Question

Derive the transformation equations for normal strain and shear
strain acting on the inclined

plane (for 2D case)

Answer #1

A wooden block rests on an inclined wooden plane. The
significant forces acting on the block are (select all that
apply)
A. the block's acceleration.
B. the normal force that the inclined plane exerts
on the block.
C. friction.
D. air resistance.
E. the gravitational force that the inclined plane
exerts on the block.
F. the gravitational force that the Earth exerts
on the block.
G. the tension force that the inclined plane
exerts on the block.
H. another force...

The state of strain at the point has components of ϵx =
200(10−6), ϵy = -120(10^−6) and γxy = -100 (10−6).
1) Use the strain-transformation equations to determine the
in-plane principal strains.
ϵ1,,ϵ2
2) Specify the orientation of the element.
3)Determine the maximum in-plane shear strain.
4) Specify the orientation of the element.
(θs)1,(θs)2
5) Determine average normal strain. ϵavg

Find equations of the normal plane and osculating plane of the
curve at the given point
x = sin(2t), y = t, z = cos(2t)
at (0, pi, 1)

Find an equation of the tangent plane and find the equations for
the normal line to
the following surface at the given point.
3xyz = 18 at (1, 2, 3)

Find equations of the tangent plane and normal line to the
surface z+2=xeycosz at the point (2, 0, 0).

Find the equations of (i) the tangent plane and (ii) the normal
line to the surface 2(x − 2)^2 + (y − 1)^2 + (z − 3)^2 = 10, at the
point (3, 3, 5)

A) Find the equations of the tangent plane and normal line to
the graph of f(x, y) =(x/1+x2y) (1, 2).
B)Evaluate the limit or explain why it does not exist .
lim(x,y)→(0,0)
(2x2+5y)2/x4+4y2

Compute equations of tangent plane and normal line to the
surface z = x cos (x+y) at point (π/2, π/3, -√3π/4).

Find equations of the tangent plane and normal line to the
surface x=3y^2+1z^2−40x at the point (-9, 3, 2).
Tangent Plane: (make the coefficient of x equal to 1).
=0.
Normal line: 〈−9,〈−9, , 〉〉
+t〈1,+t〈1, , 〉〉.

Find equations of the tangent plane and normal line to the
surface x=2y^2+2z^2−159x at the point (1, -4, 8).
Tangent Plane: (make the coefficient of x equal to 1).
=0.
Normal line: 〈1,〈1, , 〉〉
+t〈1,+t〈1, ,

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