Question

Trivia - Concept of friction

In the diagram shown, the coefficient of friction between the blocks is 'k' and that between the bigger block and ground is 'k1'. Find out the acceleration of both the blocks.

Answer 1

Well, somehow OS wont let me draw the diagram :'(

Answer 2

Diagram in attachment.

Answer 3

Unless it tips, I do not see why M would move at all.
No friction between M and n unless there is a leftward force on m toward M. Maybe I am missing something?

Answer 4

The mass m is hanging; so it will go downwards. As the string is inextensible; block M will be forced to move forward. (Note: The thing, which may look like a mirror, is actually a fixed wall. I somehow forgot to label it.)

Answer 5

I do not see why M is forced to move "forward," but I could see it tipping.
Without a lateral (horizontal force) pushing M and m together, friction between these two will not occur.

Answer 6

Just to make the question more clear -
-No need to consider toppling (as it will happen only on a subset of the values of variables)
-You can assume that friction cannot prevent the motion (or in other words, consider using kinetic friction)

Answer 7

I find \(a = g\Large \frac{m-k_1M}{M+(2+k)m}\)

Answer 8

@Vincent-Lyon.Fr
Can you please upload your solution ?

Answer 9

My answer was \[a=g \frac{ m-k _{1}M-(k _{1}m) }{ M+(2+k)m-(k _{1}m) }\]

Answer 10

For those who are facing problem with Draw and Equation tool; visit http://openstudy.com/study#/updates/52de57e0e4b003c643a10b24

Answer 11

Is it the answer you came up with, or is it the answer given by your book?

Answer 12

The question is from the notes of my coaching institution. I have a solution for my answer (if that helps).

Answer 13

Okay, I am posting my solution now -

Answer 14

@douglaswinslowcooper
Consider the (green) system boundary. If we assume that the whole system is in a state of rest then it implies that -
T=0
mg=friction

But then, the normal reaction between the blocks would also be zero; making friction zero too.

Hence, by contradiction, we can say that the system cannot be in equilibrium.

Answer 15

Oops, if forgot to attach the figure..

Answer 16

For complete solution - see the free body diagram (I am too lazy to make one separately for each block)

Make the (obvious) equations.

Use A = a (to cut-short your solution)
How I got the above ^^ equation; we call it tension trick (for proof - wait for my next question).

Finally, you'll get \[a=g \frac{ m-k _{1}M-(k _{1}m) }{ M+(2+k)m-(k _{1}m) }\]

Answer 17

Yea, again missed to upload..

Answer 18

For Tension Trick; visit - http://openstudy.com/study#/updates/52dff5dde4b0942cc9ddb51d