Consider the curve a2=2-2 (a) (3 points) Find the 1st derivative, diz of the curve. (b) (3

Consider the curve a²2²=2²-2³
(a) (3 points) Find the 1st derivative, diz of the curve.
(b) (3 points) Find the 2nd derivative, /ar of the curve.
Continue considering the curve zy²-²-y" (like we did in Question 1).
(a) (1 points) Find, using any means you please, a point (r, y) on the curve other than the point (0.0).
Round each coordinate to 4 decimal places. Show (numerically) that the point satisfies the equation.
(b) Calculate the curvature of the equation at the point you found for Part (a).
(c) Find the equation for circle of curvature for the point you found in Part (a).
Have Desmos (or other software) draw the graph, your point, and the circle of curvature. Make sure.
it shows the point, and is zoomed to clearly show the details of the circle and the curve near the
po
Suppose we have a uniform beam that is 60 centimetres long, and is simply supported at both ends.
If the beam has a load of f(x) = 11 / applied to it, and has a flexural rigidity of 10,000 Nm², then:
(a)  Calculate the deflection function y(r) for this beam assuming small deflections.
(b) Find the maximum (magnitude of) deflection for the beam (and where that deflection
occurs).

For the beam in Question 3, suppose that instead of the simple support on the right end, we instead have
a fixed support instead.
(a) (3 points) Calculate the deflection function y(r) for this beam assuming small deflections.
Hint: you can use your solution from Question 3 with the different boundary conditions.
(b) (3 points) Which of the two beams has the larger maximum (magnitude of) deflection, and by how
much (assuming small deflections)?
More questions on the next page
 Suppose I have a plastic ruler and I bend it so that it forms the shape of a hyperbolic
cosine (that is, it makes the same shape as the graph y = cosh after I have bent it). If the absolute value
of the curvature of the ruler is greater than I at any point, then the ruler will break.
For the purposes of this question, assume that is measured in metres.
(a) (3 points) Calculate the curvature equation for the bent ruler.
(b) (3 points, Challenge) Answer all the following (they combine to form a single question):
. If the ruler after being bent-has takes up the space between=0). and = 1, then how long
is the ruler?