In class you had said that the area of the sliding distance will equal the area under the rectangle (that we know how to calculate). For one of the trials our rubber band had a pull back of -6.5, a force of 0.5, and a sliding distance of 17 cm. I calculated the area to be 1.625 cm* N. I know the area for the sliding distance would be the same but how do I calculate it with these numbers.
Excellent question.
1.625 cm * N, rounded off to 1.6 N * cm because your estimate of the area under a curving graph won't be accurate to more than 2 significant figures, is about right for the work under the first graph, according to your figures.
The area under the rectangle representing frictional force for a sliding distance of 17 cm should therefore be -1.6 N * cm. The frictional force is nearly constant, so the region would be a rectangle. Its dimensions would be f_friction * 17 cm, where f_friction stands for the frictional force.
So f_friction * 17 cm = -1.6 N * cm.
Solving for f_friction we get
f_friction = -1.6 N * cm / (17 cm) = -.093 N, approximately.
We'll go over this in class.