2 hanging masses with springs, find spring constant

[Hyperfluxe]

Homework Statement

http://i.imgur.com/0gexJ.png

Homework Equations

F=kx (Hooke's Law), ƩFy=0

The Attempt at a Solution

I drew a free-body diagram for each block. For block A, I get the equilibrium equation: Fa = (10kg)(9.81ms^-2) = 98.1N = kx_a
x_a = 300mm-250mm = 50mm
k = 1.962kN/m

For block B I get the equilibrium equation of Fb = 98.1 - Wa = kx_b but it seems as I don't need this equation.

Is this correct, and if not, should I draw a "combined" FBD? If so, how? Thanks.

 

[Doc Al]

Is this correct, and if not, should I draw a "combined" FBD? If so, how?

Your equation is not obtained from analyzing block A alone, but by treating A and B as a combined object. So you answered your own question, even if you didn't realize it.

If you analyzed A alone, you'd have to include the force from each spring and only the weight of A.

 

[Hyperfluxe]

Oh I see. From drawing separate FBD's, I get the equations:
kx_a = kx_b + m_ag (block A)
kx_b = m_bg (block B)
Substitute kx_b back into the first equation to get kx_a = (m_a + m_b)g, where x_a = 300mm - 250mm, thus k = 1.962kN/m.

Is this correct? Thank you.

 

[Doc Al]

Perfectly correct. Note that your final equation is equivalent to what you did earlier.

 

[Hyperfluxe]

Thank you for you time and help =)