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A block of mass m = 650g is released from rest and slides down a frictionless track of height h = 71.3 cm. At the bottom of the track the block slides freely along a horizontal table until it hits a spring attached to a heavy, immovable wall. The spring compressed by 2.65 cm at the maximum compression. What is the value of the spring constant k?

Added Fri, 26 Jun '15

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block slides from a height of 71.3 cm and come to horizontal level where it hits the spring.

so taking horizontal as ground (zero potential energy)

so at height 71.3 cm its potential energy is

mgh = 0.65(kg)*9.8 (m/s2)*0.713 (m)

=4.542 J

and this potential energy becomes the kinetic energy at the ground/horizontal level and when the block compresses the spring at maximum then its velocity is zero and all of its kinetic eenergy has transfered to spring.

and spring energy = 0.5kx2

where k is spring constant

so 4.542 = 0.5k(0.0265)2

K = 1.29355 *104N/m

Added Fri, 26 Jun '15

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