Mechanics
A block slides down a curved frictionless track
A block slides down a curved frictionless track and then up an inclined plane as in Figure. The coefficient of kinetic friction between the block and the incline is mu_ k. Use energy methods to show that the maximum height reached by the block is:
OMG! but what the hell is this ... when we read that they asking us to demonstrate maximum height.
Our brain associates the term with launching projectiles. the unwary could lose a few minutes or even tens of minutes trying to solve this problem using methods and equations of launching projectile.
The truth is that we have in our hands a energy problem.
Problems that include energy balance are truly easy to solve just have to raise a starting point after an end point and start make the energy balance between the two points. Let us always present in our lives that energy can neither be created nor destroyed be transform.
We will do what we discussed in earlier, rewriting figure that provides the problem to set a starting point (which we will call an "A") and an end point (which we will call point "B"). let's see how is all this in the next picture.
All right! so good! at this moment we understood that it is a problem of energy balance, then it left us a couple of fundamental questions of human existence that is what we are?
And where did we come from? OK no .. those are not the questions ...
That is for the end of the course after taking a few beers. by now the questions before us are what energies are present at point A? and what energies are present at point B?
The answers to these questions are not difficult. At point A all the energy that is present is potential and at point B there is potential energy (because we are at a height y_max) but ..
Part of the potential energy that was present at point A is transformed into heat. Heat is the work done by non-conservative forces, in our case it is the force of friction.
The work will be then, multiplied friction force by displacement. What is this displacement? the hypotenuse of triangle that have opposite leg whose magnitude is y_max (data we have) and the angle theta (other data we have).
We have all the ingredients to solve. we will see how our demonstration is:
beautiful! I love these problems you are asked to prove something because you know right now if you will be success or not in the examination! Hahaha!
As a curiosity I can tell (ever not tell a teacher) is that such problems also operates an old technique called "reverse engineering" you start from result and will operate then clear inversive to obtain an expression that you know his origin. so ...
Clear all and paste upside down as you did to make it appear that you came to the result as the examination asked you. (this trick saved me a lot in subjects such as classical mechanics and mathematical methods for physicists)
This was all in this post. if you like our work share it with your friends! see you later! and remember ... physics it's easy! very easy... ;)
Our brain associates the term with launching projectiles. the unwary could lose a few minutes or even tens of minutes trying to solve this problem using methods and equations of launching projectile.
The truth is that we have in our hands a energy problem.
Problems that include energy balance are truly easy to solve just have to raise a starting point after an end point and start make the energy balance between the two points. Let us always present in our lives that energy can neither be created nor destroyed be transform.
We will do what we discussed in earlier, rewriting figure that provides the problem to set a starting point (which we will call an "A") and an end point (which we will call point "B"). let's see how is all this in the next picture.
And where did we come from? OK no .. those are not the questions ...
That is for the end of the course after taking a few beers. by now the questions before us are what energies are present at point A? and what energies are present at point B?
The answers to these questions are not difficult. At point A all the energy that is present is potential and at point B there is potential energy (because we are at a height y_max) but ..
Part of the potential energy that was present at point A is transformed into heat. Heat is the work done by non-conservative forces, in our case it is the force of friction.
The work will be then, multiplied friction force by displacement. What is this displacement? the hypotenuse of triangle that have opposite leg whose magnitude is y_max (data we have) and the angle theta (other data we have).
We have all the ingredients to solve. we will see how our demonstration is:
As a curiosity I can tell (ever not tell a teacher) is that such problems also operates an old technique called "reverse engineering" you start from result and will operate then clear inversive to obtain an expression that you know his origin. so ...
Clear all and paste upside down as you did to make it appear that you came to the result as the examination asked you. (this trick saved me a lot in subjects such as classical mechanics and mathematical methods for physicists)
This was all in this post. if you like our work share it with your friends! see you later! and remember ... physics it's easy! very easy... ;)
Your explanation is simply awesome, easy to understand and you are giving what just a few teachers give to students, that is the way one can analyze the problem to come to the solution.
ReplyDeleteGreat work!