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Fw mg AFiy Frx e f.x Axis The ladder in the picture has a mass of 39 kilograms and a length 3 meters. What is the normal force pushing the ladder up from the floor? This force is labeled Ff y in the picture. FN N. Assume that the ladder's weight is evenly distributed, so it can be treated as a single force through the middle. If the ladder is at a 69° angle from the ground, what is the torque exerted by the weight (using the floor as the pivot point)? N.m The torque from the ladder must be balanced by the torque caused by the normal force on the wall, labeled Fw in the picture. Calculate this force. Fw N. %3D

Fw mg AFiy Frx e f.x Axis The ladder in the picture has a mass of 39 kilograms and a length 3 meters. What is the normal force pushing the ladder up from the floor? This force is labeled Ff y in the picture. FN N. Assume that the ladder's weight is evenly distributed, so it can be treated as a single force through the middle. If the ladder is at a 69° angle from the ground, what is the torque exerted by the weight (using the floor as the pivot point)? N.m The torque from the ladder must be balanced by the torque caused by the normal force on the wall, labeled Fw in the picture. Calculate this force. Fw N. %3D

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 Website Content:** ### Understanding Forces on a Ladder The diagram shows a ladder leaning against a wall, characterized by the following specifications: - **Mass of Ladder**: 39 kilograms - **Length of Ladder**: 3 meters - **Position**: Ladder makes a 69° angle with the ground The forces acting on the ladder are labeled as follows: - **\( F_{f,y} \)**: Normal force from the floor - **\( F_{f,x} \)**: Frictional force from the floor - **\( mg \)**: Gravitational force acting downward - **Axis**: Rotation or pivot point on the floor #### Key Problems to Solve: 1. **Normal Force from the Floor:** - Determine the force pushing the ladder up from the floor, labeled \( F_{f,y} \). 2. **Torque Exerted by the Ladder's Weight:** - Assume the ladder's weight is evenly distributed. Calculate the torque when the ladder is at a 69° angle. Use the floor as the pivot point. 3. **Torque Balance:** - Balance the torque from the ladder with the torque caused by the normal force on the wall, labeled \( F_w \). 4. **Friction and Coefficient of Friction:** - Ensure the normal force from the wall matches the frictional force from the floor. Determine the minimum coefficient of friction (\( \mu \)) to prevent the ladder from slipping. **Equations and Calculations:** - **Normal Force (\( F_N \)):** - \( F_N = \_\_\_\_ \) N - **Torque (τ):** - \( \tau = \_\_\_\_ \) N·m - **Wall Force (\( F_w \)):** - \( F_w = \_\_\_\_ \) N - **Coefficient of Friction (\( \mu \)):** - \( \mu = \_\_\_\_ \) ### Diagram Explanation - **Forces and Angles:** - The diagram includes the ladder's contact points with the wall and floor, showing the directions of forces applied. - Arrows indicate the direction and type of forces acting, such as gravitational force, normal force, and frictional force. This setup helps learners visualize and calculate the equilibrium and forces in physics problems involving ladders
Transcribed Image Text:**Educational Website Content:** ### Understanding Forces on a Ladder The diagram shows a ladder leaning against a wall, characterized by the following specifications: - **Mass of Ladder**: 39 kilograms - **Length of Ladder**: 3 meters - **Position**: Ladder makes a 69° angle with the ground The forces acting on the ladder are labeled as follows: - **\( F_{f,y} \)**: Normal force from the floor - **\( F_{f,x} \)**: Frictional force from the floor - **\( mg \)**: Gravitational force acting downward - **Axis**: Rotation or pivot point on the floor #### Key Problems to Solve: 1. **Normal Force from the Floor:** - Determine the force pushing the ladder up from the floor, labeled \( F_{f,y} \). 2. **Torque Exerted by the Ladder's Weight:** - Assume the ladder's weight is evenly distributed. Calculate the torque when the ladder is at a 69° angle. Use the floor as the pivot point. 3. **Torque Balance:** - Balance the torque from the ladder with the torque caused by the normal force on the wall, labeled \( F_w \). 4. **Friction and Coefficient of Friction:** - Ensure the normal force from the wall matches the frictional force from the floor. Determine the minimum coefficient of friction (\( \mu \)) to prevent the ladder from slipping. **Equations and Calculations:** - **Normal Force (\( F_N \)):** - \( F_N = \_\_\_\_ \) N - **Torque (τ):** - \( \tau = \_\_\_\_ \) N·m - **Wall Force (\( F_w \)):** - \( F_w = \_\_\_\_ \) N - **Coefficient of Friction (\( \mu \)):** - \( \mu = \_\_\_\_ \) ### Diagram Explanation - **Forces and Angles:** - The diagram includes the ladder's contact points with the wall and floor, showing the directions of forces applied. - Arrows indicate the direction and type of forces acting, such as gravitational force, normal force, and frictional force. This setup helps learners visualize and calculate the equilibrium and forces in physics problems involving ladders
**Diagram Explanation:** The diagram depicts a ladder leaning against a wall. The ladder is shown with its weight acting downward and different forces labeled at the base and the top end: - \( F_W \) (Force on the wall): the horizontal force exerted by the ladder on the wall. - \( mg \) (Weight of the ladder): acts downward due to gravity. - \( F_{f,y} \) (Normal force on the floor): acts perpendicular to the floor, pushing up on the ladder. - \( F_{f,x} \) (Friction force on the floor): horizontal force exerted by the floor. - \(\theta\) is the angle between the ladder and the floor. - The axis of rotation is at the base where the ladder contacts the floor. - The \( x \) and \( y \) axes are marked for reference. **Text Explanation:** The ladder in the picture has a mass of 39 kilograms and a length of 3 meters. What is the normal force pushing the ladder up from the floor? This force is labeled \( F_{f,y} \) in the picture. \[ F_N = \, \_\_\_\_ \, \text{N} \] Assume that the ladder’s weight is evenly distributed, so it can be treated as a single force through the middle. If the ladder is at a 69° angle from the ground, what is the torque exerted by the weight (using the floor as the pivot point)? \[ \tau = \, \_\_\_\_ \, \text{N}\cdot\text{m} \] The torque from the ladder must be balanced by the torque caused by the normal force on the wall, labeled \( F_W \) in the picture. Calculate this force. \[ F_w = \, \_\_\_\_ \, \text{N} \] The normal force from the wall must be balanced by the friction force from the floor, labeled \( F_{f,x} \) in the picture. Determine the minimum coefficient of friction to keep the ladder from slipping.
Transcribed Image Text:**Diagram Explanation:** The diagram depicts a ladder leaning against a wall. The ladder is shown with its weight acting downward and different forces labeled at the base and the top end: - \( F_W \) (Force on the wall): the horizontal force exerted by the ladder on the wall. - \( mg \) (Weight of the ladder): acts downward due to gravity. - \( F_{f,y} \) (Normal force on the floor): acts perpendicular to the floor, pushing up on the ladder. - \( F_{f,x} \) (Friction force on the floor): horizontal force exerted by the floor. - \(\theta\) is the angle between the ladder and the floor. - The axis of rotation is at the base where the ladder contacts the floor. - The \( x \) and \( y \) axes are marked for reference. **Text Explanation:** The ladder in the picture has a mass of 39 kilograms and a length of 3 meters. What is the normal force pushing the ladder up from the floor? This force is labeled \( F_{f,y} \) in the picture. \[ F_N = \, \_\_\_\_ \, \text{N} \] Assume that the ladder’s weight is evenly distributed, so it can be treated as a single force through the middle. If the ladder is at a 69° angle from the ground, what is the torque exerted by the weight (using the floor as the pivot point)? \[ \tau = \, \_\_\_\_ \, \text{N}\cdot\text{m} \] The torque from the ladder must be balanced by the torque caused by the normal force on the wall, labeled \( F_W \) in the picture. Calculate this force. \[ F_w = \, \_\_\_\_ \, \text{N} \] The normal force from the wall must be balanced by the friction force from the floor, labeled \( F_{f,x} \) in the picture. Determine the minimum coefficient of friction to keep the ladder from slipping.
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