please help--I don't understand how to get started!
A small particle of mass 2.0 x 10^-19 kg is attached to a nanofiber of relaxed length 0.50 nm (Recall that 1.0 nm = 10^-9 m) . The nanofiber is attached to a substrate (an immovable wall). The plot is a graph of the force needed to stretch the nanofiber by pulling to the right on it. Call that the length of the nanofiber for simplicity.
a) calculate the force constant-the “spring constant” k for this nanofiber.
b) assume that the nanofiber is stretched to a total length of x = 3.0 nm and released from rest. Then the particle will move back and forth along the x direction. Use your k from part a to compute the maximum speed of the particle as it oscillates back and forth.
No plot is shown with your question. The slope of the Force (F) vs Stretch (X) line is the spring constant k.
Get the maximum speed (Vmax) from conservation of energy as follows
(1/2) k Xmax^2 = (1/2) M Vmax^2
The Xmax in this case is 3.0 - 0.5 = 2.5 nm. That is a lot of stretching compared to the original length. I am surprised that it would not break first. Few, if any, materials will remain elastic (linear) and not break when stretched to 6 times their original length.