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Calculate the normal force acting on the 3kg crate.

Calculate the normal force acting on the 3kg crate.

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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Calculate the normal force acting on the 3kg crate.

The image depicts a diagram of a block resting on an inclined plane. **Description:** - **Block:** The block is a blue quadrilateral shape with a mass labeled as 3.0 kg. - **Inclined Plane:** The plane on which the block is resting is inclined at an angle of 25.0 degrees to the horizontal. **Explanation:** This scenario is often used in physics to study the forces acting on a body on an inclined plane. Here are some key concepts related to this setup: 1. **Gravitational Force (Weight - \(W\)):** This is the force due to gravity acting on the block. It can be calculated using the formula \(W = mg\), where \(m\) is the mass (3.0 kg) and \(g\) is the acceleration due to gravity (approximately 9.8 m/s²). 2. **Normal Force (\(N\)):** This is the perpendicular force exerted by the inclined plane on the block. It can be calculated by resolving the gravitational force into components perpendicular and parallel to the inclined plane. 3. **Component Forces:** - The component of the gravitational force acting parallel to the inclined plane (\(mg \sin \theta\)), which tends to move the block down the incline. - The component of the gravitational force acting perpendicular to the inclined plane (\(mg \cos \theta\)), which is balanced by the normal force. 4. **Frictional Force (\(f\)):** If friction is present, it acts opposite to the direction of motion or potential motion of the block. The magnitude of friction can be calculated as \(f = \mu N\), where \(\mu\) is the coefficient of friction between the block and the inclined plane. 5. **Net Force and Acceleration:** - If the inclined plane is frictionless, the only force causing motion parallel to the surface is \(mg \sin \theta\). - The net force (\(F_{\text{net}}\)) equals \(mg \sin \theta\), and the acceleration (\(a\)) can be found using \(F_{\text{net}} = ma\). **Mathematical Representation:** - Weight: \(W = mg = 3.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 29.4 \, \text
Transcribed Image Text:The image depicts a diagram of a block resting on an inclined plane. **Description:** - **Block:** The block is a blue quadrilateral shape with a mass labeled as 3.0 kg. - **Inclined Plane:** The plane on which the block is resting is inclined at an angle of 25.0 degrees to the horizontal. **Explanation:** This scenario is often used in physics to study the forces acting on a body on an inclined plane. Here are some key concepts related to this setup: 1. **Gravitational Force (Weight - \(W\)):** This is the force due to gravity acting on the block. It can be calculated using the formula \(W = mg\), where \(m\) is the mass (3.0 kg) and \(g\) is the acceleration due to gravity (approximately 9.8 m/s²). 2. **Normal Force (\(N\)):** This is the perpendicular force exerted by the inclined plane on the block. It can be calculated by resolving the gravitational force into components perpendicular and parallel to the inclined plane. 3. **Component Forces:** - The component of the gravitational force acting parallel to the inclined plane (\(mg \sin \theta\)), which tends to move the block down the incline. - The component of the gravitational force acting perpendicular to the inclined plane (\(mg \cos \theta\)), which is balanced by the normal force. 4. **Frictional Force (\(f\)):** If friction is present, it acts opposite to the direction of motion or potential motion of the block. The magnitude of friction can be calculated as \(f = \mu N\), where \(\mu\) is the coefficient of friction between the block and the inclined plane. 5. **Net Force and Acceleration:** - If the inclined plane is frictionless, the only force causing motion parallel to the surface is \(mg \sin \theta\). - The net force (\(F_{\text{net}}\)) equals \(mg \sin \theta\), and the acceleration (\(a\)) can be found using \(F_{\text{net}} = ma\). **Mathematical Representation:** - Weight: \(W = mg = 3.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 29.4 \, \text
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