# How to Approach Solving a Variable-Mass System with a Falling Drip?

• Michael_0039
In summary, a variable-mass system is any physical system where the mass changes over time. The "falling drip" experiment is a commonly used demonstration for studying variable-mass systems, where a droplet of liquid is dropped onto a scale and the change in mass is observed. The mass of the system decreases as the droplet falls due to the loss of mass from evaporation, and gains kinetic energy which is then converted into heat upon impact. The results of the experiment can be affected by factors such as the type of liquid, height, temperature, humidity, and scale sensitivity. The "falling drip" experiment has practical applications in fields such as fluid mechanics, meteorology, and chemistry, and can also be used in educational settings
Michael_0039
Homework Statement
Falling drip surrounding by water vapor. For t=0, initial mass=M and Uo=0. Prove the following equation...
Relevant Equations
nil
S(t)=

Hi all!

Μy attempt to solve it:

I'm stuck here. An opinion ?

Thanks.

Edit last line:

S=t (ud-(gt/2)-ud(m/M))

* I dont't know what happened there

I made a new attempt to solve it, and reading more for those kind of problems. I made some errors at the previous posts, so this is my attempt now:

I'm on the right track ?

Thanks.

Note:

This is the description:

From: Fundamental University Fhysics Volume 1 (Mechanics), Marcelo Alonso & Edwart J. Finn

Last edited:

## 1. What is a variable-mass system?

A variable-mass system is a physical system where the mass of the object changes during the course of its motion. This can occur due to the addition or removal of mass, or due to a change in the density of the object.

## 2. How does a falling drip demonstrate a variable-mass system?

A falling drip is an example of a variable-mass system because as it falls, it continuously loses mass through evaporation. This change in mass affects the acceleration and velocity of the drip as it falls.

## 3. What are the forces acting on a falling drip in a variable-mass system?

The forces acting on a falling drip in a variable-mass system include gravity, air resistance, and surface tension. Gravity pulls the drip downward, air resistance slows it down, and surface tension helps to maintain its shape as it falls.

## 4. How does the rate of evaporation affect the motion of a falling drip?

The rate of evaporation plays a significant role in the motion of a falling drip in a variable-mass system. As the drip loses mass, its acceleration and velocity decrease. This is because there is less mass for the forces of gravity and air resistance to act on.

## 5. Can a falling drip ever have constant velocity in a variable-mass system?

No, a falling drip cannot have constant velocity in a variable-mass system. This is because as the drip falls, it continuously loses mass through evaporation, causing its acceleration and velocity to change over time. It will eventually reach a terminal velocity where the force of air resistance is equal to the force of gravity, but this velocity is not constant.

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