When the end of a spring is displaced from its rest position by 8.5 cm, the spring’s restoring force has a magnitude of 4.4 N. What is the spring constant? in N/m??
Review the definition of the spring constant and the answer should be obvious.
To calculate the spring constant, we can use Hooke's Law, which states that the restoring force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, it can be expressed as:
F = -kx
Where:
F is the restoring force,
k is the spring constant,
x is the displacement from the equilibrium position.
In this case, we are given that the displaced distance is 8.5 cm (0.085 m) and the magnitude of the restoring force is 4.4 N.
Rearranging the equation, we have:
k = -F / x
Plugging in the given values:
k = -4.4 N / 0.085 m
Now, let's calculate the spring constant.
k = -4.4 / 0.085 ≈ -51.8 N/m
Therefore, the spring constant is approximately 51.8 N/m.