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**Problem Statement:** A girl is pulling a sled with a mass of 16.0 kg across a level patch of grass by exerting a force of 22.0 N along a rope that forms an angle of 33.0 degrees above the ground. If the coefficient of kinetic friction between the sled and the grass is 0.25, draw a force diagram for the problem and find the acceleration of the sled. **Explanation and Diagram:** To solve this problem, first draw a force diagram (free body diagram) depicting all the forces acting on the sled: 1. **Applied Force (F):** A force of 22.0 N is exerted at an angle of 33.0 degrees with respect to the horizontal. 2. **Normal Force (N):** Acts perpendicular to the surface upward, balancing part of the sled's weight. 3. **Gravitational Force (Weight, W):** Acts downward, equal to the mass of the sled times the acceleration due to gravity (W = m * g). 4. **Frictional Force (f):** Acts opposite to the direction of motion, calculated using the formula f = μ * N, where μ is the coefficient of friction. **Calculations:** 1. **Resolve the Applied Force:** - Horizontal Component: \( F_x = F \cdot \cos(\theta) \) - Vertical Component: \( F_y = F \cdot \sin(\theta) \) 2. **Calculate the Normal Force:** - \( N = m \cdot g - F_y \) 3. **Determine the Frictional Force:** - \( f = \mu \cdot N \) 4. **Calculate Acceleration (a):** - Use Newton’s Second Law: \( F_{net} = m \cdot a \) - Net Force: \( F_{net} = F_x - f \) - Rearrange to solve for acceleration: \( a = \frac{F_{net}}{m} \) These steps will allow you to find the acceleration of the sled based on the given forces and conditions.

**Problem Statement:** A girl is pulling a sled with a mass of 16.0 kg across a level patch of grass by exerting a force of 22.0 N along a rope that forms an angle of 33.0 degrees above the ground. If the coefficient of kinetic friction between the sled and the grass is 0.25, draw a force diagram for the problem and find the acceleration of the sled. **Explanation and Diagram:** To solve this problem, first draw a force diagram (free body diagram) depicting all the forces acting on the sled: 1. **Applied Force (F):** A force of 22.0 N is exerted at an angle of 33.0 degrees with respect to the horizontal. 2. **Normal Force (N):** Acts perpendicular to the surface upward, balancing part of the sled's weight. 3. **Gravitational Force (Weight, W):** Acts downward, equal to the mass of the sled times the acceleration due to gravity (W = m * g). 4. **Frictional Force (f):** Acts opposite to the direction of motion, calculated using the formula f = μ * N, where μ is the coefficient of friction. **Calculations:** 1. **Resolve the Applied Force:** - Horizontal Component: \( F_x = F \cdot \cos(\theta) \) - Vertical Component: \( F_y = F \cdot \sin(\theta) \) 2. **Calculate the Normal Force:** - \( N = m \cdot g - F_y \) 3. **Determine the Frictional Force:** - \( f = \mu \cdot N \) 4. **Calculate Acceleration (a):** - Use Newton’s Second Law: \( F_{net} = m \cdot a \) - Net Force: \( F_{net} = F_x - f \) - Rearrange to solve for acceleration: \( a = \frac{F_{net}}{m} \) These steps will allow you to find the acceleration of the sled based on the given forces and conditions.

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 girl is pulling a sled with a mass of 16.0 kg across a level patch of grass by exerting a force of 22.0 N along a rope that forms an angle of 33.0 degrees above the ground. If the coefficient of kinetic friction between the sled and the grass is 0.25, draw a force diagram for the problem and find the acceleration of the sled. **Explanation and Diagram:** To solve this problem, first draw a force diagram (free body diagram) depicting all the forces acting on the sled: 1. **Applied Force (F):** A force of 22.0 N is exerted at an angle of 33.0 degrees with respect to the horizontal. 2. **Normal Force (N):** Acts perpendicular to the surface upward, balancing part of the sled's weight. 3. **Gravitational Force (Weight, W):** Acts downward, equal to the mass of the sled times the acceleration due to gravity (W = m * g). 4. **Frictional Force (f):** Acts opposite to the direction of motion, calculated using the formula f = μ * N, where μ is the coefficient of friction. **Calculations:** 1. **Resolve the Applied Force:** - Horizontal Component: \( F_x = F \cdot \cos(\theta) \) - Vertical Component: \( F_y = F \cdot \sin(\theta) \) 2. **Calculate the Normal Force:** - \( N = m \cdot g - F_y \) 3. **Determine the Frictional Force:** - \( f = \mu \cdot N \) 4. **Calculate Acceleration (a):** - Use Newton’s Second Law: \( F_{net} = m \cdot a \) - Net Force: \( F_{net} = F_x - f \) - Rearrange to solve for acceleration: \( a = \frac{F_{net}}{m} \) These steps will allow you to find the acceleration of the sled based on the given forces and conditions.
Transcribed Image Text:**Problem Statement:** A girl is pulling a sled with a mass of 16.0 kg across a level patch of grass by exerting a force of 22.0 N along a rope that forms an angle of 33.0 degrees above the ground. If the coefficient of kinetic friction between the sled and the grass is 0.25, draw a force diagram for the problem and find the acceleration of the sled. **Explanation and Diagram:** To solve this problem, first draw a force diagram (free body diagram) depicting all the forces acting on the sled: 1. **Applied Force (F):** A force of 22.0 N is exerted at an angle of 33.0 degrees with respect to the horizontal. 2. **Normal Force (N):** Acts perpendicular to the surface upward, balancing part of the sled's weight. 3. **Gravitational Force (Weight, W):** Acts downward, equal to the mass of the sled times the acceleration due to gravity (W = m * g). 4. **Frictional Force (f):** Acts opposite to the direction of motion, calculated using the formula f = μ * N, where μ is the coefficient of friction. **Calculations:** 1. **Resolve the Applied Force:** - Horizontal Component: \( F_x = F \cdot \cos(\theta) \) - Vertical Component: \( F_y = F \cdot \sin(\theta) \) 2. **Calculate the Normal Force:** - \( N = m \cdot g - F_y \) 3. **Determine the Frictional Force:** - \( f = \mu \cdot N \) 4. **Calculate Acceleration (a):** - Use Newton’s Second Law: \( F_{net} = m \cdot a \) - Net Force: \( F_{net} = F_x - f \) - Rearrange to solve for acceleration: \( a = \frac{F_{net}}{m} \) These steps will allow you to find the acceleration of the sled based on the given forces and conditions.
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