Velocity of an object on an inclined plane

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Homework Help Overview

The discussion revolves around a problem involving the velocity of an object on an inclined plane, specifically analyzing the forces and energy involved as the object moves down the slope. The scenario includes a varying coefficient of friction and the application of the work-energy theorem.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the work-energy theorem and differentiation to find maximum velocity. There are questions about the validity of the expressions used and the integration of friction forces. Some participants reflect on their initial approaches and seek clarification on errors made in their calculations.

Discussion Status

The discussion is active, with participants offering hints and suggestions for re-evaluating their approaches. There is acknowledgment of the need for clearer justification of expressions and the integration of forces. Some participants have indicated they found correct answers through alternative methods, while others are still exploring their mistakes.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the amount of direct assistance provided. There is a focus on understanding the underlying principles rather than simply obtaining the correct answer.

Prabs3257
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Homework Statement
A body starts from rest on a long incline plane of slope 45 degree the coefficient of friction between the body and the plane varies as u=0.3x where x is the distance traveled down the plane the body will have maximum speed when x is
Relevant Equations
Work energy theorem
I used work energy theorem between initial top point and point x along the incline(downwards) i got the expression of v then diffrentiated it to get a maxima but it gives me a wrong ans which is 10/6 but the actual ans is 10/3 please tell me what i did wrong
 

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Prabs3257 said:
Homework Statement:: A body starts from rest on a long incline plane of slope 45 degree the coefficient of friction between the body and the plane varies as u=0.3x where x is the distance traveled down the plane the body will have maximum speed when x is
Homework Equations:: Work energy theorem

I used work energy theorem between initial top point and point x along the incline(downwards) i got the expression of v then diffrentiated it to get a maxima but it gives me a wrong ans which is 10/6 but the actual ans is 10/3 please tell me what i did wrong

There is a simple approach to this problem. Hint: what can you say about the forces when the body reaches its maximum speed?
 
PeroK said:
There is a simple approach to this problem. Hint: what can you say about the forces when the body reaches its maximum speed?
Ya i first did it using forces only and got the correct answer but i want to know what i did wrong with this
 
Prabs3257 said:
Ya i first did it using forces only and got the correct answer but i want to know what i did wrong with this

You'd need to post your working. I'm not sure if it's worth it, though.
 
PeroK said:
You'd need to post your working. I'm not sure if it's worth it, though.
I did post an img of it in the ques
 
Prabs3257 said:
I did post an img of it in the ques
There's almost no working there at all. You have an expression for ##v(x)## that you haven't justified. Did you integrate the friction force down the slope?

PS It looks like you just mixed up a factor of ##\sqrt 2## at some point.
 
Prabs3257 said:
I did post an img of it in the ques

Here's a neat trick. Maximising ##v## is the same as maximising ##v^2##. That makes the differentiation easier.
 
PeroK said:
There's almost no working there at all. You have a very simple expression for ##v(x)## that you haven't justified and is wrong in any case. Did you integrate the friction force down the slope?
Oh sorry i just forgot f was not constant and i integrated it now and got the correct ans thanks
 

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