6. 0/1 points | Previous Answers OSColPhys2016 16.5.WA.039 My Notes An object wi

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6. 0/1 points | Previous Answers OSColPhys2016 16.5.WA.039 My Notes An object with a mass m = 79.6 g is attached to a spring with a force constant k 13.3 N m and released rom rest hen the spring is stretched 30 If it is oscillating on a horizontal frictionless surface, determine the velocity of the mass when it is halfway to the equilibrium position cm Is energy conserved for this mass-spring oscillating system? m/s Additional Materials Reading Submit Answer Save Progress Practice Another Version

Explanation / Answer

Using Energy Conservation between both positions, when it was released from rest and it was at halfway to the equilibrium position:

KEi + PEi = KEf + PEf

KEi = 0, Sicne released from rest

PEi = 0.5*k*x^2

PEf = 0.5*k*(x/2)^2

KEf = 0.5*m*V^2

0 + 0.5*k*x^2 = 0.5*m*V^2 + 0.5*k*(x/2)^2

m*V^2 = k*x^2 - k*x^2/4

m*V^2 = 3*k*x^2/4

V = sqrt (3*k*x^2/(4*m))

Using given values:

m = 79.6 gm = 79.6*10^-3 kg

x = 30.2 cm = 0.302 m

V = sqrt (3*13.3*0.302^2/(4*79.6*10^-3))

V = 3.38 m/sec

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