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A 1500-N crate is to be held in place on a ramp that rises at 30° above the horizontal (see figure). The massless rope attached to the crate makes a 22° angle above the surface of the ramp. The coefficients of friction between the crate and the surface of the ramp are µk = 0.45 and µs = 0.65. The pulley has no appreciable mass or friction. What is the MAXIMUM weight w that can be used to hold this crate stationary on the ramp? W=? Crate 22.0° - -- Ramp 30,0

A 1500-N crate is to be held in place on a ramp that rises at 30° above the horizontal (see figure). The massless rope attached to the crate makes a 22° angle above the surface of the ramp. The coefficients of friction between the crate and the surface of the ramp are µk = 0.45 and µs = 0.65. The pulley has no appreciable mass or friction. What is the MAXIMUM weight w that can be used to hold this crate stationary on the ramp? W=? Crate 22.0° - -- Ramp 30,0

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Problem Statement A 1500-N crate is to be held in place on a ramp that rises at 30° above the horizontal. The massless rope attached to the crate makes a 22° angle above the surface of the ramp. The coefficients of friction between the crate and the surface of the ramp are μₖ = 0.45 and μₛ = 0.65. The pulley has no appreciable mass or friction. What is the MAXIMUM weight \( w \) that can be used to hold this crate stationary on the ramp? ### Diagram Description The diagram accompanying the problem statement depicts: - A ramp inclined at an angle of 30° above the horizontal. - A crate situated on the ramp. - A rope attached to the crate, extending upwards and making a 22° angle with the surface of the ramp. - The rope passes over a pulley, which is depicted as frictionless and massless. - The end of the rope is attached to a weight labeled \( w = ? \), which hangs vertically downward. ### Explanation The problem requires calculating the maximum weight that can hold the crate stationary on the inclined ramp, considering the static and kinetic friction coefficients provided. The analysis involves resolving the forces acting along and perpendicular to the inclined plane. The static friction and tension in the rope play crucial roles in determining the maximum permissible weight.
Transcribed Image Text:### Problem Statement A 1500-N crate is to be held in place on a ramp that rises at 30° above the horizontal. The massless rope attached to the crate makes a 22° angle above the surface of the ramp. The coefficients of friction between the crate and the surface of the ramp are μₖ = 0.45 and μₛ = 0.65. The pulley has no appreciable mass or friction. What is the MAXIMUM weight \( w \) that can be used to hold this crate stationary on the ramp? ### Diagram Description The diagram accompanying the problem statement depicts: - A ramp inclined at an angle of 30° above the horizontal. - A crate situated on the ramp. - A rope attached to the crate, extending upwards and making a 22° angle with the surface of the ramp. - The rope passes over a pulley, which is depicted as frictionless and massless. - The end of the rope is attached to a weight labeled \( w = ? \), which hangs vertically downward. ### Explanation The problem requires calculating the maximum weight that can hold the crate stationary on the inclined ramp, considering the static and kinetic friction coefficients provided. The analysis involves resolving the forces acting along and perpendicular to the inclined plane. The static friction and tension in the rope play crucial roles in determining the maximum permissible weight.
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