A 0.59 kg object connected to a light spring with a force constant of 21.2 N/m o

Question

A 0.59 kg object connected to a light spring with a force constant of 21.2 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest.
(a) Determine the maximum speed of the object.
.
Your response differs from the correct answer by more than 10%. Double check your calculations. cm/s
(b) Determine the speed of the object when the spring is compressed 1.5 cm.
cm/s
(c) Determine the speed of the object when the spring is stretched 1.5 cm.
cm/s
(d) For what value of x does the speed equal one-half the maximum speed?

Explanation / Answer

a.) energy stored initially= 1/2kx^2 =1/2*21.2* (.04)^2 at max velocity initial energy= K.E= 1/2 m v^2 21.2*(0.4)^2= 0.59*(v)^2 v=23.98 cm/sec b.) energy initially= K.E + energy stored 21.2*(4)^2 = 0.59*v^2 + 21.2*1.5^2 v= 22.23 cm/sec c.) same as b.) =22.23cm/sec d.) energy initially= K.E + energy stored 3*21.2*4 = 21.2*x^2 x= 3.36 cm

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