Deeply flawed friction problems

[Count Iblis]

See here:


https://www.physicsforums.com/showthread.php?t=299561


And:


https://www.physicsforums.com/showthread.php?t=297204


The correct solution to both problems posted by me was, of course, not the intended solution. How can it be that physics professors give such flawed problems to students?

 

[russ_watters]

As was correctly stated in the first thread:

no value for height is given in the question, therefore for all intensive purposes I think it has been ignored

You are overthinking the problems.

The nature of high school physics is such that problems have to be kept simple and that means when constructing real-world examples to use as problems, certain information is necessarily ignored. If a student went to his/her teacher and pointed out this issue, the teacher would help, telling them to ignore it. So there really isn't any problem.

What's more, accurately accounting for the effect of the drop height is extremely complicated (if it is even solvable at all). You might ask such a question of a sophomore in college level engineering student and have it be the only problem they solve that day. So I think a high school student would be able to figure out relatively quickly that it could safely be ignored.

I'm also not sure your method (it isn't a solution, it is a method) is even correct. It assumes the cart acts as a perfect spring to retard the fall, then doesn't spring back or oscillate. It also doesn't take into account that the friction coefficient changes as the bottom surface of the cart deforms.

For the second thread, your method certainly isn't correct, as it assumes a near instantaneous transition from sliding on the ramp to sliding on the ground. But that's impossible as you have three flat surfaces interacting with each other. The transition actually happens over a pretty long time in which contact is made between the front edge and the ground and the back edge and the ramp.

In the second problem, you also said this:

Here we assume that the transition from the ramp to the ground happens over a very short distance so that we can ignore gravity here.

So you made a simplifying assumption. I'm fine with that, but I have to ask: why are yours ok and the ones intended by the teacher not?

 

[Count Iblis]

One of the problem involves a change of direction. If the ramp has a smooth bend, then it will work ok.

In case of the cart/block springing back, what ultimately matters is that the momentum in the vertical direction must ultimately become zero. So, it gives you a universal result between the decrease of the momentum in the vertical direction that and the decrease of the momentum in the horizontal direction, assuming that the friction is still proportional to the normal force.

When I was in high school we actually did an experiment with a falling block and we had to take into account the impulse of the friction force at the moment of touch down...

 

[Count Iblis]

Corection, if the block/cart will spring back then, assuming the same friction constant, you'll get larger descreases of the momentum in the horizontal direction (naively you'll expect about twice as large).

Anyway, I think that it is simply stupid to make a problem in which you on the one hand assume friction forces proportional to the normal force and then expect that when a block is dropped the huge normal forces do not lead to any additional friction forces.


Of course, one is assuming a simplified model describing the situation which may not be 100% realistic. But surely, the simplist thing to assume is that if the normal forces annihilate an amount of momentum of P in the verical direction this will cause mu times P of momentum to be lost in the horizontal direction.


The problem with the problem is not that I disagree with any assumption made by the teacher about how to account for the impulse of the friction forces at touchdown. Rather, the teacher failed to see that any such effects exist and presented the students with an inconsistent problem.


This is similar to many flawed thermodynamics problems students at high school are presented by (i.m.o.) unqualified physics teachers. At university, we end up spending quite some time letting the student unlearn the flawed ideas about temperature, heat, work and entropy they learned at high school. That's an enormous waste of time for us.

 

[rcgldr]

The first problem could have been stated as a block being dragged at 80 kph and then released to allow friction to slow it down.