Efficient Path Tracing: Solving for Time and Motion with Inclined Planes

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Homework Help Overview

The discussion revolves around a physics problem involving a small disk on an inclined plane, where the disk is given an initial velocity and is subject to friction. Participants are tasked with determining the time it takes for the disk to come to rest and the equations of motion governing its movement.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the acceleration components in both the x and y directions and express uncertainty about how to proceed with the problem. There are questions regarding the interpretation of the initial velocity's direction and the meaning of the initial moment angle of velocity. Some suggest the need to eliminate variables to simplify the equations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem setup. Some guidance has been offered regarding the formulation of differential equations, but there is no consensus on the best approach to take at this point.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a question about the relationship between the angles involved in the problem.

Brilli
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Homework Statement


A small disk A is placed on an inclined plane forming an angle (alpha) with horizontal and is imparted an initial velocity v. Given coefficient of friction =k and ant initial moment angle of velocity =90 degrees. Find out how long it takes to come ro rest and give the equation of motion.

Homework Equations

The Attempt at a Solution


I found out that acceleration in x-axis is kgcosαcos(θ)/
In y-axis is gsinα-kgcosαsinθ
Tanθ=vy/vx.
I don't know how to proceed ahead.
 
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Brilli said:
I don't know how to proceed ahead.
Make a sketch.
[edit] Don't you think ##\alpha = \theta ## ?
Brilli said:
initial moment angle of velocity =90 degrees
What does this mean ?
 
@BvU I believe the initial velocity v is horizontal (90 degrees with the uphill/downhill direction). If you take the initial velocity to be the -x direction and downhill to be +y, then that is the situation his equations seem to describe.If that’s a correct interpretation then the problem at this point boils down to solving a system of 2 differential equations. (Well first we must eliminate θ, or one of the velocity components I suppose, or even both components if we introduce the total speed.)

Maybe there’s a clever way to solve that system of equations but I don’t see a good way. (I don’t think I can help at this point.)
 
Brilli said:

Homework Statement


A small disk A is placed on an inclined plane forming an angle (alpha) with horizontal and is imparted an initial velocity v. Given coefficient of friction =k and ant initial moment angle of velocity =90 degrees. Find out how long it takes to come ro rest and give the equation of motion.

Homework Equations

The Attempt at a Solution


I found out that acceleration in x-axis is kgcosαcos(θ)/
In y-axis is gsinα-kgcosαsinθ
Tanθ=vy/vx.
I don't know how to proceed ahead.
Can you write the differential equations for the x and y directions?
Can you see how to get one differential equation that does not involve θ?
 

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