Why is this force the mgCos while the other is mgSin?

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Homework Help Overview

The problem involves a block on an inclined ramp at a 60-degree angle, with a focus on understanding the forces acting on the block, specifically the roles of mgSin(theta) and mgCos(theta) in relation to the block's motion and the normal force.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the reasoning behind the use of trigonometric functions to describe the forces acting on the block, questioning why mgSin(theta) represents the force down the ramp while mgCos(theta) represents the normal force.

Discussion Status

Participants are actively engaging in clarifying the geometric relationships and trigonometric applications relevant to the problem. There is a focus on understanding the placement of angles and the implications of changing the angle of inclination on the normal force.

Contextual Notes

The discussion is framed within the context of a physics homework assignment, with specific attention to the definitions and roles of forces in an inclined plane scenario. The original poster expresses curiosity about the underlying principles rather than seeking a direct solution.

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Homework Statement


A block is placed on a ramp that is inclined to 60 degrees to the horizon. If the block weighs 10kg and the coefficient of kinetic friction is 0.3, how fast does the block accerlate down the ramp?

Homework Equations


Theta=60 degrees
m=10kg
g=10m/s^2
mu=0.3

The Attempt at a Solution


So far, all I have is the diagram that he gave us in class. I can somewhat tell why we're using the trig functions, but what I'm curious about is why mgsin(theta) is the block sliding down the ramp and mgcos(theta) is the reactionary force of gravity. Why not the other way around?

gQh9Ct1.jpg
 
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Draw the vertical lines from the down edge of mg to the opposite sides of plane and see which angle is ##\theta## in the right triangle that is formed. In this triangle, find each vertical side using trigonometry.
 
upload_2017-2-8_16-36-36.png
This is where theta is to be placed. If you understand why, try to figure it out from there.
 
You can also ask yourself what happens to the normal force as theta approaches zero? Would Sin or Cos do that?
 

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