To find the spring 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 equilibrium position.
The formula for Hooke's Law is given by:
F = -kx
where F is the force, k is the spring constant, and x is the displacement of the spring.
In this case, we are given the mass of the rock (m = 12 kg) and the displacement of the spring (x = 0.12 m).
Since the rock is at rest, the force exerted by the spring must be equal to the force due to gravity acting on the rock:
F_spring = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Therefore, we have:
-kx = m * g
Now we can solve for the spring constant (k). Rearranging the equation, we get:
k = -F_spring / x
Substituting the values, we have:
k = -(m * g) / x
Plugging in the given values, we have:
k = -(12 kg * 9.8 m/s^2) / 0.12 m
Calculating the expression, we find:
k โ -117.6 N/m
The negative sign signifies that the force exerted by the spring is in the opposite direction as the displacement. However, for simplicity, we usually consider the spring constant as a positive value representing the magnitude of the force exerted by the spring.