In physics, the definition of "work" is different from that used in everyday language. In particular, the term "work" is used when a physical force causes an object to move. In general, if an intense force moves an object very far from the starting position, the amount of work produced is large, while if the force is less intense or the object does not move very much, the amount of work produced is small. Strength can be calculated on the basis of the formula Work = F x s x Cosθ, where F = force (in Newtons), s = displacement (in meters), and θ = the angle between the force vector and the direction of motion.
Steps
Part 1 of 3: Work Calculation in One Dimension
Step 1. Find the direction of the force vector and the direction of motion
To begin, it is important to first identify both the direction in which the object is moving and the direction from which the force is being applied. Keep in mind that the direction of motion of objects is not always in line with the force applied: for example, if you pull a cart by the handle, to move it forward you apply a force in an oblique direction (assuming you are taller than the cart). In this section, however, we deal with situations where the force and movement of the object have the same direction. To find out how to find work when they are not in the same direction, go to the next section.
To make this method easier to understand, let's continue with an example. Suppose a toy train car is pulled forward by the tractor in front of it. In this case, the force vector and the movement of the train have the same direction: in come on. In the next few steps, we will use this information to understand how to calculate the work done on the object.
Step 2. Calculate the displacement of the object
The first variable we need in the formula to calculate the work, is s, moving, usually easy to find. Displacement is simply the distance that the object in question has traveled from its starting position following the application of force. Usually in school problems, this information is a given of the problem or it is possible to deduce it from the other data. In real problems, all you have to do to find the displacement is to measure the distance traveled by the object.
- Note that the distance measurements must be in meters to be able to use them correctly in the job formula.
- In the toy train example, let's say we need to calculate the work done on the wagon as it moves along the track. If it starts at a specific point and ends about 2 meters later, we can write 2 meters instead of the "s" in the formula.
Step 3. Find the strength intensity value
The next step is to find the value of the force used to move the object. This is the measure of the "intensity" of the force: the more intense the force, the greater the thrust on the object which, as a consequence, will undergo a greater acceleration. If the value of the intensity of the force is not a given of the problem, it can be calculated using the values of mass and acceleration (assuming that there are no other forces interfering with it) with the formula F = m x a.
- Note that the force measure, to be used in the work formula, must be expressed in Newton.
- In our example, suppose we don't know the value of force. However, we know that the toy train has a mass of 0.5 kg and that the force causes an acceleration of 0.7 meters / second.2. That being the case, we can find the value by multiplying m x a = 0.5 x 0.7 = 0, 35 Newton.
Step 4. Multiply Force x Distance
When you know the value of the force acting on the object and the extent of the displacement, the calculation is easy. Just multiply these two values together to get the value of the work.
- At this point we solve the problem of our example. With a force value of 0.35 Newton and a displacement measurement of 2 meters, the result is obtained with a single multiplication: 0.35 x 2 = 0.7 joules.
- You may have noticed that, in the formula presented in the introduction, there is one more element: like this. As explained above, in this example the force and the movement have the same direction. This means that the angle they form is 0or. Since cos 0 = 1, there is no need to include it in the formula: it would mean multiplying by 1.
Step 5. Write the unit of measurement of the result, in joules
In physics, the values of work (and some other quantities) are almost always expressed in a unit of measurement called the joule. A joule is defined as 1 newton of force which produces a displacement of 1 meter, or, in other words, one newton x meter. The sense is that, since a distance is being multiplied by a force, it is logical that the unit of measurement of the response corresponds to the multiplication of the unit of measurement of force by that of distance.
Note that there is another alternative definition for joule: 1 watt of radiated power per 1 second. Below you will find a more detailed explanation on potency and its relationship to work
Part 2 of 3: Work Calculation if Force and Direction Form an Angle
Step 1. Find the force and displacement as in the previous case
In the previous section we looked at those work-related problems where the object moves in the same direction as the force applied to it. In reality, this is not always the case. In cases where force and movement have two different directions, this difference must be taken into account. To begin with to calculate an accurate result; calculates the intensity of the force and the displacement, as in the previous case.
Let's look at another problem, by way of example. In this case, let's look at the situation where we are pulling a toy train forward as in the previous example, but this time we are applying the force diagonally upwards. In the next step, we will also consider this element, but for now, we stick to the fundamental aspects: the movement of the train and the intensity of the force acting on it. For our purpose, it suffices to say that force has an intensity of 10 newtons and that the distance traveled are the same 2 meters forward, as before.
Step 2. Calculate the angle between the force vector and the displacement
Unlike the previous examples, the force has a different direction from that of the movement of the object, so it is necessary to calculate the angle formed between these two directions. If this information is not available, it may need to be measured or inferred using the other problem data.
In our example problem, suppose the force is applied at an angle of 60or than the floor. If the train is moving directly forward (i.e., horizontally), the angle between the force vector and the train's movement is 60or.
Step 3. Multiply Force x Distance x Cos θ
When the displacement of the object, the intensity of the force acting on it, and the angle between the force vector and its movement are known, the solution is almost as easily calculated as in the case where you didn't have to take the 'angle. To find the answer in joules, just take the cosine of the angle (you might need a scientific calculator) and multiply it by the strength of the force and by the displacement.
Let's solve the problem of our example. Using a calculator, we find that the cosine of 60or is 1/2. We substitute the data in the formula, and calculate as follows: 10 newtons x 2 meters x 1/2 = 10 joules.
Part 3 of 3: How to Use Work Value
Step 1. You can calculate distance, force, or angle width using the inverse formula
The work calculation formula is not only useful for calculating the work value: it is also useful for finding any of the variables in the equation when the work value is known. In these cases, it is enough to isolate the variable you are looking for and carry out the calculation using the basic rules of algebra.
-
For example, suppose we know that our train is being pulled by a force of 20 Newtons, with the direction of the applied force making an angle with the direction of movement, for 5 meters producing 86.6 joules of work. However, we do not know the magnitude of the angle of the force vector. To find out the angle, we'll just isolate the variable and solve the equation as follows:
-
- 86.6 = 20 x 5 x cos θ
- 86.6/100 = cos θ
- ArcCos (0, 866) = θ = 30or
-
Step 2. To calculate power, divide by the time it takes to move
In physics, work is closely related to another type of measurement called "power". Power is simply a way of quantifying how quickly work is done in a given system over time. So, to find the power, all you have to do is divide the work done to move an object by the time it takes to complete the move. The unit of measurement of power is the watt (equal to joules per second).
For example, in the problem from the previous step, suppose it took 12 seconds for the train to move 5 meters. In this case, all we have to do is divide the work done by the distance of 5 meters (86.6 joules) by the 12 seconds, to calculate the power value: 86.6/12 = 7.22 watts
Step 3. Use formula Ethe + Wnc = Ef to find the mechanical energy of a system.
Work can also be used to find the energy of a system. In the above formula, Ethe = the initial total mechanical energy of a system, Ef = the final total mechanical energy of the system, and Lnc = the work done on the system due to non-conservative forces. In this formula, if the force is applied in the direction of movement, it has a positive sign, if it is applied in the opposite direction, it is negative. Note that both energy variables can be found with the formula (½) mv2 where m = mass and V = volume.
- For example, given the problem of the two previous steps, suppose that the train initially had a total mechanical energy of 100 joules. Since the force is exerted on the train in the direction of movement, the sign is positive. In this case, the final energy of the train is E.the+ Lnc = 100 + 86, 6 = 186.6 joules.
- Note that non-conservative forces are forces whose power to influence the acceleration of an object depends on the path followed by the object. Friction is a classic example: the effects of friction on an object moved in a short, straight path are less than in an object that undergoes the same movement following a long and tortuous path.
Advice
- When you can solve the problem, smile and congratulate yourself!
- Try to solve as many problems as you can, so that you can gain a certain level of familiarity.
- Don't stop exercising, and don't give up if you don't succeed on the first try.
-
Learn the following aspects related to work:
- The work done by a force can be positive and negative - in this case, we use the terms positive and negative in their mathematical meaning, not in the sense given in everyday language.
- The work done is negative if the force that is applied has the opposite direction with respect to the displacement.
- The work done is positive if the force is applied in the direction of the displacement.
