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Block on Frictionless Incline

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A 12 kg block is released from rest on a 30 degree frictionless incline. Below is a block that can be compressed 2.0 cm by a force of 270 N. The block momentarily stops when it compresses the spring by 5.5 cm. How far does the block move down the incline from its rest position to this stopping point? What is the speed of the block just as it touches the spring?

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Solution Summary

This solution calculates the compression of a spring by a block moving down a frictionless incline.

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Formulas to use:
<br>Kinetic energy of block = 0.5 * m * (v ^ 2).
<br>Potential energy of block = m * g * h.
<br>Potential energy of spring = 0.5 * k * [(compression) ^ 2].
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<br>The spring constant, k = 270 N / 0.02 m = 13,500 N / m.
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<br>When the block starts to go down the slope it ...

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