Difference between revisions of "Calculate Joules"
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== Steps == | == Steps == | ||
=== Calculating Work in Joules === | === Calculating Work in Joules === | ||
| − | #Understand what work means in physics. If you push a box across the room, you've done work. If you lift it upward, you've done work. There are two important qualities that have to be there for "work" to happen:<ref>http://education-portal.com/academy/lesson/work-definition-characteristics-and-examples.html</ref> | + | #Understand what work means in physics. If you push a box across the room, you've done work. If you lift it upward, you've done work. There are two important qualities that have to be there for "work" to happen:<ref name="rf1">http://education-portal.com/academy/lesson/work-definition-characteristics-and-examples.html</ref> |
#*You're applying constant force. | #*You're applying constant force. | ||
#*The force is causing the object to move in the direction of the force. | #*The force is causing the object to move in the direction of the force. | ||
#Define work. Work is easy to calculate. Just multiply the amount of force used, and the amount of distance traveled. Usually, scientists measure force in Newtons, and distance in meters. If you use these units, your answer will be work in units of Joules. | #Define work. Work is easy to calculate. Just multiply the amount of force used, and the amount of distance traveled. Usually, scientists measure force in Newtons, and distance in meters. If you use these units, your answer will be work in units of Joules. | ||
| − | #*Whenever you read a word problem about work, stop and think where the force is being applied. If you lift a box, you're pushing upward, and the box is moving up — so the distance is however much it rises. But if you then walk forward holding the box, there's no work happening at all. You're pushing upward still, to keep the box from falling, but the box isn't moving up.<ref>http://www.physicsclassroom.com/Class/energy/u5l1a.cfm#waiter</ref> | + | #*Whenever you read a word problem about work, stop and think where the force is being applied. If you lift a box, you're pushing upward, and the box is moving up — so the distance is however much it rises. But if you then walk forward holding the box, there's no work happening at all. You're pushing upward still, to keep the box from falling, but the box isn't moving up.<ref name="rf2">http://www.physicsclassroom.com/Class/energy/u5l1a.cfm#waiter</ref> |
#Find the mass of the object being moved. You need to know the mass to figure out how much force you need to move it. For our first example, we'll use a person lifting a weight from the floor to her chest, and calculate how much work that person exerts on the weight. Let's say the weight has a mass of 10 kilograms (kg). | #Find the mass of the object being moved. You need to know the mass to figure out how much force you need to move it. For our first example, we'll use a person lifting a weight from the floor to her chest, and calculate how much work that person exerts on the weight. Let's say the weight has a mass of 10 kilograms (kg). | ||
#*Avoid using pounds or other non-standard units, or your final answer won't be in terms of joules. | #*Avoid using pounds or other non-standard units, or your final answer won't be in terms of joules. | ||
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#Measure the distance being moved. For this example, let's say the weight is being lifted 1.5 meters (m). The distance must be measured in meters, or your final answer will not be written in Joules. | #Measure the distance being moved. For this example, let's say the weight is being lifted 1.5 meters (m). The distance must be measured in meters, or your final answer will not be written in Joules. | ||
#Multiply the force by the distance. To lift a 98 Newton weight 1.5 meters upward, you'll need to exert 98 x 1.5 = 147 Joules of work. | #Multiply the force by the distance. To lift a 98 Newton weight 1.5 meters upward, you'll need to exert 98 x 1.5 = 147 Joules of work. | ||
| − | #Calculate work for objects moving at an angle. Our example above was simple: someone exerted a force upward on the object, and the object moved upward. Sometimes, the direction of the force and the movement of the object aren't quite the same, due to multiple forces acting on the object. In the next example, we'll calculate the amount of Joules needed for a kid to drag a sled 20 meters across flat snow by pulling on a rope angled upward at 30º. For this scenario, Work = force x cosine(θ) x distance. The θ symbol is the Greek letter "theta," and describes the angle between the direction of force and the direction of movement.<ref>http://www.physicsclassroom.com/Class/energy/u5l1a.cfm</ref> | + | #Calculate work for objects moving at an angle. Our example above was simple: someone exerted a force upward on the object, and the object moved upward. Sometimes, the direction of the force and the movement of the object aren't quite the same, due to multiple forces acting on the object. In the next example, we'll calculate the amount of Joules needed for a kid to drag a sled 20 meters across flat snow by pulling on a rope angled upward at 30º. For this scenario, Work = force x cosine(θ) x distance. The θ symbol is the Greek letter "theta," and describes the angle between the direction of force and the direction of movement.<ref name="rf3">http://www.physicsclassroom.com/Class/energy/u5l1a.cfm</ref> |
#Find the total force applied. For this problem, let's say the kid is pulling on the rope with a force of 10 Newtons. | #Find the total force applied. For this problem, let's say the kid is pulling on the rope with a force of 10 Newtons. | ||
#*If the problem gives you the "rightward force," "upward force," or "force in the direction of motion," it has already calculated the "force x cos(θ)" part of the problem, and you can skip down to multiplying the values together | #*If the problem gives you the "rightward force," "upward force," or "force in the direction of motion," it has already calculated the "force x cos(θ)" part of the problem, and you can skip down to multiplying the values together | ||
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===Calculating Joules from Watts=== | ===Calculating Joules from Watts=== | ||
#Understand power and energy. Watts are a measure of ''power'', or how fast energy is used (energy over time). Joules is a measure of ''energy''. In order to convert from watts to joules, you need to specify a length of time. The longer a current flows, the more energy it uses. | #Understand power and energy. Watts are a measure of ''power'', or how fast energy is used (energy over time). Joules is a measure of ''energy''. In order to convert from watts to joules, you need to specify a length of time. The longer a current flows, the more energy it uses. | ||
| − | #Multiply watts by seconds to get joules. A 1 Watt device consumes 1 Joule of energy every 1 second. If you multiply the number of watts by the number of seconds, you'll end up with joules. To find out how much energy a 60W light bulb consumes in 120 seconds, simply multiply (60 watts) x (120 seconds) = 7200 Joules.<ref>http://electronicsclub.info/power.htm</ref> | + | #Multiply watts by seconds to get joules. A 1 Watt device consumes 1 Joule of energy every 1 second. If you multiply the number of watts by the number of seconds, you'll end up with joules. To find out how much energy a 60W light bulb consumes in 120 seconds, simply multiply (60 watts) x (120 seconds) = 7200 Joules.<ref name="rf4">http://electronicsclub.info/power.htm</ref> |
#*This formula works for any form of power measured in watts, but electricity is the most common application. | #*This formula works for any form of power measured in watts, but electricity is the most common application. | ||
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#*If the bicyclist is accelerating at constant acceleration and doesn't change direction, calculate his speed at time ''t'' with the formula "speed at time t = (acceleration)(''t'') + initial speed. Use seconds to measure time, meters/second to measure speed, and m/s<sup>2</sup> to measure acceleration. | #*If the bicyclist is accelerating at constant acceleration and doesn't change direction, calculate his speed at time ''t'' with the formula "speed at time t = (acceleration)(''t'') + initial speed. Use seconds to measure time, meters/second to measure speed, and m/s<sup>2</sup> to measure acceleration. | ||
#Enter these numbers into the following formula. Kinetic energy = (1/2)mv<sup>2</sup>. For instance, if the bicyclist is traveling at 15 m/s, its kinetic energy K = (1/2)(70 kg)(15 m/s)<sup>2</sup> = (1/2)(70 kg)(15 m/s)(15 m/s) = 7875 kgm<sup>2</sup>/s<sup>2</sup> = 7875 newton meters = 7875 joules. | #Enter these numbers into the following formula. Kinetic energy = (1/2)mv<sup>2</sup>. For instance, if the bicyclist is traveling at 15 m/s, its kinetic energy K = (1/2)(70 kg)(15 m/s)<sup>2</sup> = (1/2)(70 kg)(15 m/s)(15 m/s) = 7875 kgm<sup>2</sup>/s<sup>2</sup> = 7875 newton meters = 7875 joules. | ||
| − | #*The kinetic energy formula can be derived from the definition of work, W = FΔs, and the kinematic equation v<sup>2</sup> = v<sub>0</sub><sup>2</sup> + 2aΔs.<ref>http://physics.info/energy-kinetic/</ref> Δs refers to "change in position," or the amount of distance traveled. | + | #*The kinetic energy formula can be derived from the definition of work, W = FΔs, and the kinematic equation v<sup>2</sup> = v<sub>0</sub><sup>2</sup> + 2aΔs.<ref name="rf5">http://physics.info/energy-kinetic/</ref> Δs refers to "change in position," or the amount of distance traveled. |
=== Calculating Heat in Joules=== | === Calculating Heat in Joules=== | ||
#Find the mass of the object being heated. Use a balance or spring scale for this. If the object is a liquid, first weigh the empty container the liquid will be held in and find its mass. You'll need to subtract this from the mass of the container and liquid together to find the liquid's mass. For this example, we'll assume the object is 500 grams of water. | #Find the mass of the object being heated. Use a balance or spring scale for this. If the object is a liquid, first weigh the empty container the liquid will be held in and find its mass. You'll need to subtract this from the mass of the container and liquid together to find the liquid's mass. For this example, we'll assume the object is 500 grams of water. | ||
#*Use grams, not any other unit, or the result will not be in Joules. | #*Use grams, not any other unit, or the result will not be in Joules. | ||
| − | #Find the object's specific heat capacity. This information can be found in a chemistry reference, either in book form or online. For water, the specific heat capacity ''c'' is 4.19 joules per gram for each degree Celsius it is heated – or 4.1855, if you need to be very precise.<ref>http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html</ref> | + | #Find the object's specific heat capacity. This information can be found in a chemistry reference, either in book form or online. For water, the specific heat capacity ''c'' is 4.19 joules per gram for each degree Celsius it is heated – or 4.1855, if you need to be very precise.<ref name="rf6">http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html</ref> |
#*Specific heat capacity actually varies slightly based on temperature and pressure. Different organizations and textbooks use different "standard temperatures," so you may see the specific heat capacity of water listed as 4.179 instead. | #*Specific heat capacity actually varies slightly based on temperature and pressure. Different organizations and textbooks use different "standard temperatures," so you may see the specific heat capacity of water listed as 4.179 instead. | ||
#*You can use Kelvin instead of Celsius, since a difference in temperature is the same in both units (heating something by 3ºC is the same as heating by 3 Kelvin). Do not use Fahrenheit, or your result will not be in Joules. | #*You can use Kelvin instead of Celsius, since a difference in temperature is the same in both units (heating something by 3ºC is the same as heating by 3 Kelvin). Do not use Fahrenheit, or your result will not be in Joules. | ||
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===Calculating Electrical Energy in Joules=== | ===Calculating Electrical Energy in Joules=== | ||
| − | #Use the steps below to calculate energy flow in an electrical circuit. The steps below are written as a practical example, but you can use the method to understand written physics problems as well. First, we'll calculate the power P using the formula P = I<sup>2</sup> x R, where I is the current in amperes (amps) and R is the resistance in ohms.<ref | + | #Use the steps below to calculate energy flow in an electrical circuit. The steps below are written as a practical example, but you can use the method to understand written physics problems as well. First, we'll calculate the power P using the formula P = I<sup>2</sup> x R, where I is the current in amperes (amps) and R is the resistance in ohms.<ref name="rf4" /> These units give us the power in watts, so from there, we' can use the formula in the previous step to calculate the energy in joules. |
#Choose a resistor. Resistors are rated in ohms, with the rating either labeled directly or indicated with a series of colored bands. You can also test a resistor's resistance by connecting it to an ohmmeter or multimeter. For this example, we'll assume the resistor is rated at 10 ohms. | #Choose a resistor. Resistors are rated in ohms, with the rating either labeled directly or indicated with a series of colored bands. You can also test a resistor's resistance by connecting it to an ohmmeter or multimeter. For this example, we'll assume the resistor is rated at 10 ohms. | ||
#Connect the resistor to a current source. Either connect wires to the resistor with Fahnestock or alligator clips, or plug the resistor into a testing board. | #Connect the resistor to a current source. Either connect wires to the resistor with Fahnestock or alligator clips, or plug the resistor into a testing board. | ||
