14.8 Lagrange Multipliers
In this section, we learn Lagranges method for maximizing or minimizing a general function f (x, y) subject to a
constraint of the form g(x, y) = k.
We seek the extreme values of f when the point is restricted to lie on the level
14.8 Lagrange Multipliers
In this section, we learn Lagranges method for maximizing or minimizing a general function f ( x, y ) subject to a
constraint of the form g ( x, y) k .
We seek the extreme values of f when the point is restricted to lie on the le
Math 1226 Written Homework 4
Name:
Print, complete and hand in at the start of class on WEDNESDAY (February 24). You must show
work to receive credit.
Z
1. Simplify x2 (9x2 4)3/2 dx using an appropriate trigonometric substitution. DO NOT EVALUATE
the int
ESM 2204 Mechanics of Deformable Bodies
Axial Load
Stress Transformation
Normal Stress and Strain, Hookes Law
Plane Stress (2-D)
0
=
=
Displacement
Z
X
()
=
=
=
0 ()
X
= =
+
+
cos 2 + sin 2
2
2
0 0 =
sin 2 + cos 2
2
Principal Stress
ESM 2104
Statics
Mock Test 1
Name:_
Sign the following pledge:
I have neither given nor received unauthorized aid on this exam.
_
Time allowed: 50 minutes
Closed book, but you may use one 8.5x 11" formula sheet (one side only).
You should attempt to answe
Homework No. 1 Due Wednesday, 1/25
(1) A ball is tossed upward vertically from A and it lands on the top of the cliff
B as shown. If it takes the ball 5 seconds to reach point B, determine the
impact speed vB.
Ans: vB = 70.5 ft/sec
(2) 2/11
Ans: v2 = 139.
Homework No. 5 Due Wednesday, 2/8
(1) A football player releases a ball with the initial velocity
shown. Determine the radius of curvature of the trajectory and
the time rate of change of the speed (a) just after release (b) at
the apex, and (c) 2 seconds
Homework No. 2 Due Friday, 1/27
(1) A particle is moving along a straight line and during an interval of its motion its
velocity is related its position as v2 = k/s where k is a constant. If v = 2 in/sec at s = 9 in
when t = 0, determine the velocity of t
Homework No. 3 Due Wednesday, 2/1
(1) A particle is moving along a curved path that is defined by xy2 = 100 where x and y
are positive and measured in inches. During one part of the motion the particle is
observed to move with a constant velocity of 5 in/
Homework No. 4 Due Friday, 2/3
(1) 2/93
Ans: 50.7
Note: You must show numerical calculations to confirm that there is only one
acceptable angle.
(2) 2/97
Ans: 6.77 m/s2
(3) 2/106
Ans: 266 m
Note: The given 2 m/s2 is the trains total acceleration.
(4) The
3-D Moment Moment about a point and moment about an arbitrary line
1. The rigid pole and cross-arm assembly is attached to three cables as shown. The tension in cable CD acting on
point C is T =1.2 kN. (a) Determine the moment of the tension force about p
3-D Force Rectangular components
1. A force of magnitude F = 3.5 kN is applied to a machine part as shown. Express F as a vector. Also determine
the angle between the force vector and +y-axis.
Ans: F =3.03i 1.341 j 1.125k kN, y = 112.5
2. The 900 N force
3-D Force Projection onto an arbitrary line
1. The tension in cable AB is T = 1750 lb acting on point A. Determine the projection of the tension force onto line
CD. Also express the projection as a vector.
96.0i 332 j 384k lb
Ans: TCD = 517 lb, TCD =
2. D
ESM 2304 Dynamics of Particles and Rigid Bodies
TEST 1 September 22, Fall 2016
Last Name _ First Name_
Pledge: I have neither given nor received any unauthorized aid on this test.
Signature _KEY_
Please circle your lecture session:
MWF 11:15 AM
TR 8 AM
Sh
ESM 2304 Dynamics of Particles and Rigid Bodies
TEST 2 October 25, Fall 2016
Last Name _ First Name_
Pledge: I have neither given nor received any unauthorized aid on this test.
Signature _KEY_
Please circle your lecture session:
MWF 11:15 AM
TR 8 AM
Show
ESM 2304 Dynamics of Particles and Rigid Bodies
TEST 3 November 17, Fall 2016
Last Name _ First Name_
Pledge: I have neither given nor received any unauthorized aid on this test.
Signature _KEY_
Please circle your lecture session:
MWF 11:15 AM
TR 8 AM
Sho
ESM 2304 Dynamics of Particles and Rigid Bodies
TEST 4 December 5, Fall 2016
Last Name _ First Name_
Pledge: I have neither given nor received any unauthorized aid on this test.
Signature _KEY_
Please circle your lecture session:
MWF 11:15 AM
TR 8 AM
Show
ESM 2104 Statics
TEST 1 September 26, Fall 2016
Last Name _ First Name_
Pledge: I have neither given nor received any unauthorized aid on this test.
Signature _KEY_
Please circle your lecture session:
MWF 9:05 AM
TR 9:30 AM
PART I: No partial credit. You
ESM 2104 Statics
TEST 2 October 24, Fall 2016
Last Name _ First Name_
Pledge: I have neither given nor received any unauthorized aid on this test.
Signature _KEY_
Please circle your lecture session:
MWF 9:05 AM
TR 9:30 AM
PART I: No partial credit. You mu
ESM 2104 Statics
TEST 3 November 15, Fall 2016
Last Name _ First Name_
Pledge: I have neither given nor received any unauthorized aid on this test.
Signature _KEY_
Please circle your lecture session:
MWF 9:05 AM
TR 9:30 AM
PART I: No partial credit. You m
ESM 2104 Statics
TEST 3 November 15, Fall 2016
Last Name _ First Name_
Pledge: I have neither given nor received any unauthorized aid on this test.
Signature _KEY_
Please circle your lecture session:
MWF 9:05 AM
TR 9:30 AM
PART I: No partial credit. You m
ESM 2104 Statics
Exam 1
NAME: 50 (mlion
Sign the following pledge:
I have neither given nor received unauthorized aid on this exam. Problem 1 (15 pts)
The vertical force F acts downward at A on the two-membered frame. Determine the magnitudes of the two
c