A certain spring stores 10.0J of potential energy when it isstretched by 2.00cm

Question

A certain spring stores 10.0J of potential energy when it isstretched by 2.00cm from its equilibrium position. How much potential energy would the spring store if it werestretched an additional 2.00cm? How much potential energy would it store if it were compressedby 2.00cm from its equilibrium position? How far from the equilibrium position would you have tostretch the string to store 20.0J of potential energy? What is the force constant of this spring? A certain spring stores 10.0J of potential energy when it isstretched by 2.00cm from its equilibrium position. How much potential energy would the spring store if it werestretched an additional 2.00cm? How much potential energy would it store if it were compressedby 2.00cm from its equilibrium position? How far from the equilibrium position would you have tostretch the string to store 20.0J of potential energy? What is the force constant of this spring?

Explanation / Answer

Sreachness x = 2 cm = 0.02 m Potential energy P = 10 J we know P = ( 1/ 2) k x ^ 2 from this spring constant k = 2P / x ^ 2                                         = 50000 N / m Energy stored if it were streached an additional 2 cm is P ' = ( 1/ 2) k x ' ^ 2   where x ' = 4 cm = 0.04m                                                                                         = 40 J (b).    potential energy would it store ifit were compressed by 2.00cm from its equilibrium position = ( 1/2) k x ^ 2                                                                                                                                                     = 10 J (c). Potential energy P " = 20 J we know P " = ( 1/ 2) k x " ^ 2               x " = [ 2P " / k ]                    = 0.0282 m = 2.82 cm

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