# Engineering Mechanics

**Situation**

The three-hinged arch shown below is loaded with symmetrically placed concentrated loads as shown in the figure below.

The loads are as follows:

$$P_1 = 90 ~ \text{kN} \qquad P_2 = 240 ~ \text{kN}$$

The dimensions are:

$$H = 8 ~ \text{m} \qquad S = 4 ~ \text{kN}$$

Calculate the following:

**1.** The horizontal reaction at *A*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

**2.** The total reaction at *B*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

**3.** The vertical reaction at *C*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

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**Problem**

A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

A. 74.95 m/sec^{2} |
C. 49.57 m/sec^{2} |

B. 94.75 m/sec^{2} |
D. 59.47 m/sec^{2} |

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**Problem**

What is the angle between zero-based vectors ${\bf V_1} = (-\sqrt{3}, ~ 1)$ and ${\bf V_2} = (2\sqrt{3}, ~ 2)$ in an *x*-*y* coordinate system?

A. 0° | C. 150° |

B. 180° | D. 120° |

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**Problem**

Compute the value of *b* if **A** and **B** are orthogonal.

$${\bf A} = 2{\bf i} + b{\bf j} + {\bf k}$$

$${\bf B} = 4{\bf i} - 2{\bf j} - 2{\bf k}$$

A. 6 | C. 4 |

B. 5 | D. 3 |

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**Problem**

A catapult is placed 100 ft from the castle wall, which is 35 feet high. The soldier wants the burning bale of hay to clear the top of the wall and land 50 feet inside the castle wall. If the initial velocity of the bale is 70 feet per second, then at what angle should the bale of hay be launched so that it travel 150 feet and pass over the castle wall. Use *g* = 32 ft/sec^{2}.

A. 49.8° | C. 39.2° |

B. 50.8° | D. 40.2° |

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**Situation**

Diagonals *BG*, *CF*, *CH*, and *DG* of the truss shown can resist tension only.

If *W* = 3 kN and *P* = 0, find the following:

1. the force in member *CF*.

A. 4.76 kN | C. 4.67 kN |

B. 4.32 kN | D. 4.23 kN |

2. the force in member *BF*.

A. 3.2 kN | C. 3.4 kN |

B. 3.3 kN | D. 3.5 kN |

3. the force in member *DH*.

A. 2.8 kN | A. 2.5 kN |

B. 2.8 kN | D. 2.7 kN |

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**Situation**

Flexible cables *BE* and *CD* are used to brace the truss shown below.

1. Determine the load *W* to cause a compression force of 8.9 kN to member *BD*.

A. 7.80 kN | C. 26.70 kN |

B. 35.64 kN | D. 13.35 kN |

2. Which cable is in tension and what is the tensile reaction?

A. BE = 12.58 kN |
C. BE = 6.29 kN |

B. CD = 6.29 kN |
D. CD = 12.58 kN |

3. If *W* = 20 kN, what will be the tensile reaction of member *CE*?

A. 6.67 kN | C. 0 |

B. 13.33 kN | D. 10 kN |

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