A block of mass m is attached to a sprind having a spring constant k. The other

Question

A block of mass m is attached to a sprind having a spring constant k. The other end of the spring is attached to a mount that is fixed to an incline (of angle theta = 30 degrees). The block has compressed the spring by an amount d relative to its unstretched length and is being held at rest in this position.

This is scenario that will be on my physics final. Please help me with possible questions and solutions that could be asked.

Thanks!

unstreched length Scenario 6: A block of mass m is attached to a spring having spring constant k. The other end of the spring is attached to a mount that is fixed to an incline (of angle =30°), as shown in the diagram. The block has compressed the spring by an amount d relative to its unstretched length and is being held at rest in this position.

Explanation / Answer

initially spring is compressed so it will have spring PE .

initial spring PE, SPEi = k d^2 /2

as block moves up,

this spring PE converts into gravitational PE and KE.

block will move up until its KE becomes zero again, (suppose it traveled distance x above)

Applying energy conservation,

initial enegy = final energy

kd^2/2 + 0 + 0 = k(x-d)^2 /2 + mgxsin@ + 0

kd^2 /2 = kx^2/2 - kxd + kd^2 /2 + mgxsin@

kx^2 - 2kxd + 2mgsin30 = 0

kx^2 - 2kxd + mg = 0

x = 2kd +- sqrt(4k^2d^2 - 4kmg) / 2k

x = d +- sqrt(d^2 - mg/k)

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