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A meter stick with a mass of 0.57 kg is held perpendicular to a vertical wall by a cord of length d= 1.8 m attached to the end of the meter stick and also to the wall above the other end of the meter stick. (a) Determine the tension in the cord. 5.01 x Where is a good point about which to take the torques? Which condition of equilibrium will allow us to write an expression that will allow us to determine the tension in the cord? See if you can obtain an expression for the tension T in the cord in terms of the mass m of the meter stick, the acceleration due to gravity g, and the angle between the direction of the force and displacement vector. Be careful which angle you use when writing an expression for the torque due to the tension in the cord. N (b) Will the tension in the cord will be greater than, less than, or the same as that found in part (a) if the string is shortened? To clarify, when the string is shortened, the location where the string is attached to the wall is lowered so that the meter stick remains horizontal. greater than O less than the same as X

A meter stick with a mass of 0.57 kg is held perpendicular to a vertical wall by a cord of length d= 1.8 m attached to the end of the meter stick and also to the wall above the other end of the meter stick. (a) Determine the tension in the cord. 5.01 x Where is a good point about which to take the torques? Which condition of equilibrium will allow us to write an expression that will allow us to determine the tension in the cord? See if you can obtain an expression for the tension T in the cord in terms of the mass m of the meter stick, the acceleration due to gravity g, and the angle between the direction of the force and displacement vector. Be careful which angle you use when writing an expression for the torque due to the tension in the cord. N (b) Will the tension in the cord will be greater than, less than, or the same as that found in part (a) if the string is shortened? To clarify, when the string is shortened, the location where the string is attached to the wall is lowered so that the meter stick remains horizontal. greater than O less than the same as X

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Educational Content on Torque and Equilibrium **Problem Statement:** A meter stick with a mass of 0.57 kg is held perpendicular to a vertical wall by a cord of length \( d = 1.8 \, \text{m} \) attached to the end of the meter stick and also to the wall above the other end of the meter stick. #### (a) Determine the tension in the cord. **Student Input:** - Answer submitted: **5.01** - Result: **Incorrect** **Instructor Note:** - Consider points for torque calculation carefully. - Use conditions of equilibrium to express the tension \( T \) in terms of: - Mass \( m \) of the meter stick - Acceleration due to gravity \( g \) - Angle \( \theta \) between the force and displacement vector - Pay attention to the angle used for torque due to the tension in the cord. #### (b) Will the tension in the cord be greater than, less than, or the same as that found in part (a) if the string is shortened, keeping the meter stick horizontal? **Options:** 1. Greater than 2. **Less than** (Selected, Correct) 3. The same as ### Explanation: **Concepts:** - **Torque**: A measure of the force that can cause an object to rotate about an axis. \( \tau = r \times F \times \sin(\theta) \), where \( \tau \) is torque, \( r \) is the length from pivot point to the point where force is applied, \( F \) is the force, and \( \theta \) is the angle between \( r \) and \( F \). - **Equilibrium Condition**: For an object to be in equilibrium, the sum of forces and the sum of torques must both be zero. **Analysis:** - When shortening the string while keeping the meter stick horizontal, the angle or position where the force is applied changes, affecting the torque and hence the tension needed in the cord.
Transcribed Image Text:### Educational Content on Torque and Equilibrium **Problem Statement:** A meter stick with a mass of 0.57 kg is held perpendicular to a vertical wall by a cord of length \( d = 1.8 \, \text{m} \) attached to the end of the meter stick and also to the wall above the other end of the meter stick. #### (a) Determine the tension in the cord. **Student Input:** - Answer submitted: **5.01** - Result: **Incorrect** **Instructor Note:** - Consider points for torque calculation carefully. - Use conditions of equilibrium to express the tension \( T \) in terms of: - Mass \( m \) of the meter stick - Acceleration due to gravity \( g \) - Angle \( \theta \) between the force and displacement vector - Pay attention to the angle used for torque due to the tension in the cord. #### (b) Will the tension in the cord be greater than, less than, or the same as that found in part (a) if the string is shortened, keeping the meter stick horizontal? **Options:** 1. Greater than 2. **Less than** (Selected, Correct) 3. The same as ### Explanation: **Concepts:** - **Torque**: A measure of the force that can cause an object to rotate about an axis. \( \tau = r \times F \times \sin(\theta) \), where \( \tau \) is torque, \( r \) is the length from pivot point to the point where force is applied, \( F \) is the force, and \( \theta \) is the angle between \( r \) and \( F \). - **Equilibrium Condition**: For an object to be in equilibrium, the sum of forces and the sum of torques must both be zero. **Analysis:** - When shortening the string while keeping the meter stick horizontal, the angle or position where the force is applied changes, affecting the torque and hence the tension needed in the cord.
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