A spring is stretched by 0.72 m from its orginal length with an external force of 10.5. What is the spring constant, k, of the spring?
F = k x
10.5 = k (.72
k = 10.5 N/.72 m
To find the spring constant of the spring, we can use 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. Mathematically, it can be expressed as:
F = -kx
Where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
In this case, we have the force (F) as 10.5 N and the displacement (x) as 0.72 m. Substituting these values into Hooke's Law equation, we can solve for the spring constant (k).
10.5 N = -k * 0.72 m
To solve for k, we rearrange the equation:
k = -10.5 N / 0.72 m
k ≈ -14.58 N/m
Therefore, the spring constant of the given spring is approximately -14.58 N/m. The negative sign indicates that the spring is being stretched (opposite to its natural position).