RENSSELAER POLYTECHNIC INSTITUTE TROY, NY

FINAL EXAM -- Makeup -- INTRODUCTION TO ENGINEERING ANALYSIS (ENGR-1100)

NAME: ______________________________ Section: ___________ RIN: _______________________________

Monday, May 7th, 2017

Problem Points

Score

1

20

2

20

3

20

4

20

5

20

6

20

Total

100

N.B.: You will be graded on 5 problems, 20 points per problem. Problems 1, 2, and 3 are mandatory and

will be graded. Before turning in your exam, please make sure you have circled the two problems you want to be graded out of problems 4, 5 and 6.

You may write on the front and back of each sheet Clearly show all steps and state all assumptions made in order for full credit to be given.

Circle your section below:

Sections Days Start End Instructor 1 M R 8:00 AM 9:50 AM Uchida 2 M R 12:00 PM 1:50 PM Taylor 3 M R 2:00 PM 3:50 PM Taylor 4 TF 12:00 PM 1:50 PM Scott 5 TF 2:00 PM 3:50 PM Dobry

Problem #1 (20 points) The toggle clamp is subjected to the force F = 100 N at F in the indicated direction. There is no horizontal force at the handle E.

(a) Identify two-force member(s). (2 pts) (b) Determine the reaction forces at A, B and C and the vertical force, Ey, at E. (18 pts)

You must show two separate free body diagrams (4 pts) and write down equations of equilibrium for each free body diagram. (8 pts)

Problem #2 (20 points) Consider the following linear equations:

3𝑥 + 2𝑦 − 2𝑧 = 5

5𝑥 + 3𝑦 − 4𝑧 = −2

4𝑥 + 2𝑦 − 3𝑧 = −1

A) Write these equations in the form 𝑨𝑿 = 𝑩. (1 pt) B) Find the cofactor matrix for 𝑨. (10 pts) C) Find the adjoint of 𝑨. (2 pts) D) Find 𝑨 𝟏 using the adjoint of 𝑨. (3 pts) E) Solve for 𝑦 using Cramer’s Rule. (4 pts)

Problem #3 (20 points)

The drum has a weight of 100 lb and rests on the floor for which the coefficient of friction is μ = 0.6. If a = 2 ft and b = 3 ft:

a) Draw the FBD and determine the value of the force P that corresponds to impending motion by tipping. (8 pts)

b) Draw the FBD and determine the value of the force P that corresponds to impending motion by sliding. (10 pts)

c) Determine the value of P at which the drum starts moving. (2 pts)

Problem #4 (20 points)

The weight of block A in the figure is 2500 N. Block A is supported by a small frictionless wheel that is free to roll on the continuous cable between supports B and C. The length of the cable is 42 m.

a) Draw the FBD for the wheel. (4 pts) b) Using force equilibrium, obtain the relation between the angles formed by the cable and the horizontal.

(3 pts) c) Calculate the values of these angles. (3 pts) a) Calculate the distance x shown in the figure. (5 pts). b) Calculate the tension T in the cable. (5 pts)

Problem #5 (20 Points)

Given a lamp that weighs 48 lbs. hanging from three ropes, as pictured. Point D is located at (2.2,2.3,-2.5) ft. Point B is located on vertical plane xz, and Point C is located on vertical plane yz.

a. Draw a FBD for particle D. (4 pts) b. Express all the forces acting on particle D in Cartesian Vector Form. (7 pts) c. Write Equations of Equilibrium for that particle. (6 pts) d. Determine the force in the cables that extend from D to points A, B, and C. (3 pts)

Notes: You may use your calculator to solve the equations that are set up in part d. Also, point D is located 1.5 feet below the plane defined by the X and Y axes.

Problem #6 (20 points)

For the truss shown, find:

A.) The reactions at supports A and E. (4 pts) B.) The zero force members, if any. (2 pts) C.) The forces in members AB, AH, and BH using method of joints. (6 pts) D.) The forces in members CD, CF, and GF using method of sections (use only one section). (8 pts)