What is the Effective Spring Constant for a System in Series?

[student 1]

Homework Statement

A light spring with spring constant _k1 hangs from a second light spring, which has spring constant _K2. An object of mass m hangs at rest from the lower end of the second spring. A. Find the total extension distance of the pair of springs. B. Find the effective spring constant of the pair of springs as a system. We describe these springs as in a series.

Homework Equations

Hooke's Law K=mg/d

The Attempt at a Solution

Where should I start? Would just combine the k's I do not know where to go with this problem?

 

[EngageEngage]

You should draw out the force diagram and get the force equations from them. You should get 2 equations and they are all you need

 

[cryptoguy]

I'd actually do part B first. They are asking you for k, the spring constant for both springs. If the springs are in series, as a rule, $$k = \frac{1}{k1} + \frac{1}{k2}$$. Notice that the resulting k value will be less then both k1 and k2, meaning that the resultant spring will oscillate more then k1 or k2.

Now that you know the k value, you can plug that into hooke's law to get the distance

 

[student 1]

So my D=(mg)(K1K2)/(K1+K2)

 

[alphysicist]

Hi student 1,

So my D=(mg)(K1K2)/(K1+K2)

No, that's not quite right. Notice that it does not have the right units (meters on the left, N$^2$/m on the right).

 

[cryptoguy]

blaaaah i forgot a very important part in the equation i gave you: $$\frac{1}{k} = \frac{1}{k1} +\frac{1}{k2}$$. My apologies, student1