- #1
IQScience
- 6
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Okay, so I've got a question on graphs and areas under curves.
For example, a force-distance graph, with force on the y-axis and distance on the x-axis, where you find work done from that graph.
I understand that a constant force will produce a horizontal line on the graph, like so:
Force
|
|-------------
|
|
|___________distance
So the area under the line is just force x distance.
This matches the equation, work = force x distance.
But I'm having trouble understanding a proportional graph, or one that looks like a triangle, like this:
Force
|------/-----
|-----/-----
|----/------
|---/-------
|--/--------
|-/---------
|/_________distance
i.e. force increases at a constant rate.
To find work done from this, you find the area under the line, which is a triangle.
But this doesn't match the equation (work = force x distance) which is confusing me.
Why is it not force x distance like the equation?
Why is is 1/2 force x distance now?
I understand that this is because the area under the line is a triangle, but why is work done the area under the graph?
For example, a force-distance graph, with force on the y-axis and distance on the x-axis, where you find work done from that graph.
I understand that a constant force will produce a horizontal line on the graph, like so:
Force
|
|-------------
|
|
|___________distance
So the area under the line is just force x distance.
This matches the equation, work = force x distance.
But I'm having trouble understanding a proportional graph, or one that looks like a triangle, like this:
Force
|------/-----
|-----/-----
|----/------
|---/-------
|--/--------
|-/---------
|/_________distance
i.e. force increases at a constant rate.
To find work done from this, you find the area under the line, which is a triangle.
But this doesn't match the equation (work = force x distance) which is confusing me.
Why is it not force x distance like the equation?
Why is is 1/2 force x distance now?
I understand that this is because the area under the line is a triangle, but why is work done the area under the graph?