what is correct graph

vkash

1. The problem statement, all variables and given/known data

see it https://docs.google.com/leaf?id=0B5Z...thkey=COG4hNcE

sorry for low quality image if you are feeling problem in reading question in image then see this is question
Block A is placed on Block B whoose mass greater than that of A. there is a friction between the blocks, while the ground is smooth. A horizontal force P, is increasing linearly with time, begin act on A The acceleration a₁ a₂ of A and B respectively are plotted against time choose correct graph.


there is a question as well as options. I think all options are incorrect.

2. Relevant equations

F=M*a
f=u*N

3. The attempt at a solution

i think curve should straight line for a little time after a specific time. After a time when upper block slipped from lower one after that time acceleration of upper block is zero(no force) so a₁ became zero after a time but this is not zero in any figure.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

AJKing

Lets work through some logic because the answer is an option on the work sheet.

So, we know that friction comes in two states: Static Friction and Kinetic Friction.
When an object is static, there is a higher coefficient of friction than when an object is sliding on top of another one.

You can test this out by applying force to any object on your desk right now. You'll need to apply more force to get it into motion than to keep it in motion.

In the terms of our question, this means that since there is no friction under the large box, it will move when very little force is applied to it. And because there is friction between box A and box B, it will take more force to get box A into motion than to keep it in motion.

With that in mind, how will the two boxes act when you apply a very light force to box A?

PhanthomJay

There is always a variable force P acting on the upper block A (given). What about the force on B during that time?

vkash

when force P cross limit of static friction there is kinetic friction which is lower than static friction so force on B is lesser than it was (when there was static friction). If so then acceleration of B decrease by little amount and acceleration A should increase by little it is most likely the third curve but it in this graph acceleration of A is shown too higher(). should i tick c as correct option it is most closer to answer and this is also given as correct answer in the book. i don't think about this answer last time i try to answer because static and kinetic friction concept doesn't strike at that time. after all thanks for your useful reply.

PhanthomJay

Well that's strange, graph c is incorrect and graph b is better (and correct if us = uk), but what's that graph you hand sketched in the upper left corner? That one looks even better if us > uk, but also not quite correct for that case.

vkash

I draw that graph(upper left part) as correct answer of this question. this graph is in case when block block A fall down as it start slip over B.

If block A does not fall from B but it just slip On block B in that condition what will correct graph. this condition is not in question but i want to know in that case C should most appropriate but slope of a1 should little smaller it's around tan(90) and this is impossible.

You say B is better when block A start slipping it's acceleration(a1) will increase with greater rate and in that curve that rate of increase in acceleration is constant

AJKing

I think it's safe to say that this question was poorly planned. It leaves too much room for speculation.

I would say that C is the most correct except for the impossibility of box A suddenly increasing its acceleration into infinity.

PhanthomJay

Let's assume that block B is very long so that Block A never falls off it.

Let's focus on the lower block, Block B. After Block A starts slipping, what is the horizontal force acting on Block B (Hint: Draw a Free Body Diagram of Block B). What is the acceleration of Block B at this time? Now a few seconds later, what is the horizontal force acting on Block B, and now what is its accelerataion? None of the given graph's correctly show this.

vkash

I think we all think so(as in quote) and quit posting on this incorrect question. OK........

SammyS

After Block A begins to slip on block B, the force on block B will be constant, so its acceleration will also be constant. Since these are graphs of acceleration vs. time, in my opinion, graph c is far from correct.

I like graph b better, although it should show that the slope of a₁ increases at the point a₂ becomes constant.

vkash

But now slope of the curve for a1 should increase with more rate and that's constant during the whole process.

PhanthomJay

And that is why I view the hand graph you drew on the upper left corner as the correct graph (for us =uk), even though you gave the wrong reason for its correctness.