# (ENGR-1100) – Fall 15 NAME - Rensselaer Polytechnic Institute

```RENSSELAER POLYTECHNIC INSTITUTE
TROY, NY
EXAM NO. 2 INTRODUCTION TO ENGINEERING ANALYSIS
(ENGR-1100) – Fall 15
NAME:
Section: ___________
RIN:
_______________________________
Wednesday, October 21, 2015
8:00 – 9:50
Please state clearly all assumptions made in order for full credit to be given.
Problem
Points
1
25
2
25
3
25
4
25
Total
100
Score
Problem #1 (25)
Consider the following matrices
−5 0 −2
8 8 3
5 5 −7
Determine the following expressions. If an expression is not valid, STATE THE REASON.
=
0 −9
5 −7
=
6 −2
6 0
=
−1 0 0
5 −7 6
=
(a)
+
(b)
−2
(c) det( ) and
(d)
(e) det( ) using the duplicate column method
(4)
(4)
(5)
(9)
(3)
Note: show all steps.
(a)
(b)
(c)
(d)
(e)
Problem #2 (25)
A lamp weighs 120 N and is supported by two cables AB and AC and a pole OA. The force in
the pole acts along the axis of the pole.
(a) Identify the particle to be analyzed (1).
(b) Draw complete and separate Free-body diagram for the particle (5).
(c) Express all forces in Cartesian vector form (7)
(d) Write Equations-of-Equilibrium for the particle (9).
(e) Determine the magnitudes of tensions in AB and AC and the support force along pole OA (3).
Value
TAB =
TAC =
FOA =
Free-body diagram:
Unit
Problem #3 (25)
The pipe assembly is subject to forces and couple moments as shown.
(a) Determine the magnitude of moment of F1 about the pipe segment CD (5).
(b) Replace the force-couple system by equivalent resultant force and couple moment at O (17).
(c) Can this system be reduced to a single result force? Explain. (3).
Value
(a) M1CD =
(b) FR =
CR =
(c) Yes/No (check 1) Explain:
unit
Problem #4 (25)
A ship’s loading ramp has mass of 120 kg and a center of
gravity at G. The ramp is attached to the ship at A by a
smooth pin. The cable CD provides just enough force that
the reaction at B is zero.
a. Draw a complete and separate FBD of the ramp.(5)
b. Write the equations of equilibrium for the ramp.
(10)
c. Solve the equations to determine the unknown
reactions at A and C.
(10)
2m
1m
1.5 m
(b)
(c)
```