Velocity of an object on an inclined plane

[Prabs3257]

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

 

[PeroK]

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?

 

[Prabs3257]

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

 

[PeroK]

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.

 

[Prabs3257]

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

 

[PeroK]

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.

 

[PeroK]

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.

 

[Prabs3257]

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