EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137569830
Author: HIBBELER
Publisher: VST
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Chapter 2, Problem 22FP
To determine
The expression of force as a Cartesian
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In MATLAB write out a program to integrate the equations of motion of a rigid body. The inertia matrix is given by I = [125 0 0; 0 100 0; 0 0 75] which is a diagonal, where diag operator provides a matrix with given elements placed on its diagonal. Consider three cases where the body rotates 1 rad/sec about each principal axis. Integrate the resulting motion and study the angular rates and the resulting attitude (use any attitude coordinates). For each principal axis case, assume first that a pure spin about the principal axis is performed, and then repeat the simulation where a small 0.1 rad/sec motion is present about another principal axis. Discuss the stability of each motion. The code should produce a total of 6 simulations results when it is ran.
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A strain gauge rosette that is attached to the surface of a stressed component
C). If the strain gauge rosette is of the D°
gives 3 readings (a = A, b = B, &c =
type (indicating the angle between each of the gauges), construct a Mohr's Strain
Circle overleaf. You should assume that gauge A is aligned along the x-axis.
Using the Mohr's Strain Circle calculate the:
[10 marks]
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(i) principal strains (1, 2)?
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[5 marks]
(ii) principal angles (1, 2)?
You should measure these anticlockwise from the y-axis.
20
[5 marks]
(iii) maximum shear strain in the plane (ymax)?
Ex = Ea
Ey = εc
[5 marks]
(epol)
(apob) é
Ea = A = -210
2
B=E₁ = -50
E₁ = C = 340
D = 45°
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1)
Solve and show which is converage or diyverage
a = 2+(0.1)"
3
16) a =
n
1-2n
2)
a
=
In n
1+2n
17) a =
n
1-5n4
3)
an
=
n* +8n³
18) a =√4"n
n² -2n+1
n!
20) a =
4)
a₁ =
10
n-1
(Ina)
5)
a=1+(-1)"
21) a=
6)
a
7)
an
=
* = (12+) (1-1)
2n
(-1)+1
2n-1
3n+1
22) a=
3n-1
x"
23) a=
.x>0
2n+1
2n
3"x6"
8) a =
24) a =
n+1
π
9)
a = sin
2
sin n
10) an =
n
+
2 x n!
25) a = tanh(n)
n²
1
26) a = -sin-
2n-1
27) a = tan(n)
n
n
11) a =
2"
12) a =
n
13) a = 8/
+=(1+2)"
14) a =
15) a = √10n
In(n+1)
29) a =
n
30) an-√n²-1
1
28) a =
+
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(In n)200
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31) a=-
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nix
Chapter 2 Solutions
EBK ENGINEERING MECHANICS
Ch. 2 - Determine the magnitude of the resultant force...Ch. 2 - Two forces act on the hook. Determine the...Ch. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Resolve the 30-lb force into components along the...Ch. 2 - The force F = 450 lb acts on the frame. Resolve...Ch. 2 - If force F is to have a component along the u axis...Ch. 2 - Determine the magnitude of the resultant force FR...Ch. 2 - Resolve the force F1 into components acting along...Ch. 2 - Resolve the force F2 into components acting along...Ch. 2 - Prob. 10P
Ch. 2 - Determine the angle for connecting member A to...Ch. 2 - Determine the magnitude and direction of the...Ch. 2 - Determine the magnitude and direction of the...Ch. 2 - Determine the magnitude and direction of FA SO...Ch. 2 - If the resultant force of the two tugboats is 3...Ch. 2 - If FB = 3 kN and = 45, determine the magnitude of...Ch. 2 - If the resultant force of the two tugboats is...Ch. 2 - Resolve each force acting on the post into its x...Ch. 2 - Determine the magnitude and direction of the...Ch. 2 - Prob. 9FPCh. 2 - If the resultant force acting on the bracket is to...Ch. 2 - If the magnitude of the resultant force acting on...Ch. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Resolve each force acting on the gusset plate into...Ch. 2 - Determine the magnitude of the resultant force...Ch. 2 - Prob. 39PCh. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Express F1, F2, and F3 as Cartesian vectors.Ch. 2 - Prob. 43PCh. 2 - Determine the magnitude and orientation of FB so...Ch. 2 - Prob. 48PCh. 2 - Express F1, F2, and F3 as Cartesian vectors.Ch. 2 - Prob. 56PCh. 2 - If the resultant force acting on the bracket is...Ch. 2 - Prob. 58PCh. 2 - If F = 5 kN and = 30, determine the magnitude of...Ch. 2 - Determine the coordinate direction angles of the...Ch. 2 - Prob. 14FPCh. 2 - Prob. 15FPCh. 2 - Prob. 16FPCh. 2 - Prob. 17FPCh. 2 - Prob. 18FPCh. 2 - Prob. 61PCh. 2 - Prob. 66PCh. 2 - Determine the magnitude and coordinate direction...Ch. 2 - Specify the magnitude and coordinate direction...Ch. 2 - Prob. 73PCh. 2 - Prob. 74PCh. 2 - Prob. 75PCh. 2 - Prob. 77PCh. 2 - Prob. 79PCh. 2 - Prob. 81PCh. 2 - Prob. 82PCh. 2 - If the direction of the resultant force acting on...Ch. 2 - Express the position vector rAB in Cartesian...Ch. 2 - Prob. 20FPCh. 2 - Express the force as a Cartesian vector. Prob....Ch. 2 - Prob. 22FPCh. 2 - Prob. 23FPCh. 2 - Prob. 24FPCh. 2 - Determine the length of the connecting rod AB by...Ch. 2 - Prob. 88PCh. 2 - Prob. 90PCh. 2 - Prob. 91PCh. 2 - Determine the magnitude and coordinate direction...Ch. 2 - Prob. 98PCh. 2 - Prob. 25FPCh. 2 - Determine the angle between the force and the...Ch. 2 - Prob. 27FPCh. 2 - Prob. 28FPCh. 2 - Find the magnitude of the projected component of...Ch. 2 - Prob. 30FPCh. 2 - Determine the magnitudes of the components of the...Ch. 2 - Determine the components of F that act along rodAC...Ch. 2 - Determine the magnitudes of the components of F =...Ch. 2 - Prob. 111PCh. 2 - Prob. 112PCh. 2 - Determine the angle between the two cables...Ch. 2 - Determine the angle between the cables AB and AC....Ch. 2 - Determine the magnitude of the projected component...Ch. 2 - Determine the magnitude of the projected component...Ch. 2 - Determine the magnitudes of the projection of the...Ch. 2 - Determine the magnitude of the resultant force FR...Ch. 2 - Prob. 5RPCh. 2 - Prob. 6RPCh. 2 - Prob. 7RPCh. 2 - Prob. 8RP
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