Final answer:
The work required to compress the spring another 1 in is 0.01324 Btu.
Step-by-step explanation:
To determine the work required to compress the spring, we can use the formula:
Work = (1/2) k x^2
Where k is the spring constant and x is the compression distance.
In this case, the spring constant is given as 250 lbf/in, which can be converted to N/m by using the conversion factor 1 lbf/in = 175.126836 N/m.
The force constant of the spring in N/m is therefore 250 lbf/in x 175.126836 N/m = 43,781.709 N/m.
The compression distance x is given as 1 in, which can be converted to meters by using the conversion factor 1 in = 0.0254 m.
Plugging in the values, we have:
Work = (1/2) (43,781.709 N/m) (0.0254 m)^2
Work = 13.97883 J
Finally, we can convert the work from joules to Btu using the conversion factor 1 J = 0.000947817 Btu.
Therefore, the work required to compress the spring another 1 in is 13.97883 J x 0.000947817 Btu/J = 0.01324 Btu.