A box of mass m is pressed against (but is not attached to) an ideal spring of f

Question

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligee mass, compressing the spring a distance x. After it is released ire box slides up a frictionless incline as shown m the figure and eventually stops If we repeat this experiment but instead use a spring having force constant 2k Just as it moves free of the spring the speed of the box will be Squareroot 2 times as grout as before the box will go up the Incline twice as high so before just as it moves free of the spring. the Kinetic energy of the box will be twice as grouts as before All of the above choices are correct None of the above choices is correct

Explanation / Answer

using law of conservation of energy

energy stored in spring = energy gained by the box,when it was leaving the spring = Energy at the heighest point

0.5*k*x^2 = 0.5*m*v^2 = m*g*h

0.5*k*x^2 = 0.5*m*v^2

v = sqrt(k/m)*x

if spring constant is 2k

0.5*2*k*x^2 = 0.5*m*v^2
v = sqrt(k/m)*x*sqrt(2)

speed increases by sqrt(2) times

0.5*k*x^2 = m*g*h

h = k*x^2/(2*m*g)

when the spring constant is 2k

0.5*2*k*x^2 = m*g*h

h = 2* [k*x^2/(2*m*g)]

so the box willgo up the incline twice as high as before

when the spring constant is k KE1 = 0.5*m*v^2

when the spring constant is 2k,KE2 = 0.5*m*2*v^2 = 2*KE1

So KE increases by twice

so the correct option is All of the above choices are correct

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