# Help Needed here

1) An arrangement of pulley block system is shown above. The bigger block has mass $$10$$ kg and smaller block has mass $$m$$ kg. The coefficient of friction between the blocks is $$0.1$$. and the coefficient of friction between the block and the ground is $$0.4$$. Find the maximum value of $$m$$ in kg so that the arrangement is in equilibrium.

2) A rope of length $L$ and mass $M$ is being pulled on a rough horizontal floor by a constant horizontal force $F=Mg$. The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between rope and floor is $\frac{1}{2}$. Then the tension at the mid point of the rope is

Note by Tanishq Varshney
6 years ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

img

Link if image not visible here

- 6 years ago

img

- 6 years ago

Thanks for the the sourabh $\ddot \smile$

- 6 years ago

No, actually don't need to .

- 6 years ago

Actually the friction force heredosen't at all act as variable force and as we draw a FBD we see no variable force acting on the system (rope+earth)

- 6 years ago

if it was asked to find the tension at any distance $x$ then we have integrate?? plz reply

- 6 years ago

About the second problem may i speak something?

- 6 years ago

yes surely

- 6 years ago

how do i post an image? I have solved the second problem

- 6 years ago

Dont know may be satvik knows

- 6 years ago

First upload the picture on imgur. And then type this --

! [img] (url of the image) Without spaces.

- 6 years ago

Thanks for telling the steps to upload image bro....!!!!.

- 6 years ago

You are welcome! :)

- 6 years ago

- 6 years ago

ok answer are 1) 2.5 kg and 2) $\frac{Mg}{2}$

- 6 years ago

I got 1st one. Wait I am posting. :)

- 6 years ago

Thank you guyz means a lot.

- 6 years ago

Its our pleasure Right satvik pandey ???!!!

- 6 years ago

Yeah! sure!

- 6 years ago

Hey check out this problem

- 6 years ago

I got that. I solved it by using concept of pseudo force.

- 6 years ago

yup i also did that using the concept of pseudo force , u should now try this one

- 6 years ago

I haven't studied Oscillations till now. :(

- 6 years ago

DO reply if u liked the problem.

- 6 years ago

I recently saw your this problem. Is $\mu$ coefficient of friction between A and B or B and C? Is block A fixed or movable? ??

- 6 years ago

Looks like I m late

- 6 years ago

Are you guys fine? A massive earthquake has been experienced in large parts of Northern India.

- 6 years ago

I got up late in the morning so i don't have any idea of the tremors. XD

- 6 years ago

Did you sleep till 12 noon? :P

- 6 years ago

nope Till 11. :P

- 6 years ago

The Earthquake was experienced at 11:46 AM. I was going through Saurabh's solution at that time.

I found a method to solve that question by using calculus.

- 6 years ago

Do we really need to solve that question using calculus when we can use the newton laws directly??

- 6 years ago

Hey @Saurabh Patil and @satvik pandey can i have ur views on this

- 6 years ago

Sorry bro, I am not very good in Maths. :(

- 6 years ago

We can use Newton's Law directly. There is no problem. It's just another way of solving the same question.

img

Applying Newton's law on $\Delta y$ we get--

$T(y)-T(y+\Delta y)-\mu \frac { M }{ L } \Delta y=\frac { M }{ L } \Delta y\frac { g }{ 2 }$

$lim\quad \Delta y\rightarrow 0\frac { T(y+\Delta y)-T(y) }{ \Delta y } =-\frac { Mg }{ L }$

$\frac { dT(y) }{ dy } =-\frac { Mg }{ L }$

$\int _{ T(0) }^{ T(L/2) }{ dT(y) } =\int _{ 0 }^{ L/2 }{ -\frac { Mg }{ L } }$ dy

$T(0)=Mg$

So $T\left( \frac { L }{ 2 } \right) -T(0)=-\frac { Mg }{ 2 }$

On putting the value of $T(0)$

we get $T\left( \frac { L }{ 2 } \right) =\frac { Mg }{ 2 }$

But I must say that Saurabh's method is better that this.

- 6 years ago

img

From the FBD of block of mass $m$

The block will be at rest if

$T+f_{2}=mg$

But there is a horizontal force acting on the block. If the block has to be at rest then $N=0$ So $f_{2}=0$

So $T=mg$

Now only horizontal force acting on block of mass $M$ is $f_{1}$ and $T$

So $T=f_{1}$

So $mg=f_{1}$

As the friction is static so it can have variable magnitude. The value of m will be maximum when $f_{1}$ is maximum. And the limiting value of f1 is $\mu N_{0}$. No force is acting in vertical direction other than Normal reaction from ground and Mg. So $N_{0}=Mg$

So the value of m will be maximum when $mg=\mu Mg$. Just put the values. You will get the answer. :)

- 6 years ago

yup i missed that thing that no horizontal force will act on the the block m , i ended up on thinking how to find $N$, any ways thanx a lot, what about the second

- 6 years ago

I am trying second one. :)

- 6 years ago

but u get 4kg from here but the answer is 2.5 kg

- 6 years ago

Hi satvik, You missed two forces i.e. tension forces on the 10 kg block, one downward and other rightwards . They are acting on clamped pulley, and should be included in fbd, because clamped pulley is part of 10kg mass.

- 6 years ago

Hi Kushal. Thanks for pointing the mistake. I made a blunder mistake is a hurry. :( Also I substituted the wrong value of $\mu=1/4$ that's why the the answer came out to be 2.5 kg. :(

- 6 years ago