A 12 kg rock sits quietly on a spring, having displaced the end of the spring 0.12 m. What is the spring constant?
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 ≈ -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.