A block of a mass m is initially moving to the right on a horizontal frictionles

Question

A block of a mass m is initially moving to the right on a horizontal frictionless surface at a speed. Then compresses a spring of spring is constant. At the instent when the KE of the block equal to PE of spring, the spring is compressed a distance of ? A block of a mass m is initially moving to the right on a horizontal frictionless surface at a speed. Then compresses a spring of spring is constant. At the instent when the KE of the block equal to PE of spring, the spring is compressed a distance of ?

Explanation / Answer

Given

let mass of object is m , moving with a velocity v on a frictionless surface

then the kinetic energy of the block is k.e = 0.5*m*v^2

and compresses the spring say if it is fixed at one end with a force constant k

as the block compresses the spring a restroring force acts in the opposite direction to the motion of the block and potential energy will be developed in the spring

so that k.e block = p.e of spring

o.5*mv^2 = 0.5*k*x^2

x ^2 = m*v^2/k

x = sqrt(mv^2/k)

so the block can compress the spring through a distance of x = sqrt(mv^2/k)

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