To find the spring's force constant, 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 natural length.
First, we need to find the displacement of the spring. The spring is stretched from its natural length of 2m to a length of 5m.
Displacement = Final length - Initial length
Displacement = 5m - 2m
Displacement = 3m
Now, we can calculate the force constant using Hooke's Law formula:
Work = (1/2) * k * x^2
Where:
Work is the amount of work done (1800 J),
k is the force constant (what we are trying to find),
x is the displacement (3m).
Rearranging the formula for k, we get:
k = (2 * Work) / (x^2)
Plugging in the values, we have:
k = (2 * 1800 J) / (3m)^2
k = 3600 J / 9m^2
k = 400 J/m^2
Therefore, the spring's force constant is 400 J/m^2.