Question

Solve each problem. See Examples $1-4.$ A crate is supported by two ropes. One rope makes an angle of $46^{\circ} 20^{\prime}$ with the horizontal and has a tension of 89.6 Ib on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal rope.

Name: Problem 44, Chapter 8: Precalculus
Uploaded: 2021-07-26T09:03:47-08:00
Duration: 1 min 43 s
Channel: Abhishek Kumar
Description: Solve each problem. See Examples 1-4. A crate is supported by two ropes. One rope makes an angle of 46^∘ 20^' with the horizontal and has a tension of 89.6 Ib on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal rope.

   Solve each problem. See Examples $1-4.$
A crate is supported by two ropes. One rope makes an angle of $46^{\circ} 20^{\prime}$ with the horizontal and has a tension of 89.6 Ib on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal rope.

Precalculus

Margaret L. Lial,… 6th Edition

Chapter 8, Problem 44

Instant Answer

Solved by Expert Abhishek Kumar

07/26/2021

Step 1

The vertical component of the tension will be equal to the weight of the crate, and the horizontal component of the tension will be equal to the tension in the horizontal rope. Show more…

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Solve each problem. See Examples $1-4.$ A crate is supported by two ropes. One rope makes an angle of $46^{\circ} 20^{\prime}$ with the horizontal and has a tension of 89.6 Ib on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal rope.

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Key Concepts

Trigonometric Functions

Trigonometry is used to relate the angles and magnitudes of forces, translating the given force magnitude and angle into horizontal and vertical components. Functions such as sine and cosine are applied to compute these components accurately, making them integral in solving problems involving forces at an angle.

Static Equilibrium

Static equilibrium refers to a condition where all the forces acting on an object cancel each other out, resulting in no acceleration. Recognizing equilibrium is crucial for setting up equations that accurately relate the sum of forces in each direction to zero, which is used to determine unknown forces or tensions.

Vector Decomposition

When forces act at an angle, it is essential to break them down into horizontal and vertical components. This is done using trigonometric functions, allowing each component to be analyzed independently, especially in systems where forces act in different directions.

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