Easy university problem Newton's 2nd law

[Optikspik]

The question is basically, a block with a mass "m" is sliding up and down on a incline plane with an angle of inclination that is β. The leaving velocity (Start velocity v_i) is v0 and the frictionskoefficient is between the plane and the block is μ. Determine the velocity "v" when the block has returned to its starting position.

-μ*mg cos β - mg sin β=m*a

(-μ*mg cos β - mg sin β)/m=a

-v=v0+at, , however, know v and t is unknown, how i find any of them? v0 is= v0 and a is what i wrote.

Any tips ? And have i done right so far?

 

[nasu]

Did you learn about work and energy yet? It is much easier to solve it by using these concepts.

 

[Optikspik]

IF u want to use kincematic u have to do

0=v0+at on the way up, and then

v=0+at on the way down,

And use fgx positive on way down and negative on way up, right?

But how do you use energy please show :)

 

[nasu]

In both cases you will need to find how far does it go up the incline.
So you have the acceleration, you have the initial speed and you know the final speed (at the maximum height). Find the distance traveled.
You can find the time first, but is not necessary.

 

[Optikspik]

So s= 0^2- v0^2 / ( 2a)

How does this help me?

 

[nasu]

Well, then you know the distance for the second part of the motion, the motion back to the base.
For this motion you know distance, acceleration (different than when it went up) and initial velocity. You can find final velocity.

 

[Optikspik]

Okay, then i know how to solve right.

But how do you do with energy?

 

[nasu]

Well, once you know the distance, you can use the work-energy theorem to find the final KE.

 

[Optikspik]

Well, once you know the distance, you can use the work-energy theorem to find the final KE.

And that theorem is? :p

Like I just took my first course at physics at the university :p

 

[haruspex]

And that theorem is? :p

Like I just took my first course at physics at the university :p

In the present context, it means that work is conserved, except for that lost to friction.
You can use this to find the distance up, then use it again to find the velocity on returning to the bottom.
Going up, suppose it goes a distance d (up the slope). How much work is done against friction? What kinetic energy did it start with? How much KE does it have at the highest point? What other energy has it lost or gained?