# Working with Force and Mass

In summary, the conversation discusses a problem from the book Fundamentals of Engineering Thermodynamic and the asker is looking for help understanding how to solve for z in a cylinder equation. The conversation also mentions using calculus to solve for the mass of the cylinder and suggests thinking of the cylinder as composed of disks of thickness dz and integrating to find the total mass.

Hello All,

This problem comes from the book: Fundamentals of Engineering Thermodynamic.

I actually have the answer attached, but I am looking for some help understanding it.

From a non-calculus perspective, I can put the equation into this form with the position (z) left as a variable.

F = [ 7800 - 360*(z/2) ] * [$$\pi$$*(0.25^2)] * [9.78]

But I am having real trouble understanding how to solve for z.

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From a non-calculus perspective, I can put the equation into this form with the position (z) left as a variable.

F = [ 7800 - 360*(z/2) ] * [$$\pi$$*(0.25^2)] * [9.78]

But I am having real trouble understanding how to solve for z.
What do you mean 'from a non-calculus perspective'? You need calculus to solve for the mass of the cylinder. You're not solving for z, z is the position along the cylinder.

Hint: Think of the cylinder as composed of disks of thickness dz. What's the mass of each disk? Integrate to get the total mass of the cylinder.

## 1. What is force and mass?

Force is a physical quantity that can be defined as the push or pull applied on an object. It is measured in units of Newtons (N). Mass, on the other hand, is a measure of the amount of matter in an object and is measured in kilograms (kg).

## 2. How are force and mass related?

According to Newton's second law of motion, force is directly proportional to mass and acceleration. This means that the greater the mass of an object, the greater the force needed to accelerate it. In mathematical terms, force = mass x acceleration (F = ma).

## 3. What are some examples of forces?

Some common examples of forces include gravity, friction, tension, and applied forces such as pushing or pulling an object. These forces can either be contact forces (directly touching the object) or non-contact forces (acting from a distance).

## 4. How do we measure force and mass?

Force can be measured using a device called a force gauge, which measures the amount of force applied to it. Mass can be measured using a balance or scale, which compares the object's mass to a known mass. Both force and mass can also be measured indirectly using equations and other scientific methods.

## 5. How are force and mass used in everyday life?

Force and mass are used in many aspects of our daily lives. For example, we use force when we push a door open or pull a cart. Mass is used when we weigh ourselves or measure ingredients for cooking. Understanding force and mass also helps us understand the mechanics of how objects move and interact with each other.