How to find forces acting on object on a slope?

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Homework Help Overview

The discussion revolves around analyzing the forces acting on an object resting on a slope at an angle σ. Participants are attempting to resolve gravitational force G into its components, specifically the forces acting parallel (Ft) and perpendicular (Fn) to the slope.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are discussing the resolution of gravitational force into components, questioning the derivation of equations such as Ft = G sin σ and Fn = G cos σ. There is confusion regarding the application of trigonometric functions and the relevance of the SOH CAH TOA mnemonic in this context.

Discussion Status

Some participants have shared diagrams to illustrate their understanding of the force components. There is ongoing exploration of the relationships between the forces and the geometry of the situation, with no clear consensus on the reasoning behind the equations presented. The discussion remains active with participants seeking clarification on fundamental concepts.

Contextual Notes

Participants express uncertainty about the right triangle configuration and the application of trigonometric principles, indicating a potential gap in understanding the geometric relationships involved in the problem.

urbano
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Homework Statement

an object is at rest on a slope at angle of σ

Using trigonometry, solve the forces acting at Ft and Fn

2ezlnqa.jpg

Homework Equations



Soh
Cah
Toa

The Attempt at a Solution



sin σ = G/Ft
sin σ /Ft = G
G/ sin σ = Ft (my final answer)

Book says correct answer is Ft = G sinσFn = ? I wanst even sure how to strat this using σ

The book says the correct answer is Fn = G cosσ

Homework Statement


Homework Equations


The Attempt at a Solution

 
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The force G can be resolved into 2 components: one which is normal to the slope (the exact opposite to Fn), and one which is parallel to the slope (the exact opposite to Ft).

Draw the triangle of forces showing how G equals the vector sum of these two forces.
 
edited...I'll be back
 
Last edited:
Thanks NascentOxygen. Unfortunately I don't quite get why the answers are what they are. I have drawn myself a new triangle which shows the two vector forces but I still don't understand where the answers have come from.

Especially Fn = G cosσ. I thought cos in basic terms meant adjacent/hypothenuse . So if the sloped line is the hypothenuse and the bottom line is the adjacent once I draw the line which is exact opposite to Fn I now no longer have a right angle triangle...arghh! I'm just so confused...
 
Show your diagrams.
 
here is my latest diagram
2yw8ygz.jpg


I'm now starting to think Soh Cah Toa isn't actually relevant there ?

Fn = G cosσ Ft = Gσ

I'm unsure where these two formulas/equations have come from and why Soh Cah Toa isn't relevant here...

I must be missing something fundamental
 
urbano said:
here is my latest diagram
It's the triangle beneath the object which you need to focus on.
redraw it separately, and larger, and label what you know. Its vertical line represents G Newtons.
 
urbano said:
here is my latest diagram
It's the triangle beneath the object which you need to focus on. Redraw it separately, and larger, and label what you know. Its vertical line represents G Newtons.
 

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