Suppose I have a spring. I add a mass (m = 1.0 kg) and it is displaced by 15 cm. What is the spring constant k in units of (N/m)?
To find the spring constant, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. It can be expressed as:
F = -kx
where F is the force applied to the spring (in Newtons), k is the spring constant (in N/m), and x is the displacement from the equilibrium position (in meters).
In this case, you know the mass (m = 1.0 kg) and the displacement (x = 15 cm = 0.15 m). The force applied to the spring can be calculated using Newton's second law:
F = ma
where a is the acceleration, and in this case, it is equal to the gravitational acceleration, 9.81 m/s^2.
F = (1.0 kg) * (9.81 m/s^2)
F = 9.81 N
Now, rearrange Hooke's Law to solve for k:
k = -F/x
Substituting the values:
k = -(9.81 N) / (0.15 m)
k ≈ -65.4 N/m
Note that the negative sign signifies that the force exerted by the spring is in the opposite direction of the displacement. Thus, the spring constant is approximately 65.4 N/m.