How to Calculate Joules
Understand what work means in physics., Define work., Find the mass of the object being moved., Calculate the force., Measure the distance being moved., Multiply the force by the distance., Calculate work for objects moving at an angle., Find the...
Step-by-Step Guide
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Step 1: 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:
You're applying constant force.
The force is causing the object to move in the direction of the force. -
Step 2: 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., 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. , Force = mass x acceleration.
In our example, lifting a weight straight up, the acceleration we're fighting is due to gravity, which equals
9.8 meters/second2.
Calculate the force required to move our weight upward by multiplying (10 kg) x (9.8 m/s2) = 98 kg m/s2 = 98 Newtons (N).
If the object is being moved horizontally, gravity is irrelevant.
The problem may ask you to calculate the force required to overcome friction instead.
If the problem tells you how fast the object is accelerating when it is pushed, you can multiply the acceleration given with the mass. , 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. , To lift a 98 Newton weight
1.5 meters upward, you'll need to exert 98 x
1.5 = 147 Joules of work. , 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., 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 , Only some of the force is pulling the sled forward.
Since the rope is at an angle upward, the rest of the force is trying to yank the sled upward, uselessly pulling against gravity.
Calculate the force that applies in the direction of motion:
In our example, the angle θ between the flat snow and the rope is 30º.
Calculate cos(θ). cos(30º) = (√3)/2 = about
0.866.
You can use a calculator to find this value, but make sure your calculator is set to the same unit as your angle measurement (degrees or radians).
Multiply the total force x cos(θ).
In our example, 10N x
0.866 =
8.66 N of force in the direction of motion. , Now that we know how much force is actually going toward the direction of motion, we can calculate work as usual.
Our problem tells us the sled moved 20 meters forward, so calculate
8.66 N x 20 m =
173.2 joules of work. -
Step 3: Find the mass of the object being moved.
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Step 4: Calculate the force.
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Step 5: Measure the distance being moved.
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Step 6: Multiply the force by the distance.
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Step 7: Calculate work for objects moving at an angle.
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Step 8: Find the total force applied.
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Step 9: Calculate the relevant force.
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Step 10: Multiply force x distance.
Detailed Guide
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:
You're applying constant force.
The force is causing the object to move in the direction of the force.
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., 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. , Force = mass x acceleration.
In our example, lifting a weight straight up, the acceleration we're fighting is due to gravity, which equals
9.8 meters/second2.
Calculate the force required to move our weight upward by multiplying (10 kg) x (9.8 m/s2) = 98 kg m/s2 = 98 Newtons (N).
If the object is being moved horizontally, gravity is irrelevant.
The problem may ask you to calculate the force required to overcome friction instead.
If the problem tells you how fast the object is accelerating when it is pushed, you can multiply the acceleration given with the mass. , 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. , To lift a 98 Newton weight
1.5 meters upward, you'll need to exert 98 x
1.5 = 147 Joules of work. , 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., 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 , Only some of the force is pulling the sled forward.
Since the rope is at an angle upward, the rest of the force is trying to yank the sled upward, uselessly pulling against gravity.
Calculate the force that applies in the direction of motion:
In our example, the angle θ between the flat snow and the rope is 30º.
Calculate cos(θ). cos(30º) = (√3)/2 = about
0.866.
You can use a calculator to find this value, but make sure your calculator is set to the same unit as your angle measurement (degrees or radians).
Multiply the total force x cos(θ).
In our example, 10N x
0.866 =
8.66 N of force in the direction of motion. , Now that we know how much force is actually going toward the direction of motion, we can calculate work as usual.
Our problem tells us the sled moved 20 meters forward, so calculate
8.66 N x 20 m =
173.2 joules of work.
About the Author
Joan Simmons
Writer and educator with a focus on practical DIY projects knowledge.
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