consider a spring with mass m=1g in Earth\'s gravitational feild (ie on Eath). S

Question

consider a spring with mass m=1g in Earth's gravitational feild (ie on Eath). Suppose that when the spring has an end to end length of x, the spring exerts a force given by F(x)=-k(x-x0), when k=10N/cm is the spring constant and x0=1.0cm is the spring's equilibrium lenth. Note that F<0 when x>x0 is a restoring force pulling in, while f>0 when x<x0 is a restoring force pushing out. Suppose that the spring also has a well-defined temperature T.

A) what variables are necesary to specify the therodynamic equilibrium state of the spring?

B) suppose that tin the process of interest the following happens

THE SPRING COMPRESSED FROM X1=1.0CM TO X2 =0.5CM

the spring is lifted a height dh=am

10J of heat are transferred into the spring

assume that durring the compression the applied force is equal to the spring restoring force and that the spring is lifted in the presence of a uniform gravitational field with G = 9.80 m/s2

part 1: determine the work done on the spring by compressing it

part 2 : determine the work done by the spring durring the compression

part 3: determine the energy transfer tot he spring by lifting it

part 4: determin the total change in the spring's thermodynamic energy from this preocess.

Explanation / Answer

mgh = k(x2-x1)

1) work done is 1/2 k(x2^2-x1^2)

Work done is W = 0.5 (0.01^2-0.005^2)*1000

W = 75*10^-3 J

2) W = 75*10^-3 J

3) Energy = mg (h2-h1) = 10^-3*9.8*0.005 = 0.049*10^-3 N

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