Question

Fish are hung on a spring scale to determine their mass (most fishermen feel no obligation to report the mass truthfully).

What is the force constant (in N/m) of the spring in such a scale if it stretches 8.20 cm for a 14.0 kg load?

Answer 1

The force constant of the spring in the scale is 1673.17 N/m.

Step-by-step explanation:

The force constant of a spring can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The formula for Hooke's Law is:

F = kx

where F is the force exerted by the spring, k is the force constant, and x is the displacement of the spring.

To calculate the force constant, we can rearrange the formula:

k = F / x

Given that the spring stretches 8.20 cm and the load is 14.0 kg, we can convert the displacement to meters and the mass to Newtons:

x = 8.20 cm = 0.082 m (convert cm to m)

F = 14.0 kg * 9.8 m/s^2 = 137.2 N (convert kg to N)

Plugging these values into the formula for the force constant, we get:

k = 137.2 N / 0.082 m = 1673.17 N/m

Therefore, the force constant of the spring in such a scale is 1673.17 N/m.