A scale used to weigh fish consists of a spring hung from a support. The spring's equilibrium length is 10.0 cm. When a 4.0 kg f

A) 1153 N/m

We determine the spring constant using Hooke's law:

where

F represents the force exerted on the spring

k denotes the spring constant

x signifies the spring's displacement

In this case, a fish with mass m = 4.0 kg is hanging from the spring, and hence, the force applied is the fish's weight:

and the spring's displacement is:

thus the spring constant amounts to

B) 16.8 cm

For the second situation, a fish of mass

m = 8.0 kg

is attached to the spring. Hence, the force applied to the spring is

Thus, we can ascertain the spring's displacement:

Considering the spring's equilibrium length of

the new length of the spring becomes