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
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00df77ed-0934-473b-8f97-2f45e80b48d6%2Fba10d536-ab6d-435a-9df5-92108b383ac2%2Fj78h5qm_processed.jpeg&w=3840&q=75)
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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