Spring and Work Question

[Jacko1394]

The answers say its 0.28J, but im not sure why it's not 0.56
at 6cm = 12N and at 8cm = 16N
12+16 = 28 (which is like the answer, 0.28)
but 2cm (difference between 6 and 8cm) is equal to 0.02m
and since work is force*distance shouldn't the answer be 0.56J??
any help is much appreciated

[Phy124]

The work done is given by the area under a Force x Extension graph.

Since we want the the work done in stretching the spring between 6.0 cm and 8.0 cm we need to calculate the area under the curve between these two points.

This can be done in multiple ways. I'll show you two.

1) Calculating the triangular area under the graph between 0 and 8 and subtracting the triangular area under the graph between 0 and 6.
2) Calculating the rectangular area and the triangular area between 6 and 8.



Let's say we used "1)", the "y" value at the top of the orange triangle will be 16 N (as the gradient of the graph is 2) and "x" value  will be the change in length, 8cm which is 0.08m. The "y" value top of the yellow triangle will be 12 N and "x" will be the change in length 6cm which is 0.06m.

Therefore;







Alternatively, using option "2)";

The "y" value at the top of the rectangle will be 12 N and the change in length will be 2cm which is 0.02m. The "y" value at the top of the triangle will be 16 N and given that the bottom of it is 12 N, the height of the triangle will be 4 N. Similarly to the rectangle the change in length will be 0.02m.

Therefore;