You attach one end of a spring with a force constant k = 833 N/m to a wall and t

Question

You attach one end of a spring with a force constant k = 833 N/m to a wall and the other end to a mass m = 2.52 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position xi = 5.16 cm from equilibrium and release it.

(a) Determine the potential energy stored in the spring before the block is released.
_______ J

(b) Determine the speed of the block as it passes through the equilibrium position.
_______ m/s

(c) Determine the speed of the block when it is at a position xi/4.

_______m/s

Explanation / Answer

(A) Spring PE = k x^2 / 2

= (833)(0.0516^2)/2

= 1.11 J

(B) at equilibrium. x = 0 so PE = 0

Applying energy conservation,

PEi + KEi = PEf + KEf

1.11 + 0 = 0 + 2.52 v^2 /2

v = 0.938 m/s

(C) PEi + KEi = PEf + KEf

1.11 + 0 = (1.11/16) + 2.52 v^2 /2

v = 0.908 m/s

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