How do you determine the force constant of a spring when given the mass of an object being hung vertically, and the distance the spring stretches? What formula and logic do I need?
Sorry, I forgot to mention the question also gives the period of the oscillations. This confused me.. why would I need that piece of information. Don't I simply use F=-kx, then mg=-kx and solve for k??
It appears to be oscillating, not hanging still. You cant use kx if it is moving.
Okay.
But I don't understand where to go from here.
Do I use the formula T=2pi*sprt(m/k) ?
I'm just confused because it seems like I have an extra piece of info I should be using (in this case x).
To determine the force constant of a spring, you 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:
F = -kx
where F is the force exerted by the spring, k is the force constant (also known as the spring constant), and x is the displacement of the spring.
In the case of a spring hanging vertically with a mass attached, the force exerted by gravity on the mass is equal to the force exerted by the spring when it is stretched. So you can set up the equation:
mg = -kx
Here, m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), k is the force constant of the spring, and x is the distance the spring stretches.
To determine the force constant (k), rearrange the equation:
k = -mg / x
Now you have the formula to calculate the force constant of the spring. Simply substitute the given values of mass (m) and displacement (x) into the formula, making sure to account for any units that need to be converted or maintained.