"A spring is suspended above a tank of water with its lower end in the water. An object with a mass of 0.35 kg is attached to the bottom of the spring, causing it to stretch 0.013 meters (the object is fully immersed in water). The spring has a spring constant of 200 N/m. Find the density of the object."

I know the restoring force of the spring is 2.6 N, so the applied force of the object on the spring is -2.6 N. I know the formula for density is ρ = m/v, and I know the formula for buoyancy is Fb = (volume of submerged object)(density of fluid)(force of gravity).

Question

"A spring is suspended above a tank of water with its lower end in the water. An object with a mass of 0.35 kg is attached to the bottom of the spring, causing it to stretch 0.013 meters (the object is fully immersed in water). The spring has a spring constant of 200 N/m. Find the density of the object."

I know the restoring force of the spring is 2.6 N, so the applied force of the object on the spring is -2.6 N. I know the formula for density is ρ = m/v, and I know the formula for buoyancy is Fb = (volume of submerged object)(density of fluid)(force of gravity).

anonymous · Answer

I'm not sure how to proceed from here. If someone could walk me through it, I'd really appreciate it.

irishboy123 · Answer

step by step process:

archimedes principle: a body in fluid (floating or submerged) is bouyed up by a force equal to the weight of the displaced ***fluid***.

so calc how much the spring ought to extend but for the water, using Hook F = kx = mg.  

calc the *effective weight* from the actual extension in the water, ie net of upward force

the difference is the "bouyant force" = volume water displaced * density of water * g, and water specific density = 1, 

this gives you volume of water displaced.

and that is the volume of **object**.  you know object's mass.

anonymous · Answer

Okay, thank you so much, I really appreciate it!