block and spring physics?

A 5 kg block is placed near the top of a frictionless ramp, which makes an angle of 30o degrees to the horizontal. A distance d = 1.3 m away from the block is an unstretched spring with k = 3 × 103 N/m. The block slides down the ramp and compresses the spring. Find the maximum compression of the spring.

max

I got .147 but thats an incorrect answer.

1 Answer

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  • Jim
    Lv 7
    4 years ago
    Favorite Answer

    There are two ways of interpreting the words: "A distance d = 1.3 m aways from the block..."

    1) this "d" distance could be measured along the ramp (parallel to ramp) to spring which would give ANS-1

    2) this "d" distance could be measured horizontally from block to spring which would give ANS-2

    {diagrams usually solve such interpretive problems :>}

    KE of block transferred to spring = mgh = 5(9.8)(1.3)(sin 30°) = 31.85 J

    max SPE = 31.85 = 1/2kx² = (0.5)(3000)x² = 1500x²

    x² = 31.85/3000 = 0.02123333

    x = 0.146 m ANS-1

    KE of block transferred to spring = mgh = 5(9.8)(1.3)(tan 30°) = 36.78 J

    max SPE = 36.78 = 1500x²

    x² = 36.78/1500 = 0.02452

    x = 0.157 m ANS-2

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