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**Problem Statement:** A block of mass \( m = 7.0 \, \text{kg} \) is pushed down a \( \theta = 35^\circ \) incline as in the figure with a force of magnitude \( F = 9.0 \, \text{N} \). The coefficient of kinetic friction between the block and incline is 0.15. 1. **Tasks:** - (a) Draw the free body diagram of the block. - (b) Apply Newton's second law to each axis (write down \( x \) and \( y \) components of the net force). - (c) Find the acceleration of the block. **Illustration Description:** - The figure shows a block labeled with mass \( m \) on an inclined plane. - The incline makes an angle \( \theta \) with the horizontal. - A force \( F \) is applied parallel to the incline. - There are axes labeled \( x \) (along the incline) and \( y \) (perpendicular to the incline). **Explanation of Concepts:** - **Free Body Diagram (FBD):** The FBD is critical for visualizing the forces acting on the block, such as gravitational force (\( mg \)), normal force, frictional force, and the applied force (\( F \)). - **Newton's Second Law:** Break down forces into \( x \) and \( y \) components for analysis: - \( x \)-axis: \( F_{\text{net},x} = ma_x \) - \( y \)-axis: \( F_{\text{net},y} = ma_y = 0 \) (assuming no motion perpendicular to the plane) - **Kinetic Friction:** Calculated as \( f_k = \mu_k N \), where \( N \) is the normal force, and \( \mu_k \) is the coefficient of kinetic friction. Analyzing this problem involves understanding the balance of forces and how they contribute to the block's acceleration down the inclined plane.

**Problem Statement:** A block of mass \( m = 7.0 \, \text{kg} \) is pushed down a \( \theta = 35^\circ \) incline as in the figure with a force of magnitude \( F = 9.0 \, \text{N} \). The coefficient of kinetic friction between the block and incline is 0.15. 1. **Tasks:** - (a) Draw the free body diagram of the block. - (b) Apply Newton's second law to each axis (write down \( x \) and \( y \) components of the net force). - (c) Find the acceleration of the block. **Illustration Description:** - The figure shows a block labeled with mass \( m \) on an inclined plane. - The incline makes an angle \( \theta \) with the horizontal. - A force \( F \) is applied parallel to the incline. - There are axes labeled \( x \) (along the incline) and \( y \) (perpendicular to the incline). **Explanation of Concepts:** - **Free Body Diagram (FBD):** The FBD is critical for visualizing the forces acting on the block, such as gravitational force (\( mg \)), normal force, frictional force, and the applied force (\( F \)). - **Newton's Second Law:** Break down forces into \( x \) and \( y \) components for analysis: - \( x \)-axis: \( F_{\text{net},x} = ma_x \) - \( y \)-axis: \( F_{\text{net},y} = ma_y = 0 \) (assuming no motion perpendicular to the plane) - **Kinetic Friction:** Calculated as \( f_k = \mu_k N \), where \( N \) is the normal force, and \( \mu_k \) is the coefficient of kinetic friction. Analyzing this problem involves understanding the balance of forces and how they contribute to the block's acceleration down the inclined plane.

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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**Problem Statement:** A block of mass \( m = 7.0 \, \text{kg} \) is pushed down a \( \theta = 35^\circ \) incline as in the figure with a force of magnitude \( F = 9.0 \, \text{N} \). The coefficient of kinetic friction between the block and incline is 0.15. 1. **Tasks:** - (a) Draw the free body diagram of the block. - (b) Apply Newton's second law to each axis (write down \( x \) and \( y \) components of the net force). - (c) Find the acceleration of the block. **Illustration Description:** - The figure shows a block labeled with mass \( m \) on an inclined plane. - The incline makes an angle \( \theta \) with the horizontal. - A force \( F \) is applied parallel to the incline. - There are axes labeled \( x \) (along the incline) and \( y \) (perpendicular to the incline). **Explanation of Concepts:** - **Free Body Diagram (FBD):** The FBD is critical for visualizing the forces acting on the block, such as gravitational force (\( mg \)), normal force, frictional force, and the applied force (\( F \)). - **Newton's Second Law:** Break down forces into \( x \) and \( y \) components for analysis: - \( x \)-axis: \( F_{\text{net},x} = ma_x \) - \( y \)-axis: \( F_{\text{net},y} = ma_y = 0 \) (assuming no motion perpendicular to the plane) - **Kinetic Friction:** Calculated as \( f_k = \mu_k N \), where \( N \) is the normal force, and \( \mu_k \) is the coefficient of kinetic friction. Analyzing this problem involves understanding the balance of forces and how they contribute to the block's acceleration down the inclined plane.
Transcribed Image Text:**Problem Statement:** A block of mass \( m = 7.0 \, \text{kg} \) is pushed down a \( \theta = 35^\circ \) incline as in the figure with a force of magnitude \( F = 9.0 \, \text{N} \). The coefficient of kinetic friction between the block and incline is 0.15. 1. **Tasks:** - (a) Draw the free body diagram of the block. - (b) Apply Newton's second law to each axis (write down \( x \) and \( y \) components of the net force). - (c) Find the acceleration of the block. **Illustration Description:** - The figure shows a block labeled with mass \( m \) on an inclined plane. - The incline makes an angle \( \theta \) with the horizontal. - A force \( F \) is applied parallel to the incline. - There are axes labeled \( x \) (along the incline) and \( y \) (perpendicular to the incline). **Explanation of Concepts:** - **Free Body Diagram (FBD):** The FBD is critical for visualizing the forces acting on the block, such as gravitational force (\( mg \)), normal force, frictional force, and the applied force (\( F \)). - **Newton's Second Law:** Break down forces into \( x \) and \( y \) components for analysis: - \( x \)-axis: \( F_{\text{net},x} = ma_x \) - \( y \)-axis: \( F_{\text{net},y} = ma_y = 0 \) (assuming no motion perpendicular to the plane) - **Kinetic Friction:** Calculated as \( f_k = \mu_k N \), where \( N \) is the normal force, and \( \mu_k \) is the coefficient of kinetic friction. Analyzing this problem involves understanding the balance of forces and how they contribute to the block's acceleration down the inclined plane.
Expert Solution
Step 1

m = 7.0kg

F = 9.0N

Coefficient of kinetic friction, μ=0.15

θ = 35o

 

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