00:01
In this problem on energy and energy transfer, we are told that a particle is subject to a force that is varies with position as given in the diagram.
00:12
We want to find the work done by the force on the particle as it moves between different positions.
00:20
So we use the graphical representation of the definition of work.
00:25
Now we know the work done is the area under the force displacement curve, which is simply the.
00:32
Integral of the force fx dx but since we have a nice geometrical shape we will use the triangles and rectangles on this graph so for part a we want to calculate the work the work done for the region between zero and five meters so when the particle moves between zero and five meters we have the work to be the area under the first triangle and this is simply three newtons times five meters divided by two and so the work done over the first five meters is seven point five joules now for part b we want to calculate the work done as the particle moves between the position five meters that's a press the units here, so between 5 and 10.
02:02
Again, the work done is now the area under the rectangular portion of the graph.
02:13
And so this work is simply length times breadth.
02:18
So this is 3 newton's over a position change of 5 meters.
02:26
And this gives us the work done over this distance to be 15...