Help, static equilibrium solving for maximum angle of incline

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The discussion centers on solving for the maximum angle of incline at which a machine can pull blocks of ice weighing 1.21 * 10^4 N using a force of 3.3 * 10^2 N, assuming no friction. Participants explore various equations related to forces acting on the blocks, including tension, gravitational force, and normal force. One user initially struggles with the complexity of their equations but later simplifies their approach, leading to a calculated angle of approximately 1.56 degrees. The final consensus indicates that this angle is indeed correct for the given parameters. The discussion highlights the importance of simplifying equations in physics problems to find accurate solutions.
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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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