A 30.0 g object connected to a spring witha force constant of 35.0 N/m oscillate

Question

A 30.0 g object connected to a spring witha force constant of 35.0 N/m oscillates ona horizontal, frictionless surface with an amplitude of7.00 cm. (a) Find the total energy of the system.
1 mJ
(b) Find the speed of the object when the position is 1.25 cm.
2 m/s
(c) Find the kinetic energy when the position is 2.50 cm.
3 mJ
(d) Find the potential energy when the position is 2.50 cm.
4 mJ (a) Find the total energy of the system.
1 mJ
(b) Find the speed of the object when the position is 1.25 cm.
2 m/s
(c) Find the kinetic energy when the position is 2.50 cm.
3 mJ
(d) Find the potential energy when the position is 2.50 cm.
4 mJ

Explanation / Answer

mass m = 30 g = 0.03 kg force constant k = 35 N / m amplitude A = 7 cm = 0.07 m (a). total energy E = ( 1/ 2) k A ^ 2                              =0.08575 J                             = 85.75 mJ (b). speed of the object when the position is 1.25 cm is v = [ A ^ 2 - x ^ 2] where = angular frequency = [ k / m]             x = displacement = 1.25 cm = 0.0125 m (c). kinetic energy at position 2.5 cm is K = E - ( 1/2) k x ' ^ 2 where x ' = 2.5 cm = 0.025 m substitue values we get   K =0.0748125 J                                         = 74.8125 mJ (d). potential energy U = ( 1/ 2) k x ' ^ 2                                    = 0.0109375 J                                    = 10.9375 mJ

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