Work done by friction on an incline plane

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Homework Help Overview

The discussion revolves around calculating the work done by friction on an inclined plane, focusing on the forces involved, particularly the normal force and the coefficient of friction. The original poster presents their approach to solving the problem, including relevant equations and their attempts at deriving the necessary relationships.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the derivation of the angle θ using the sine function and its implications for calculating the normal force. There are inquiries about simplifying the approach and concerns about extraneous equations in the original poster's work. Questions arise regarding the necessity of solving for acceleration in the context of the force balance equation.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's calculations and seeking clarification on how to streamline their approach. There is no explicit consensus on the best method yet, but suggestions for improvement and simplification are being explored.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the methods they can use or the information they can assume. The original poster's equations and reasoning are under scrutiny for accuracy and efficiency.

idllotsaroms
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Homework Statement



http://postimage.org/image/gprwhko37/

Could someone check my work to make sure I'm doing this problem correctly?
Where:
s : hypotenuse or distance
h : height
uk : coef friction

Homework Equations



W = F*D
Force Normal = mgcosθ
Wfriction = (uk * N) * s(distance)

The Attempt at a Solution


Solve for θ to use to find force normal
Sinθ = h / s
θ = arcsin(h/s)

Y component of weight of box = mgcos*arcsin(h/s)
Fy = may = N - mgcos*arcsin(h/s)
N = mgcos*arcsin(h/s)

Then plug N into equation Wfriction = -uk * N * s
Wfriction = -uk*mgcos*arcsin(h/s)*s
 
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After a few extraneous equations, the result looks right.
 
rude man said:
After a few extraneous equations, the result looks right.

Thank you Rude man, but how would I remove the extraneous equations? Could you show me an alternate shorter way to go about doing this?

Also, would I have to solve for a when using Fy = may = N - mgcos*arcsin(h/s)?
 
Last edited:
idllotsaroms said:

Homework Statement



http://postimage.org/image/gprwhko37/

Could someone check my work to make sure I'm doing this problem correctly?
Where:
s : hypotenuse or distance
h : height
uk : coef friction

Homework Equations



W = F*D
Force Normal = mgcosθ
Wfriction = (uk * N) * s(distance)

The Attempt at a Solution


Solve for θ to use to find force normal
Sinθ = h / s
θ = arcsin(h/s)

Y component of weight of box = mgcos*arcsin(h/s)
Fy = may = N - mgcos*arcsin(h/s)
Omit the red.

N = mgcos*arcsin(h/s)
Then plug N into equation Wfriction = -uk * N * s
Wfriction = -uk*mgcos*arcsin(h/s)*s

see above.
 

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