A load of 46 N attached to a spring that is
hanging vertically stretches the spring 0.23 m.
What is the spring constant?
Answer in units of N/m.
The spring constant (k) can be found using Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position.
Hooke's Law can be expressed as:
F = -kx
Where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring.
In this case, the force exerted by the spring (F) is equal to the weight of the load (46 N). The displacement of the spring (x) is given as 0.23 m.
So, we can rewrite Hooke's Law equation as:
46 N = -k * 0.23 m
To find the spring constant, we need to rearrange the equation:
k = -46 N / 0.23 m
Now, let's calculate the spring constant:
k = -46 N / 0.23 m
k ≈ -200 N/m
Therefore, the spring constant is approximately -200 N/m. Note that since the spring stretches downward, the spring constant is negative.
To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. The equation can be written as:
F = k * x
Where:
F is the force exerted by the spring,
k is the spring constant,
x is the displacement from the equilibrium position.
In this case, we are given the force (46 N) and the displacement (0.23 m), so we can rearrange the equation to solve for k:
k = F / x
Now, we can substitute the given values into the equation:
k = 46 N / 0.23 m
Calculating this, we find that the spring constant is approximately 200 N/m.