RENSSELAER POLYTECHNIC INSTITUTE



RENSSELAER POLYTECHNIC INSTITUTE

TROY, NY

EXAM NO. 2 INTRODUCTION TO ENGINEERING ANALYSIS

(ENGR-1100)

Solutions

NAME: ______________________________ SECTION: _________

ID: _______________________________ March 24, 2004

INSTRUCTOR: _______________________________

| | | |

|Problem |Points |Score |

| | | |

|1 |25 | |

| | | |

|2 |25 | |

| | | |

|3 |25 | |

| | | |

|4 |25 | |

| | | |

|Total |100 | |

| | | |

Problem 1 (25 Points)

Two bodies weighing 150 lb and 200 lb, respectively, rest on a cylinder and are connected by a rope as shown in the figure. Find:

the reactions of the cylinder on the bodies

the tension in the rope

and the angle (.

Assume all surfaces to be smooth.

[pic]

Solution:

From a free-body diagram for body 1:

(a) + ( [pic]

(b) + ([pic]

From a free-body diagram for Body 2:

(c) + ( [pic]

(d) + ( [pic]

From Eqs. (a) and (d): [pic]

From Eqs. (b) and (c): [pic] lb

Therefore: [pic] Ans.

With ( = 36.87(:

Egs. (a) and (b) yield: T = 120.0 lb Ans.

F1 = 160.0 lb Ans.

Eqs. (c) and (d) yield: F2 = 90.0 lb Ans.

Problem 2 (25 Points)

Column AB in the figure can support a maximum axial compressive force of 7500 N. Set-up the equilibrium equations that would need to be solved in order to determine the tensions in each of the cables when this level of load exists in the column (there is no need to solve the system of equations).

Solution:

[pic](0.3865 [pic] - 0.1932 [pic] - 0.9018 [pic]) FC

[pic] (-0.3769 [pic] - 0.5384 [pic] - 0.7537 [pic]) FD

[pic] (-0.2540 [pic] + 0.3810 [pic] - 0.8890 [pic]) FE

FB = 7500 [pic]

[pic]

= (0.3865 FC - 0.3769 FD - 0.2540 FE) [pic]

+ (-0.1932 FC - 0.5384 FD + 0.3810FE) [pic]

+ (-0.9018 FC - 0.7537 FD - 0.8890 FE + 7500) [pic]= 0

Thus:

0.3865 FC + 0.3769 FD - 0.2540 FE = 0

-0.1932 FC + 0.5384 FD - 0.3810FE = 0

-0.9018 FC - 0.7537 FD - 0.8890 FE = - 7500

Problem 3 (25 Points)

A 2500-lb jet engine is suspended from the wing of an airplane as shown in the figure. Determine the moment produced by the engine at point A in the wing when the plane is:

a. On the ground with the engine not operating.

b. In flight with the engine developing a thrust T of 15,000 lb.

Solution:

(a) [pic]

= 11,472 [pic] ft ( lb [pic] 11.47 ft ( kip Ans.

(b) [pic]

= -86,827 [pic] ft ( lb [pic] -86.8 ft ( kip Ans.

Problem 4 (25 Points)

Three couples are applied to a bent bar as shown in the figure. Determine:

a. The magnitude of the resultant couple C and the direction angles (θx, θy, θz) associated with the resultant couple vector.

b. The scalar component of the

resultant couple C about line OA.

Solution:

(a) For the 125-lb forces:

[pic]

For the 100-lb forces:

[pic]

For the 150-lb forces:

[pic]

[pic] = - 2950 [pic] - 2000 [pic] in. ( lb

C = [pic] 3564 in. ( lb [pic] 3.56 in. ( kip Ans.

[pic] Ans.

[pic] Ans.

[pic] Ans.

(b) [pic]

[pic] = - 2561 in. ( lb [pic] -2.56 ft ( kip Ans.

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