).

    Wg=

    (c) What is the kinetic energy of the block just at the bottom of the inclined plane? Express your answer in terms of g, m, L, θ, μ1, and μ2 (enter theta for θ, mu_1 for μ1, and mu_2 for μ2).

    K=

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  3. Wf= -mu_1*m*g*cos(theta)*L

    Wg= m*g*L*sin(theta)

    K= m*g*sin(theta)*L-mu_1*m*g*cos(theta)*L

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