Es230 Assignment 4

Assignment 3 ES230

Key solutions

Problem 3.1

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| |A 90-N force is applied to the control rod AB as shown. Knowing that the length of the rod is |
| |225 mm, determine the moment of the force about point B by resolving the force into components |
| |along AB and in a direction perpendicular to AB. |
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[pic]

Problem 3.5

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| |A 2.9-lb force P is applied to the lever which controls the auger of a snowblower.
Determine the|
| |value of [pic] knowing that the moment of P about A is counterclockwise and has a magnitude of |
| |17 [pic] |
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Solution 5.
| | |
| |By definition [pic] |
| |where [pic] |
| |and [pic] |
| |[pic] |
| |Also [pic]
|
| |[pic] |
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| | |
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|Then [pic] |
|or [pic] |
|or [pic] |
|[pic] |

Problem 3.10

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|[pic] |It is known that a force with a moment of [pic] about D is required |
| |to straighten the fence post CD. If [pic] in., [pic] in., and |
| |[pic] in., determine the tension that must be developed in the cable of winch puller AB to |
| |create the required moment about point D. |

[pic]

Problem 3.23

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| |Before a telephone cable is strung, rope BAC is tied to a stake at B and is passed over a pulley|
| |at A. Knowing that portion AC of the rope lies in a plane parallel to the xy plane and that the |
| |magnitude of the tension T in the rope is 62 lb, determine the moment about O of the resultant |
| |force exerted on the pulley by the rope. |
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[pic]

Problem 3.25

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| |In an arm wrestling contest, a 150-lb force P is applied to the hand of one of the contestants |
| |by his opponent. Knowing that AB = 15.2 in. and |
| |BC = 16 in., determine the moment of the force about C. |
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[pic]

Chapter 3, Problem 28.

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| |In Prob. 3.23, determine the perpendicular distance from point O to portion AC of rope BAC. |
| |Problem 3.23: Before a telephone cable is strung, rope BAC is tied to a stake at B and is passed|
| |over a pulley at A. Knowing that portion AC of the rope lies in a plane parallel to the xy plane|
| |and that the magnitude of the tension T in the rope is 62 lb, determine the moment about O of |
| |the resultant force exerted on the pulley by the rope. |
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Chapter 3, Solution 28.

| | |
| |Have [pic] |
| |where [pic] Perpendicular distance from O to rope [pic] |
| |with [pic] |
| |and [pic] |
| |[pic] |
| |[pic] |
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|Then |
|[pic] |
|[pic] |
|and [pic] |
|[pic] |
|[pic] |
|or [pic] |

Problem 37

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| |Three cables are used to support a container as shown. Determine the angle formed by cables AB |
| |and AD. |
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[pic]

Problem 46.

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| |The rectangular platform is hinged at A and B and is supported by a cable that passes over a |
| |frictionless hook at E. Knowing that the tension in the cable is 1349 N, determine the moment |
| |about each of the coordinate axes of the force exerted by the cable at D. |
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[pic]

Problem 58

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|[pic] |A rectangular tetrahedron has six edges of length a. (a) Show that two opposite edges, such as |
| |OA and BC, are perpendicular to each other. |
| |(b) Use this property and the result obtained in Prob. 3.57 to determine the perpendicular |
| |distance between edges OA and BC. |

[pic]