Solving Differential Equations for Inclined Plane.

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Homework Help Overview

The discussion revolves around solving differential equations related to the motion of a block on an inclined plane. Participants are attempting to find the function S(t), which represents the distance traveled by the block over time.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are exploring the relationship between the variables involved, questioning the correct formulation of S(t) as either S=(x^2+y^2)^0.5 or S=(x^2+(xtanφ))^0.5. There is also discussion regarding the interpretation of the force R and its implications on the equations of motion.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning the definitions and assumptions related to the forces acting on the block. Some guidance has been offered regarding the interpretation of R as the normal reaction force, but no consensus has been reached on the overall approach to solving the equations.

Contextual Notes

There are constraints related to the initial conditions provided, and participants are navigating the implications of these conditions on their attempts to solve the problem.

sergej21
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Homework Statement



http://img192.imageshack.us/img192/6482/asderl.jpg

Find S(t).

Homework Equations



I managed to find these equations, but don't know how to solve them completely.

mx``=Rsinφ
my``=Rcosφ-mg
xtgφ+y=h
x`(0)=0; x(0)=0; y`(0)=0; y(0)=h

The Attempt at a Solution


Need to find s(t). Is S=(x^2+y^2)^0.5?Thank you!
 
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sergej21 said:
Need to find s(t). Is S=(x^2+y^2)^0.5?

According to the picture, s=(x^2+(xtanφ))^0.5.

ehild
 
The question : what is R. If it is an arbitrary force, perpendicular to the surface, you have done. If it is the normal reaction force the slope exerts on the block, R=mg cos(φ).

The solution of the problem "block sliding down on slope" is much easier with a coordinate system where the axes are aligned parallel with and perpendicular to the slope.

ehild
 

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