Understanding Hooke's Law: Comparing Force Constants of Linearly Joined Springs

[Doctor Lee]

Q: How does the force constant of two springs hung linearly compare with the individual force constant??
What would be the equation that relates the total force constant, to the individual force constants, k1 and k2, of two springs joined together linearly??

A: The Total force constants is going to be k1 + k2??

 

[Andrew Mason]

Q: How does the force constant of two springs hung linearly compare with the individual force constant??
What would be the equation that relates the total force constant, to the individual force constants, k1 and k2, of two springs joined together linearly??

A: The Total force constants is going to be k1 + k2??

You should show some work.

Apply a force W = mg by hanging a mass m at the end of the bottom spring(2) (do it so the springs are stationary after stretching). The bottom end of spring 1 will have stretched x1 from its top end and spring 2 a further distance x2 from spring 2's top end.

Do a free body diagram for the forces on m. What are the upward forces? What are the downward forces on m? What do they sum to?

Do that and you should see what the answer is and why.

AM

 

[nasu]

Draw the springs and the forces. Write the appropriate relationship between forces and deformations.
If by "linearly" you mean something like one after another (series), k is not k1+k2.

 

[Doctor Lee]

Thanks a lot guys. I get it now.