Mass on a Spring semi-submerged in a liquid

Thread starter MatinSAR
Start date Oct 18, 2022
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Liquid Mass Spring

In summary, the concept behind a mass on a spring semi-submerged in a liquid is to demonstrate the relationship between the displacement of an object in a liquid and the behavior of a spring attached to it. This is known as a damped harmonic oscillator, where the motion of the spring is influenced by the surrounding medium. Several factors, such as the mass, spring constant, liquid density, and oscillation amplitude, affect the oscillation of the system. The denser the liquid, the slower the oscillation will be, which can also impact the frequency and amplitude. The amplitude of the oscillation is directly related to the displacement of the object, increasing as it moves further away from equilibrium. This concept has various real-world applications, including modeling

Oct 18, 2022

MatinSAR

Homework Statement: According to the figure, the metal cylinder with mass M and volume V is connected to a fixed point from above by a spring with spring constant k and it floats inside a liquid of density p so that half of its height is inside the liquid. What weight should we put on it so that two-thirds of the height is inside the liquid?

Relevant Equations: Fluid mechanics.

Hi , Can someone tell me wether my answer is corrrect or false ?

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Oct 18, 2022

erobz

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Gold Member

I'm getting something different from you. ~~The difference is I define ##d'## in terms of ##d## and ##h## differently.~~ Actually, they work out equivalently. If you just eliminate ##Mg## via your first equation, and put ##L## in terms of ##d## and ##h## , I think we will get the same result.

My end result is purely a function of ##k,h,\rho,g,V##

Last edited: Oct 18, 2022

1. What is the purpose of a mass on a spring semi-submerged in a liquid?

The purpose of this setup is to demonstrate the principles of simple harmonic motion and how it is affected by the medium in which it is submerged. It also allows for the study of the relationship between the mass, spring constant, and the damping force of the liquid.

2. How does the liquid affect the motion of the mass on a spring?

The liquid provides a damping force on the mass, which reduces the amplitude of the oscillations and causes the system to eventually come to rest. This is due to the resistance of the liquid to the motion of the mass through it.

3. What factors affect the period of oscillation for a mass on a spring semi-submerged in a liquid?

The period of oscillation is affected by the mass of the object, the spring constant of the spring, and the damping force of the liquid. The period can also be affected by the depth of the liquid and the temperature of the liquid.

4. How is the period of oscillation affected by changing the mass on a spring semi-submerged in a liquid?

The period of oscillation is directly proportional to the square root of the mass. This means that as the mass increases, the period of oscillation also increases. This relationship can be seen in the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.

5. What is the significance of the spring constant in a mass on a spring semi-submerged in a liquid?

The spring constant determines the stiffness of the spring and how much force is required to stretch or compress it. In the context of this setup, the spring constant affects the period of oscillation and the amplitude of the oscillations. A higher spring constant will result in a shorter period and smaller amplitude, while a lower spring constant will result in a longer period and larger amplitude.