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Ch. 7 - Applications of Trigonometry and Vectors
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 12th EditionCh. 7 - Applications of Trigonometry and Vectors문제 39
8장, 문제 39

To build the pyramids in Egypt, it is believed that giant causeways were constructed to transport the building materials to the site. One such causeway is said to have been 3000 ft long, with a slope of about 2.3°. How much force would be required to hold a 60-ton monolith on this causeway?


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검증된 단계별 안내
1
Identify the forces acting on the monolith on the inclined causeway. The main force to consider is the component of the monolith's weight pulling it down the slope due to gravity.
Convert the weight of the monolith from tons to pounds (or another consistent unit) if necessary, since force is typically measured in pounds or newtons. For example, 1 ton = 2000 pounds, so multiply 60 tons by 2000 to get the weight in pounds.
Calculate the component of the weight acting parallel to the slope using the formula: \(F = W \times \sin(\theta)\), where \(W\) is the weight of the monolith and \(\theta\) is the slope angle (2.3°).
Use the sine of the slope angle to find the force pulling the monolith down the causeway. This force is the amount of force required to hold the monolith in place (i.e., to prevent it from sliding down).
Express the final force value as the force required to hold the monolith stationary on the slope, which balances the downhill component of the weight.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Inclined Plane and Slope Angle

An inclined plane is a flat surface tilted at an angle to the horizontal. The slope angle determines how gravity affects objects on the plane, influencing the component of gravitational force acting along the slope. Understanding this helps calculate forces like the force needed to hold or move an object on the incline.
추천 영상:
04:46
Coterminal Angles

Decomposition of Forces on an Incline

When an object rests on an inclined plane, its weight can be split into two components: one perpendicular to the surface and one parallel to it. The parallel component causes the object to slide down, calculated as weight times the sine of the slope angle. This component is crucial for determining the force required to hold the object in place.
추천 영상:
3:22
Example 2

Conversion of Units and Weight Calculation

Weight is the force due to gravity acting on a mass, calculated as mass times gravitational acceleration. Converting tons to pounds or kilograms and using the correct gravitational constant is essential for accurate force calculations. This ensures the force to hold the monolith is expressed in consistent units.
추천 영상:
06:11
Introduction to the Unit Circle
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