Help, static equilibrium solving for maximum angle of incline

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Homework Help Overview

The problem involves determining the maximum angle of incline for a machine pulling blocks of ice, considering static equilibrium and the forces acting on the blocks. The context is within the subject area of physics, specifically focusing on forces, tension, and equilibrium conditions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the forces acting on the blocks, including gravitational force and the pulling force from the machine. There is a focus on equating these forces to find the angle of incline. Some participants question the complexity of the equations presented and suggest a simpler approach.

Discussion Status

The discussion is active, with participants providing feedback on each other's reasoning. One participant expresses concern about the validity of their calculated angle, which is less than 2 degrees, prompting further verification of their approach. There is acknowledgment of the correctness of the revised method.

Contextual Notes

Participants are navigating through the assumptions of no friction and the specific forces involved in the scenario. There is a mention of potential overcomplication in the initial approach to the problem.

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Homework Statement


A machine in an ice factory is capable of exerting 3.3 * 10^2 N of force to pull large blocks of ice up a slope. The blocks each weight 1.21 *10^4 N. Assuming there is no friction, what is the maximum angle that the slope can make with the horizontal if the machine is to be able to complete the task.
Fg= 1.21*10^4 N
Ft= 3.3 * 10^2 N
Fn is perpendicular to Ft

Homework Equations


(in case the symbols my teacher uses are not standard)
Fg= weight
Ft= tension force
Fn= normal force
F()x= the x component of said force ie Ftx
F()y= the y component of said force ie Fty

The Attempt at a Solution


These are the only equations I can come up with using the given data, but no matter how I substitute them, I have yet to find a solvable equation.
Ftx= Ft/sin(\theta)
Fty=Ft/cos(\theta)
Fnx=Fn/sin(90-\theta)
Fny=Fn/cos(90-\theta)
Ft= sqrt(Ftx2 + Fty2)
Fn= sqrt(Fnx2 + Fny2)
Fty+Fny=Fg
Ftx=Fnx
but no matter how I substitute them, I have yet to find a solvable equation.
ex.
1.21*10^4 N=(3.3 * 10^2 N)/cos(\theta)+(sqrt(((3.3 * 10^2 N)/sin(\theta)2 + ((1.21*10^4 N)-(3.3 * 10^2 N)/cos(\theta))2))/cos(90-\theta)
 
Last edited:
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when the object is on an incline(without friction and with the machine pulling it) 2 forces act on it along the incline... i.e: the component of gravity and the pulling of the machine.

So equating those two you can get your answer..

PS:
There is no need of so many equations you've written up there..
 
Thanks, I was completely over complicating the problem,
Am I looking at it correctly now,because I keep getting an answer of less than 2 degrees, which doesn't sound right?
2jko3.jpg

Ft=cos(90-x)*Fg
-(cos^-1(Ft/Fg)-90)=x
-(cos^-1(3.3*10^2/1.21*10^4)-90)=1.563 degrees
 
yes looks right...
 
thanks for your help :)
 
my pleasure..:smile:
 

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