Janet wants to find the spring constant of a given spring, so she hangs the spring vertically and attaches a 0.42 kg mass to the spring's other end. If the spring stretches 4.0 cm from its equilibrium position, what is the spring constant?
To find the spring constant of a given spring, you can use Hooke's law equation. Hooke's law states that the force exerted by a spring is proportional to the displacement from its equilibrium position. The equation can be written as:
F = -kx
where F is the force applied to the spring, k is the spring constant, and x is the displacement from the equilibrium position.
In this scenario, Janet hangs the spring vertically and attaches a 0.42 kg mass to the spring's other end. The force applied to the spring is equal to the weight of the mass (mg), where g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, F = (0.42 kg)(9.8 m/s^2)
The displacement of the spring is given as 4.0 cm, which is equal to 0.04 m.
Now, we can rearrange the equation to solve for the spring constant:
k = -F / x
Substituting the values we have:
k = - ((0.42 kg)(9.8 m/s^2)) / (0.04 m)
Simplifying the equation:
k = - 4.116 N / m
Since the spring constant is usually defined as a positive value, we can write the spring constant as:
k = 4.116 N / m
Therefore, the spring constant of the given spring is approximately 4.116 N/m.