A step-by-step solution please. Thank you. A work W o is required to stretch a c

Question

A step-by-step solution please. Thank you. A work Wo is required to stretch a certainspring 2 cm from its equilibrium position.
a) How much work is required to stretch the spring 1 cm fromequilibrium? b) Suppose the spring is already stretched 2 cm fromequilibrium. How much additional work is required to stretch it to3 cm from equilibrium? A step-by-step solution please. Thank you. A work Wo is required to stretch a certainspring 2 cm from its equilibrium position.
a) How much work is required to stretch the spring 1 cm fromequilibrium? b) Suppose the spring is already stretched 2 cm fromequilibrium. How much additional work is required to stretch it to3 cm from equilibrium?

Explanation / Answer

          Given that the elaongation of spring is x = 0.02m -------------------------------------------------------------       The work done is Wo =(1/2)Kx2                                     K= 2Wo / x2                                          (a) The work done required to stretch d =0.01mis                              W1=  (1/2)Kd2                                          = (1/2)[ 2Wo / x2 ]d2                                      =Wo*(d /x )2                                         = Wo/4 (b) The work done required to stretch d =0.03m is                              W3=  (1/2)Kd2                                          = (1/2)[ 2Wo / x2 ]d2                                      =Wo*(d /x )2                                         = 2.25Wo        Then the additional workdone is = W3 - Wo                                                          = 1.25 Wo                                          =Wo*(d /x )2                                         = Wo/4 (b) The work done required to stretch d =0.03m is                              W3=  (1/2)Kd2                                          = (1/2)[ 2Wo / x2 ]d2                                      =Wo*(d /x )2                                         = 2.25Wo        Then the additional workdone is = W3 - Wo                                                          = 1.25 Wo                                  W3=  (1/2)Kd2                                          = (1/2)[ 2Wo / x2 ]d2                                      =Wo*(d /x )2                                         = 2.25Wo        Then the additional workdone is = W3 - Wo                                                          = 1.25 Wo                                      =Wo*(d /x )2                                         = 2.25Wo        Then the additional workdone is = W3 - Wo                                                          = 1.25 Wo

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