A fisherman's scale stretches 3.5 cm when a 2.1 kg fish hangs from it. What is the spring stiffness constant?
k= force/distance. I would express it in N/meter
k= 2.1*g/.035 N/m
To find the spring stiffness constant, also known as the spring constant or k, you can use Hooke's Law. Hooke's Law 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 spring stiffness constant, and
x is the displacement of the spring from its equilibrium position.
In this case, we are given the displacement (x) of the fisherman's scale when a 2.1 kg fish hangs from it, which is 3.5 cm. We need to find the spring constant (k).
We can rearrange the formula to solve for k:
k = -F / x
Now, we need to calculate the force (F) exerted by the spring. The force can be calculated using the weight of the fish, which is the mass (m) of the fish multiplied by the acceleration due to gravity (g). Assuming the acceleration due to gravity is 9.8 m/s^2:
F = m * g
F = 2.1 kg * 9.8 m/s^2
F ≈ 20.58 N
Now, substitute the values into the formula for k:
k = -F / x
k = -(20.58 N) / (0.035 m)
k ≈ -588 N/m
So, the spring stiffness constant of the fisherman's scale is approximately -588 N/m.