Velocity Of An Object Accelerated By A Spring

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    Spring Velocity
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The problem involves determining the velocity of an object released from a compressed spring with a force constant k and initial compression x. The energy conservation principle is applied, equating the potential energy stored in the spring (E = 0.5kx^2) to the kinetic energy of the object (E = 0.5mv^2). The derived velocity formula is v = ((k/m)^(1/2)) * x, indicating that the object's velocity at the moment it leaves the spring depends on the spring constant, mass, and initial compression. An alternative approach using force and integration also leads to the same velocity expression. Understanding these relationships is crucial for solving similar physics problems involving springs and motion.
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Homework Statement


I'm pulling my hair out over this problem. A spring with a force constant of k is compressed x meters. An object of mass m is placed against the spring. The spring is then released. At what velocity is the object moving at the instant that is ceases to touch the spring?


Homework Equations


E=0.5kx^2

The Attempt at a Solution


I'm really unsure. All of my solutions don't seem realistic.
 
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Using Energy:
E=0.5kx^2=Kinetic Energy=0.5mv^2.

solve for v=((k/m)^1/2)*x
where x is initial displacement of spring.

Using F
F=-kx x is negative therefore
F=kx=ma

a=dv/dx*dx/dt = dv/dx*v
vdv=(kxdx)/m integrate
0.5v^2=0.5k/m x^2
v=((k/m)^1/2)*x
 
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