Answer :
The weight is 200 N of a fish that would stretch the spring by 31.0 cm.
We can use Hooke's Law to solve this problem. Hooke's Law states that the force (F) needed to stretch a spring is proportional to the amount of stretch (x). The mathematical expression for Hooke's Law is:
F = kx
where k is the spring constant.
We can rearrange this equation to solve for k:
k = F/x
We can substitute the given values for F (135 N) and x (21 cm) to calculate the spring constant:
k = 135 N/21 cm
k = 6.43 N/cm
Now that we know the spring constant, we can use Hooke's Law to calculate the force needed to stretch the spring by 31 cm.
F = kx
F = 6.43 N/cm x 31 cm
F = 199.33 N
Finally, we can use the force to calculate the weight of a fish that would stretch the spring by 31 cm. Since weight is equal to force multiplied by the acceleration due to gravity (g = 9.8 m/s2), we can use the following equation:
Weight = F x g
Weight = 199.33 N x 9.8 m
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