Calculating Spring Constant and Force for a Vertical Spring

[dg_5021]

A mass of 100g causes a vertical spring to stretch by 2.0 cm (a) Find the spring constant of the spring in N/M. (b) How much force will cause the spring to compress by 0.5 cm?

Can some help me? How do u do this? What formula do I have to use?

 

[Galileo]

If the mass is stationary, the net force acting on it is zero.
Gravity exerts a force on the mass downwards.
The spring exerts a force on the mass upwards.
Since the net force is zero, these must be equal.
The force of the spring is given by Hooke's law.

 

[dg_5021]

Hooke's law is : mg = k(y-yo)

so that would be: k= (mg)/(y-yo)
k= ((.100kg)(9.81m/s^2))/(.02m-yo)

What is yo?

 

[Galileo]

Here y0 would be the y-value when the string is not streched or compressed.
So that y-y0 measures the displacement from equilibrium of the spring.
In your problem y-y0 is 2.0 cm.