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a 3.5 kg block is accelerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the springs relaxation length.The block then travels over a horizontal floor with coefficient of kinetic friction 0.25. The friction force stops the block in a distance D = 7.8 m.
What is the increase in the thermal energy of the block+floor system?

  • physics -

    All of the stored potential energy of the spring, (1/2)kX^2, winds up as heat. X is the spring compression, which they don't tell you.

    You can compute the heat generated another way:
    Friction work = M*g*Uk*X = 66.9 J

  • physics -

    What is the original compression distance of the spring?
    Thought it would be zero but that isn't right.

  • physics -

    You can calculate the spring compression X from
    66.9 J = (1/2)kX^2, but you don't need it. 66.9 J is the thermal energy increease.

    They gave you more information than you need to answer the question

  • physics -

    (a) W=F*X
    W= u*Fn*X
    =>M*g*uk*X -> 4.3kg*0.26*7.8m

    (b) same as (a)

    (c) Us=0.5*k*x^2
    => (a)=0.5*640N/m*x^2
    figure out X from that

    [very late but someone might benefit from this]

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