How Do You Determine the Spring Constant with Mass and Displacement?

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To determine the spring constant using Hooke's Law, the force (F) must be calculated as the weight of the mass suspended from the spring, which is the product of mass (m) and gravitational acceleration (g). In this case, with a mass of 1.10 kg, the force is F = 1.10 kg * 9.81 m/s², resulting in approximately 10.79 N. The displacement (x) of the spring is 6.90 cm, or 0.069 m. By rearranging Hooke's Law (F = kx), the spring constant (k) can be found using k = F/x. The correct calculation leads to a spring constant of about 156.5 N/m.
kbyws37
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The length of a spring increases by 6.90 cm from its relaxed length when a mass of 1.10 kg is suspended from the spring.What is the spring constant?

so I know that ultimately i use hooke's law which is
F=kx
but how would i figure out F if i only have the mass?

I can't do F=ma b/c i don't have the acceleration.
I'm confused
thanks
 
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Note that this spring will be vertical when the mass is suspended from it.
 
so will i assume that the force is the mass of the spring.
so
F=kx
(1.10) = k (6.90)

but it says I'm wrong
 
kbyws37 said:
so will i assume that the force is the mass of the spring.
so
F=kx
(1.10) = k (6.90)

but it says I'm wrong

The force can't equal the mass. Weight can be a force, and it equals m*g.
 
thanks!
i think i wasn't thinking straight :)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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