Named after the British physicist James Edward Joule, the joule (J) is one of the basic units of the international metric system. The joule is used as a unit of work, energy, and heat, and is widely used in scientific applications. If you want your answer in joules, always make sure to use standard scientific units. The foot-pound or British unit of heat (BTU) is still used in some fields, but not in your physics homework.
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Method 1 of 5: Calculating Work in Joules
Step 1. Understand work in physics
If you push a box through a room, you've made an effort. If you lift the box up, you've also made an effort. There are two important criteria that must exist in the "business":
- You provide a steady style.
- This force makes objects move in the same direction as the force.
Step 2. Understand the definition of business
Effort is easy to calculate. Just multiply the amount of force and the total distance the object has traveled. Usually, scientists express force in Newtons and distance in meters. If you use both of these units, the resulting unit of work is Joules.
Whenever you read a question about business, stop and think about where the style is. If you lift the box, you push it up so the box moves up. So, the distance the box travels is how high it has moved up. However, if you subsequently walk forward carrying the box, no effort is made in this process. Even if you're still pushing the box up to keep it from falling, it's no longer moving up
Step 3. Find the mass of the object being displaced
The mass of an object is needed to calculate the force required to move it. In our example, suppose the load has a mass of 10 kilograms (kg).
Avoid using pounds or other non-standard units, or your final answer will not be in joules
Step 4. Calculate the style
Force = mass x acceleration. In our example, lifting the weight straight up, the acceleration we exert is due to gravity, which under normal circumstances accelerates the object downward at 9.8 meters/sec.2. Calculate the force required to move our load up by multiplying (10 kg) x (9.8 m/s2) = 98 kg m/s2 = 98 newtons (N).
If the object is moved horizontally, gravity has no effect. The problem may ask you to calculate the force required to resist friction. If the problem tells you the acceleration of an object as it is pushed, you can multiply the known acceleration by its mass
Step 5. Measure the displacement traveled
For this example, suppose a load is lifted to a height of 1.5 meters (m). The displacement must be measured in meters, or your final answer will not be in joules.
Step 6. Multiply the force by the displacement
To lift a 98 newton weight 1.5 meters high, you need to do 98 x 1.5 = 147 joules of work.
Step 7. Calculate the work done to move the object at a certain angle
Our example above is simple: someone exerts a forward force on an object, and the object moves forward. Sometimes, the direction of the force and the motion of the object are not the same, because there are several forces acting on the object. In the next example, we will calculate the number of joules needed for a child to pull a sled 25 meters through flat snow by pulling the rope up at an angle of 30º. For this problem, work = force x cosine(θ) x displacement. The symbol is the Greek letter theta, and describes the angle between the direction of the force and the direction of motion.
Step 8. Find the total force applied
For this problem, suppose a child pulls a string with a force of 10 newtons.
If the problem exerts a force to the right, an upward force, or a force in the direction of motion, then these forces already account for the x cosine(θ) portion of the force, and you can skip ahead and continue multiplying the values
Step 9. Calculate the corresponding force
Only a few styles pull the sled forward. As the string is pointing up, another force tries to pull it up, pulling it against gravity. Calculate the force exerted in the direction of motion:
- In our example, the angle between the flat snow and the rope is 30º.
- Calculate cos(θ). cos(30º) = (√3)/2 = approximately 0.866. You can use a calculator to find this value, but make sure your calculator uses the same units as your angle measurement (degrees or radians).
- Multiply the total force x cos(θ). In our example, 10 N x 0.866 = 8.66 forces in the direction of motion.
Step 10. Multiply the force x displacement
Now that we know the force that is advancing in the direction of motion, we can calculate work as usual. Our problem tells us that the sled moves forward 20 meters, so calculate 8.66 N x 20 m = 173.2 joules of work.
Method 2 of 5: Calculating Joules from Watts
Step 1. Understand power and energy
Watt is a unit of power or rate of energy use (energy divided by time). While Joule is a unit of energy. To convert Watts to Joules, you need to determine the time. The longer the electric current flows, the greater the energy used.
Step 2. Multiply Watts by seconds to get Joules
A 1 Watt device will consume 1 Joule of energy every 1 second. If you multiply the number of Watts by seconds, you will get Joules. To find out how much energy a 60W lamp consumes in 120 seconds, you just need to multiply 60 watts x 120 seconds = 7,200 Joules.
This formula can be used for any power expressed in Watts, but generally in electricity
Method 3 of 5: Calculating Kinetic Energy in Joules
Step 1. Understand kinetic energy
Kinetic energy is the amount of energy in the form of motion. Like other energy units, kinetic energy can be written in joules.
Kinetic energy is equal to the amount of work done to accelerate a static object to a certain speed. Once the object reaches that speed, the object will maintain a certain amount of kinetic energy until the energy turns into heat (from friction), gravitational potential energy (from moving against gravity), or other types of energy
Step 2. Find the mass of the object
For example, we measure the kinetic energy of a bicycle & a cyclist. For example, the rider has a mass of 50 kg, and his bicycle has a mass of 20 kg, for a total mass m of 70 kg. Now, we consider the two as one object with a mass of 70 kg because they will both move at the same speed.
Step 3. Calculate the speed
If you already know the speed or speed of the cyclist, just write it down and move on. If you need to calculate the speed, use one of the methods below. Note that we are looking for speed, not velocity (which is speed in a given direction), although the abbreviation v is often used. Ignore any turns the cyclist makes and assume the entire distance is covered in a straight line.
- If the cyclist is moving at a constant speed (not accelerating), measure the distance the cyclist travels in meters, and divide by the number of seconds it will take to cover that distance. This calculation will yield the average speed, which in this case is equal to the instantaneous velocity.
- If the cyclist experiences constant acceleration and does not change direction, calculate his speed at time t using the formula for speed at time t = (acceleration)(t) + initial speed. Use second to measure time, meter/second to measure speed, and m/s2 to measure acceleration.
Step 4. Plug these numbers into the following formula
Kinetic energy = (1/2) m v 2. For example, if a cyclist is moving with a speed of 15 m/s, his kinetic energy EK = (1/2)(70 kg)(15 m/s)2 = (1/2)(70 kg)(15 m/s)(15 m/s) = 7875 kgm2/s2 = 7875 newton meters = 7875 joules.
The formula for kinetic energy can be derived from the definition of work, W = FΔs, and the kinematic equation v2 = v02 + 2aΔs. s represents a change in position or distance traveled.
Method 4 of 5: Calculating Heat in Joules
Step 1. Find the mass of the object being heated
Use a scale or spring balance to measure it. If the object is a liquid, first measure the empty container in which the liquid is and find its mass. You need to subtract it from the mass of the container plus the liquid to find the mass of the liquid. For this example, let's say the object is 500 grams of water.
Use grams, not other units, or the result won't be in joules
Step 2. Find the specific heat of the object
This information can be found in chemistry references, both in book form and online. For water, the specific heat of c is 4.19 joules per gram for every degree Celsius it is heated – or 4.1855, if you need the exact value.
- The actual specific heat varies slightly based on the temperature and pressure. Different organizations and textbooks use different standard temperatures, so you may see the specific heat of water listed as 4.179.
- You can use Kelvin instead of Celsius because the temperature difference is the same for both units (heating something by 3ºC equals heating by 3 Kelvin). Don't use Fahrenheit, or your results won't be in joules.
Step 3. Find the initial temperature of the object
If the object is a liquid, you can use a mercury thermometer. For some items, you may need a probe thermometer.
Step 4. Heat the object and measure the temperature again
This will measure the heat gain of the object during heating.
If you want to measure the total amount of energy stored as heat, you can assume the initial temperature is absolute zero: 0 Kelvin or -273.15ºC. This is not very useful
Step 5. Subtract the initial temperature from the heating temperature
This reduction will result in a degree of temperature change in the object. Assuming the water was previously 15 degrees Celsius and heated to 35 degrees Celsius, the temperature changes to 20 degrees Celsius.
Step 6. Multiply the mass of the object by its specific heat and by the magnitude of the change in temperature
The formula is written Q = mc T, where T is the change in temperature. For this example, it would be 500g x 4, 19 x 20, or 41,900 joules.
Heat is more often written in the calorie or kilocalorie metric system. A calorie is defined as the amount of heat needed to raise the temperature of 1 gram of water by 1 degree Celsius, while a kilocalorie is the amount of heat needed to raise the temperature of 1 kilogram of water by 1 degree Celsius. In the example above, raising the temperature of 500 grams of water by 20 degrees Celsius will use up 10,000 calories or 10 kilocalories
Method 5 of 5: Calculating Joules as Electrical Energy
Step 1. Use the steps below to calculate the flow of energy in an electrical circuit
The steps below are listed as practical examples, but you can also use the method to understand written physics problems. First, we will calculate the power P using the formula P = I2 x R, where I is the current in amperes and R is the resistance in ohms. These units produce power in watts, so from here, we can use the formula in the previous step to calculate energy in joules.
Step 2. Choose a resistor
Resistors are measured in ohms, with sizes written directly or represented by a collection of colored lines. You can also test the resistance of a resistor by connecting it with an ohmmeter or multimeter. For this example, we assume the resistor is 10 ohms.
Step 3. Connect the resistor to the current source
You can connect the wires to the resistor with a Fahnestock or alligator clip, or you can plug the resistor into a test board.
Step 4. Flow current through the circuit for a certain time interval
For this example, we will use an interval of 10 seconds.
Step 5. Measure the current strength
Do this with an ammeter or multimeter. Most household currents are measured in milliamperes, or thousands of amperes, so we assume the current is 100 milliamperes or 0.1 amperes.
Step 6. Use the formula P = I2 x R.
To find the power, multiply the square of the current by the resistance. This results in power output in watts. Squaring 0.1 gives a result of 0.01, multiplied by 10 gives a power output of 0.1 watts or 100 milliwatts.
Step 7. Multiply the power by the elapsed time
This multiplication gives the energy output in joules. 0.1 watt x 10 seconds is equal to 1 joule of electrical energy.
