Final answer:
To find the force constant of a spring, you can use Hooke's Law. In this case, the force constant is approximately 4780 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 or stretch of the spring from its equilibrium position. The formula to calculate the force constant (k) is:
k = F / x
Where F is the force applied to the spring and x is the displacement or stretch of the spring. In this case, we are given the displacement of the spring (9.00 cm) and the work done (19.0 J).
The work done on a spring is given by the formula: W = (1/2) * k * x^2
By rearranging this formula and substituting the given values, we can solve for the force constant:
k = 2 * W / x^2
Plugging in the values, we have:
k = 2 * 19.0 J / (0.09 m)^2
After solving this equation, the force constant of the spring is approximately 4780 N/m.