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A block of mass m is at rest on an incline which is inclined angle relative to horizontal as shown in the figure. There is friction f between the block and the surface. m Ꮎ (A) Draw a free body diagram for the block on the incline, including all forces acting on the block as vectors. Make sure to label the vectors. Include x and y axes in your sketch (feel free to draw axes in any orientation you would like). (B) Use Newton's second law to write equations for forces in x and y dimensions (separately) as a function of the frictional force f, the mass of the block m, the gravitational constant g, and the angle of the incline 0. (C) If the block has a mass of 250 g and the coefficient of static friction us is 0.45, find the maximum angle max such that the block is stationary (ie does not slide).

A block of mass m is at rest on an incline which is inclined angle relative to horizontal as shown in the figure. There is friction f between the block and the surface. m Ꮎ (A) Draw a free body diagram for the block on the incline, including all forces acting on the block as vectors. Make sure to label the vectors. Include x and y axes in your sketch (feel free to draw axes in any orientation you would like). (B) Use Newton's second law to write equations for forces in x and y dimensions (separately) as a function of the frictional force f, the mass of the block m, the gravitational constant g, and the angle of the incline 0. (C) If the block has a mass of 250 g and the coefficient of static friction us is 0.45, find the maximum angle max such that the block is stationary (ie does not slide).

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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### Analyzing a Block on an Inclined Plane A block of mass \( m \) is at rest on an incline which is inclined at an angle \( \theta \) relative to the horizontal, as shown in the figure. There is friction \( f \) between the block and the surface. #### Tasks: **(A)** Draw a free body diagram for the block on the incline, including all forces acting on the block as vectors. Make sure to label the vectors. Include x and y axes in your sketch (feel free to draw axes in any orientation you would like). **(B)** Use Newton's second law to write equations for forces in the x and y dimensions (separately) as a function of the frictional force \( f \), the mass of the block \( m \), the gravitational constant \( g \), and the angle of the incline \( \theta \). **(C)** If the block has a mass of 250 g and the coefficient of static friction \( \mu_s \) is 0.45, find the maximum angle \( \theta_{\text{max}} \) such that the block is stationary (i.e., does not slide). #### Illustration Details: The figure shows a block resting on a sloped surface. The incline has an angle \( \theta \) relative to the horizontal base. The block is represented by a square with the letter \( m \) indicating its mass. The incline is directed upward and to the right.
Transcribed Image Text:### Analyzing a Block on an Inclined Plane A block of mass \( m \) is at rest on an incline which is inclined at an angle \( \theta \) relative to the horizontal, as shown in the figure. There is friction \( f \) between the block and the surface. #### Tasks: **(A)** Draw a free body diagram for the block on the incline, including all forces acting on the block as vectors. Make sure to label the vectors. Include x and y axes in your sketch (feel free to draw axes in any orientation you would like). **(B)** Use Newton's second law to write equations for forces in the x and y dimensions (separately) as a function of the frictional force \( f \), the mass of the block \( m \), the gravitational constant \( g \), and the angle of the incline \( \theta \). **(C)** If the block has a mass of 250 g and the coefficient of static friction \( \mu_s \) is 0.45, find the maximum angle \( \theta_{\text{max}} \) such that the block is stationary (i.e., does not slide). #### Illustration Details: The figure shows a block resting on a sloped surface. The incline has an angle \( \theta \) relative to the horizontal base. The block is represented by a square with the letter \( m \) indicating its mass. The incline is directed upward and to the right.
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