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QI) Knowing that the coefficient of friction between the 25-kg block and the incline is , = 0.25, determine (a) the smallest value of P required to start the block moving up the incline, (b) the corresponding value of 3. P

QI) Knowing that the coefficient of friction between the 25-kg block and the incline is , = 0.25, determine (a) the smallest value of P required to start the block moving up the incline, (b) the corresponding value of 3. P

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**Homework Assignment** **Q1:** Knowing that the coefficient of friction between the 25-kg block and the incline is μ = 0.25, determine: (a) the smallest value of P required to start the block moving up the incline. (b) the corresponding value of β. **Diagram Explanation:** The diagram shows a block of mass 25 kg placed on an inclined plane that makes an angle of 30° with the horizontal. There is a force P applied to the block at an angle β with the incline to move it up the plane. The coefficient of friction (μ) between the block and the inclined plane is given as 0.25. - The block is depicted as a green rectangular shape labeled with its mass (25 kg). - The inclined plane is illustrated with a slope of 30°. - The force P is denoted with a red arrow pointing up the incline, forming an angle β with the incline. To solve the problem: 1. Calculate the smallest value of the force P needed to overcome both the gravitational component pulling the block down the plane and the frictional force resisting the movement. 2. Determine the corresponding angle β at which this force should be applied. Use the following physics principles and formulas: - Resolving forces parallel and perpendicular to the inclined plane - Frictional force = μ * normal force - Newton's Second Law of Motion (ΣF = ma, where a = 0 at the threshold of movement)
Transcribed Image Text:**Homework Assignment** **Q1:** Knowing that the coefficient of friction between the 25-kg block and the incline is μ = 0.25, determine: (a) the smallest value of P required to start the block moving up the incline. (b) the corresponding value of β. **Diagram Explanation:** The diagram shows a block of mass 25 kg placed on an inclined plane that makes an angle of 30° with the horizontal. There is a force P applied to the block at an angle β with the incline to move it up the plane. The coefficient of friction (μ) between the block and the inclined plane is given as 0.25. - The block is depicted as a green rectangular shape labeled with its mass (25 kg). - The inclined plane is illustrated with a slope of 30°. - The force P is denoted with a red arrow pointing up the incline, forming an angle β with the incline. To solve the problem: 1. Calculate the smallest value of the force P needed to overcome both the gravitational component pulling the block down the plane and the frictional force resisting the movement. 2. Determine the corresponding angle β at which this force should be applied. Use the following physics principles and formulas: - Resolving forces parallel and perpendicular to the inclined plane - Frictional force = μ * normal force - Newton's Second Law of Motion (ΣF = ma, where a = 0 at the threshold of movement)
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