The joule (J) is a fundamental unit of measurement of the International System and is named after the English physicist James Edward Joule. The joule is the unit of measurement for work, energy and heat and is widely used in scientific applications. If you want the solution to a problem to be expressed in joules, then you need to be sure to use standard units of measurement in your calculations. The "foot-pounds" or "BTUs" (British Thermal Units) are still used in some countries, but for physics tasks there is no place for non-internationally coded units of measurement.
Steps
Method 1 of 5: Calculate the Work in Joules
Step 1. Understand the physical concept of work
If you push a box into a room, you've done some work. If you lift it, you've done some work. There are two determining factors that must be met for there to be "work":
- You have to apply constant force.
- The force must generate the displacement of the body in the direction in which it is applied.
Step 2. Define the job
It is an easy measure to calculate. Just multiply the amount of force used to move the body. Typically, scientists measure force in newtons and distance in meters. If you use these units, the product will be expressed in joules.
When you read a physics problem involving work, stop and consider where the force is applied. If you are lifting a box, then you will push up and the box will rise, so the distance is represented by the height reached. But if you walk holding a box, then know that there is no work. You are applying enough force to prevent the box from falling, but it is not generating an upward movement
Step 3. Find the mass of the object you are moving
You need to know this figure to understand the force required to move it. In our previous example, we consider a person lifting a weight from the ground up to the chest and calculate the work the person exerts on it. Suppose the object has a mass of 10 kg.
Do not use grams, pounds or other units of measurement that are not standardized by the International System, otherwise you will not get the work expressed in joules
Step 4. Calculate the force
Force = mass x acceleration. In the previous example, lifting a weight in a straight line, the acceleration we must overcome is that of gravity, which is equal to 9.8 m / s2. Calculate the force required to move the object upwards by multiplying its mass by the acceleration of gravity: (10 kg) x (9, 8 m / s2) = 98 kg m / s2 = 98 newtons (N).
If the object moves horizontally, gravity is irrelevant. The problem, however, may ask you to calculate the force needed to overcome friction. If the problem gives you the acceleration data it undergoes when pushed, then just multiply this value by the known mass of the object itself
Step 5. Measure the displacement
In this example, let's assume the weight is lifted 1.5m. It is imperative that the distance is measured in meters, otherwise you will not get a result in joules.
Step 6. Multiply the force by the distance
To lift 98 N by 1.5m you will need to exercise a work of 98 x 1.5 = 147 J.
Step 7. Calculate work for objects moving diagonally
Our previous example is quite simple: a person exerts an upward force and the object rises. However, sometimes, the direction in which the force is applied and the direction in which the object moves are not exactly identical, due to different forces acting on the body. In the example below, we will calculate the amount of joules required for a child to drag a sled for 25 m on a flat snow-covered surface by pulling a rope that forms an angle of 30 °. In this case the work is: work = force x cosine (θ) x distance. The symbol θ is the Greek letter "theta" and describes the angle formed by the direction of the force and that of the displacement.
Step 8. Find the total applied force
For this problem, suppose the child applies a force of 10 N.
If the problem gives you the data of "force in the direction of motion", this corresponds to the portion of the formula "force x cos (θ)" and you can skip this multiplication
Step 9. Calculate the relevant force
Only part of the force is effective in generating the motion of the slide. Since the rope is angled upward, the rest of the force is used to yank the sled up "wasting" it against the force of gravity. Calculate the force applied in the direction of motion:
- In our example, the angle θ formed between the flat snow and the rope is 30 °.
- Calculate the cos (θ). cos (30 °) = (√3) / 2 = approximately 0, 866. You can use a calculator to obtain this value, but make sure it is set to the same unit of measurement as the angle in question (degrees or radians).
- Multiply the total force by the cosine of θ. Then we consider the data of the example and: 10 N x 0, 866 = 8, 66 N, that is the value of the force applied in the direction of motion.
Step 10. Multiply the force by the displacement
Now that you know how much force is actually functional to the displacement, you can calculate the work as usual. The problem informs you that the child moves the sled forward 20m, so the work is: 8.66N x 20m = 173.2J.
Method 2 of 5: Calculate Joules from Watts
Step 1. Understand the concept of power and energy
Watts are the unit of measurement of power, that is, how quickly energy is used (energy in a unit of time). Joules measure energy. To derive joules from watts you need to know the value of time. The longer a current flows, the more energy it uses.
Step 2. Multiply the watts by the seconds and you will get the joules
A 1 watt device consumes 1 joule of energy every second. If you multiply the number of watts by the number of seconds, you get joules. To find how much power a 60W light bulb consumes in 120 seconds, simply do this multiplication: (60 watts) x (120 seconds) = 7200 J.
This formula is suitable for any type of power measured in watts, but electricity is the most common application
Method 3 of 5: Calculate the Kinetic Energy in Joules
Step 1. Understand the concept of kinetic energy
This is the amount of energy a moving body has or acquires. Just like any unit of energy, kinetic can also be expressed in joules.
The kinetic energy is equal to the work exerted to accelerate a stationary body up to a certain speed. Once it has reached this speed, the body retains the kinetic energy until it is converted into heat (from friction), into potential gravitational energy (moving against the force of gravity) or another type of energy
Step 2. Find the mass of the object
Let's consider we want to measure the energy of a cyclist and his bicycle. Let's assume that the athlete has a mass of 50 kg while that of the bike is 20 kg; the total mass m is equal to 70 kg. At this point we can consider the “cyclist + bike” group as a single body of 70 kg, since both will travel at the same speed.
Step 3. Calculate the speed
If you already know this information, just write it down and continue with the problem. If you need to calculate it instead, use one of the methods described below. Remember that we are interested in the scalar speed and not the vectorial one (which also takes into account the direction), to symbolize the speed we use the v. For this reason, ignore every curve and change of direction that the cyclist will make and consider as if he is always moving in a straight line.
- If the cyclist is moving at a constant speed (without acceleration), measure the distance traveled in meters and divide that value by the number of seconds it took him to complete the journey. This calculation gives you the average speed which, in our case, is constant at all times.
- If the cyclist accelerates constantly and does not change direction, calculate his speed at a given instant t with the formula of "instantaneous speed = (acceleration) (t) + initial speed. Use seconds to measure time, meters per second (m / s) for the speed eim / s2 for acceleration.
Step 4. Enter all the data in the formula below
Kinetic energy = (1/2) mv2. For example, consider a cyclist traveling at a speed of 15 m / s, his kinetic energy K = (1/2) (70 kg) (15m / s)2 = (1/2) (70 kg) (15 m / s) (15 m / s) = 7875 kgm2/ s2 = 7875 newton meters = 7875 J.
The formula for kinetic energy can be deduced from the definition of work, W = FΔs, and from the kinematic equation v2 = v02 + 2aΔs. Where Δs refers to the "change of position", ie the distance traveled.
Method 4 of 5: Calculate Heat in Joules
Step 1. Find the mass of the object to be heated
Use a scale for this. If the object is in a liquid state, first measure the empty container (tare). You will need to subtract this value from the next weighing to find the mass of the liquid alone. In our case, we consider that the object is represented by 500 g of water.
It is important to use grams and not another unit of mass measurement, otherwise the result will not be in joules
Step 2. Find the specific heat of the object
This is information available in chemistry books, but you can also find it online. In the case of water, the specific heat c is equal to 4.19 joules per gram for each degree Celsius or, to be more precise, 4.855.
- Specific heat changes slightly with pressure and temperature. Various textbooks and scientific organizations use slightly different "standard temperature" values, so you may also find that the specific heat of the water is indicated as 4, 179.
- You can use the Kelvin degrees instead of the Celsius degrees, since the temperature difference remains constant in the two scales (heating an object to increase its temperature by 3 ° C is equivalent to increasing it by 3 ° K). Do not use Fahrenheit, otherwise the result will not be expressed in joules.
Step 3. Find your current body temperature
If it is a liquid material, use a bulb thermometer. In other cases, an instrument with a probe will be required.
Step 4. Heat the object and measure its temperature again
This allows you to track the amount of heat that was added to the material.
If you want to measure the energy stored as heat, you must assume that the initial temperature is at absolute zero, 0 ° K or -273, 15 ° C. This is not a particularly useful data
Step 5. Subtract the initial temperature from the value obtained after applying heat
This difference represents the change in body temperature. We consider the initial water temperature as 15 ° C and the one after heating as 35 ° C; in this case the temperature difference is 20 ° C.
Step 6. Multiply the mass of the object by its specific heat and by the temperature difference
This formula is: H = mc Δ T, where ΔT means "temperature difference". Following the data of the example, the formula leads: 500 g x 4, 19 x 20 ° C that is 41900 j.
Heat is most commonly expressed in calories or kilocalories. A calorie is defined as the amount of heat needed to raise the temperature of 1 g of water by 1 ° C, while a kilocalorie is the amount of heat needed to raise the temperature of 1 kg of water by 1 ° C. In the previous example, by increasing the temperature of 500 g of water by 20 ° C we used 10,000 calories or 10 kilocalories
Method 5 of 5: Calculate the Electricity in Joules
Step 1. Follow the next steps to calculate the energy flow in an electrical circuit
These describe a practical example, but you can use the same method to understand a wide range of physics problems. First we must calculate the power P thanks to the formula: P = I2 x R, where I is the current intensity expressed in amperes (amp) and R is the resistance of the circuit in ohms. These units allow to obtain the power in watts and from this value to derive the energy in joules.
Step 2. Choose a resistor
These are elements of a circuit that are differentiated by the ohm value stamped on them or by a series of colored strips. You can test the resistance of a resistor by connecting it to a multimeter or ohmmeter. For our example, let's consider a 10 ohm resistor.
Step 3. Connect the resistor to a current source
You can use cables with Fahnestock clips or with alligator clips; alternatively you can insert the resistor in an experimental board.
Step 4. Turn on the flow of current in the circuit for a set period of time
Let's assume 10 seconds.
Step 5. Measure the strength of the current
To do this, you need to have an ammeter or multimeter. Most household systems use an electrical current in milliamps, that is, in thousandths of amperes; for this reason it is assumed that the intensity is equal to 100 milliamps or 0.1 ampere.
Step 6. Use the formula P = I2 x R.
To find the power, multiply the square of the current by the resistance; the product will give you the power expressed in watts. Squaring the value by 0.1 amp you get 0.01 amp2, and this multiplied by 10 ohms gives you the power of 0.1 watt or 100 milliwatts.
Step 7. Multiply the power by the time you applied electricity
By doing this, you get the value of the energy emitted in joules: 0, 1 watt x 10 seconds = 1 J of electricity.
