# Spring constant question

#### John O' Meara

I just have no idea how to approach this simple problem.
When a 300g mass is hung from the end of a vertical spring, the spring's length is 40 cm. With 500g hanging from it, its length is 50cm. What is the spring constant of the spring (N/m)?

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#### Integral

Staff Emeritus
Gold Member
How much did the length of the spring change?
How much did the mass change?

What are the units of the spring constant?

#### geosonel

John O' Meara said:
I just have no idea how to approach this simple problem.
When a 300g mass is hung from the end of a vertical spring, the spring's length is 40 cm. With 500g hanging from it, its length is 50cm. What is the spring constant of the spring (N/m)?
Hooke's Law relating spring force F to spring constant k, resting length x0, and stretched length x:

$$F \, = \, -k\{x - x_0\}$$

2 equations in 2 unknowns:

$$\mbox{ (0.300 kg)(9.8 m/sec^2) } \ = \ -k \left \{ \mbox{ (0.40 m) } \, - \, x_0 \right \}$$

$$\mbox{ (0.500 kg)(9.8 m/sec^2) } \ = \ -k \left \{ \mbox{ (0.50 m) } \, - \, x_0 \right \}$$

solve for k.

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