Double Pulley Systems/Complex Pulley System Problems

[mk8993]

Hey..
This is a question I received as part of my homework

Your great grandmother gave you an antique scale that her great grandmother gave to her. It consists of a square platform mounted on 4 identical
springs. When you step on the platform, you compress the springs, causing
the platform to descend slightly, A needle indicates by how many centimeters you have descended. Unfortunately the conversion to useful units (like
stone, or poundals) has been lost. However, your great-grandmother also
gave you an extra spring, and on its label it says that the spring constant
is 1.5 × 10
4N/m. When you get on the scale you cause the platform to
descend by 0.98cm. What is your mass?

I have no idea how to go about solving this problem or what equations to use but, do I have to use the principles of conservation of energy for this? Equating gravitational to spring?

Thanks!

 

[Sajib]

Hi mk8993 ,if I'm not wrong then this is d solution:
When you got on the platform you applies a force(=your weight) on it which causes all the 4 springs to descend.Suppose your weight is W.
From spring const. eqn. F=kx,since all the 4 springs descend through the same distance then the force is distributed into four(number of springs) parts according to their spring constants i.e here, x being constant the more the value of k the more F will be.Here all springs have same value of k so,for one spring W/4=1.5*10^4*0.98*10^-2⇔W=588N
so your mass is =588/9.8=60kg[assuming g=9.8m/s^2]