Education

# Mechanical work and its application in practice

Mechanical work is one of the basic scalars in physics. As part of the standard school curriculum, it is studied in the seventh grade in the mechanics section. Mechanical work is one of the ways to change the internal energy of a body or substance (for example, gas or liquid) along with such forms of heat transfer as heat conduction, convection and radiation, which are studied in the section of thermal phenomena.

## What is work in physics – definition and formula

Mechanical work is the amount of energy that must be expended in order for the body to begin a uniformly slowing motion and travel a certain distance.

Definition of mechanical work in physics

In physics, mechanical work is the product of a force that acts on a body, for the distance that it travels under its influence:

A = F * S

In more complex cases, a third quantity appears in the formula – the cosine of the angle at which the vectors of motion and applied force are located to each other. You can find its value using the formula:

A = F * S * cosA

## How is work measured?

The physical units in which mechanical work is expressed are Joules.

### Mechanical work unit

There are different methods for its practical measurement, which depend on the type of movement produced. In this case, the value of the force in Newtons and the distance in meters are substituted into the formula of work. The angle between vectors is measured in mathematical units – degrees.

### Frictional force work

Under the conditions existing on Earth, any moving body is influenced by a friction force that slows down its movement. Most often this is the friction of the surface on which the object is moving. This is obvious from the fact that when a constant force is applied to a body, its speed will be variable.

Therefore, there must be another force opposing it – and this is the force of friction. If the coordinate system is selected in the direction of movement of the body, then its numerical value will be negative.

### Positive and negative work

The numerical value of the work that the force does can become negative if its vector is opposite to the velocity vector.

In other words, the force can not only give the body speed for the movement, but also prevent the movement already being made. In this case, it will be called opposing.

### Useful or wasted work

The body doing the same action has two meanings of work. The first, useful, is calculated using the usual formula.

The second, spent, in its concept does not have a general formula for calculation and is measured practically. This difference between the work perfect in reality and the one that should have been done in theory is equal to the coefficient of performance – efficiency. It is calculated like this:

Efficiency = A useful / A spent,

and is expressed as a percentage. The efficiency is always less than 100.

## Power and efficiency

### Power

The average amount of work done per unit of time (second) characterizes such a value as power. The formula for calculating it looks like this:

P = A / t

As a job, you can substitute a well-known formula for its calculation, depending on the situation. The answer will be expressed in watts.

However, with uniform motion, you can use another formula:

P = F * v

Substituting the instantaneous instead of the usual speed, you can get the value of the instantaneous power.

## Examples of problem solving

Let’s look at a few simple tasks for finding mechanical work.

Problem 1

What kind of work does a lifting mechanism do that lifts a ten-kilogram block to a height of 50 meters.

Decision:

In order to lift the body, it is necessary to overcome the force of gravity acting on it. That is, the F with which the block is lifted is equal to the one with which it is attracted to the ground. Since the latter is equal to m * g, only one modified version of the standard formula mentioned above is needed to find the final result: A = S * m * g.

Using simple math, we can find the numerical answer:

A = 50 m * 10 kg * 10 N / kg;

A = 5000 J.

However, we are not always talking about the force of gravity.

What work is done by the elastic force when a spring with a stiffness of 10 N / m, compressed by 20 cm, returns to its original state? The system is closed, there are no external forces acting on the spring.

Decision:

First you need to find the very F elasticity that does the work. Its formula is F = x * | k |, where x is the length by which the spring is compressed or stretched, and k is the coefficient of its stiffness. The displacement of the spring is equal to its deformation, and therefore, the final formula in this case will look like this: A = S * x * k = x * x * k = x ^ 2 * k.

Next, using elementary calculations, we calculate the answer:

A = (0.2 m) ^ 2 * 10 N / m = 0.04 * 10 = 0.4 J.

But in all problems on this topic, the trajectory of the body is straight.