pulley problem

In the arrangement shown in figure, the mass of the body A is 4 times that of body B. The height h=20 cm . At a certain instant, the body B is released and the system is set in motion. What is the maximum height (in cm), the body B will go up? Assume enough space above B and A sticks to the ground.

Can anyone help me to understand the concept behind pulley with the help of problem

Note by Yogesh Ghadge
5 years ago

No vote yet
1 vote

  Easy Math Editor

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.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. 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 1

paragraph 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 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

LetthedisplacementofmassB=HLetthetensionatmassB=TSo,ifwecontinuefindingthetensionuptoA,weendupwith2TatmassA.Now,byVirtualworkdone,Networkdonebytheinternalforces=0ForceInt.A×DisplacementA+ForceInt.B×DisplacementB=02T×h+T×H=02hT=THCancellingTfrombothsides,H=2h()signshowsthatdisplacementisinoppositedirectiontohConsideringonlymagnitude,H=2hH=2×20H=40cmLet\quad the\quad displacement\quad of\quad mass\quad B\quad =\quad H\\ Let\quad the\quad tension\quad at\quad mass\quad B\quad =\quad T\\ So,\quad if\quad we\quad continue\quad finding\quad the\quad tension\quad upto\\ A,\quad we\quad end\quad up\quad with\quad 2T\quad at\quad mass\quad A.\\ \\ Now,\quad by\quad Virtual\quad work\quad done,\quad \\ Net\quad work\quad done\quad by\quad the\quad internal\quad forces\quad =\quad 0\\ { Force }_{ Int.A }\times { Displacement }_{ A }+{ Force }_{ Int.B }\times { Displacement }_{ B }=\quad 0\quad \\ 2T\quad \times \quad h\quad +\quad T\quad \times \quad H\quad =\quad 0\\ 2hT\quad =\quad -TH\\ Cancelling\quad T\quad from\quad both\quad sides,\\ H\quad =\quad -2h\\ (-)\quad sign\quad shows\quad that\quad displacement\quad is\quad in\quad opposite\quad direction\\ to\quad h\\ \\ Considering\quad only\quad magnitude,\\ H\quad =\quad 2h\\ H\quad =\quad 2\times 20\\ H\quad =\quad 40cm

Here @Guiseppi Butel @Yogesh Ghadge @satvik pandey

Abhineet Nayyar - 5 years ago

Log in to reply

Hello Abhineet your answer is correct but you have missed a last point that makes your answer wrong

When block B travels 40 cm then it gains a final velocity v

v^2=2as

v^2=2×g/2×0.4....................40cm in 0.4m

v^2=4

v=2m/s

Then we have to find the distance traveled by block under gravity

u^2/2g=s

4/20=s

0.2=s

0.2m=20 cm

Total distance covered = distance covered by block due to pulley + distance covered by block under gravity

=40+20=60cm

Now see if you have any doubt about the ans.

And thank you for sharing you mechanical work method

Yogesh Ghadge - 5 years ago

Log in to reply

Your answer is wrong because in taking components of force you have made an mistake force on block b is 2T and 4mg in downward direction because of taking on T it will not make any sense because both the tension are in upward direction so if you T only the force acting on block it will be totally wrong

Yogesh Ghadge - 5 years ago

Log in to reply

You are in class 10, right? There is a method in class 11, "The virtual work done method". You may learn about it on internet.

Abhineet Nayyar - 5 years ago

Log in to reply

Yes you are right bro. The answer should be 40cm

fig fig

For A

4mg2T=4ma14mg-2T=4ma_{1}...................(1)

For B

Tmg=ma2T-mg=ma_{2}..............................(2)

Also 2a1=a22a_{1}=a_{2}.............................(3)

putting this value in equation (2)

Tmg=2ma1T-mg=2ma_{1}

Multiplying this equation with 2 yields

2T2mg=4ma12T-2mg=4ma_{1}............................(4)

Adding eq. 1 and 4 yields

2mg=8ma12mg=8ma_{1}

So a1=g4a_{1}=\frac{g}{4} and a2=2g4a_{2}=\frac{2g}{4}

As S=ut+0.5at2S=ut+0.5at^{2}

So for block A 0.2=g8t2 0.2=\frac{g}{8}t^{2}

or t2=8(0.2)gt^{2}=\frac{8(0.2)}{g}

So for block B

S=0.5(2g4)(8(0.2)g)S=0.5(\frac{2g}{4})(\frac{8(0.2)}{g})=0.4 m=40cm

But I must say @Abhineet Nayyar that your method was the shortest I think.

satvik pandey - 5 years ago

Log in to reply

Satvik but when block b travel 40 cm it's gains a final velocity v which is 2m/s then block b travels a distance till its velocity is decelerated so after calculation the distance traveled by block b under gravity is 20cm . So the total distance traveled by block b is 20+40=60cm

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge Yes Yogesh you are right. I completely missed that and I think @Abhineet Nayyar missed that too. :P

Thank you Yogesh for pointing it.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey Satvik i have misconception about friction can you explain me the way to solve h c verma's book question no. 11 in friction chapter. please give a quick response

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge Q.11 of exercise?

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey yes!

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge You just need to draw FBD of the three blocks separately then use F=maF=ma.

Do have problem regarding the direction frictional force?Suppose if the blocks are accelerating towards right. Then friction forces acting on the blocks are towards left.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey see i want to buy fundamentals of physics by halliday so which edition should i buy

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge Every editions are basically same. So you can by any edition. I think the latest is 9th9^{th} edition.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey i have bought fundamentals of physics 8th edition but there is a problem . There are no answers of problem written so how would we come to know that we have solved the problem correctly.

And i was going through 42 problem of chapter no 2 i got the ans 0.94 m/s^2 is it correct?

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge In that book answers of all question in exercise are not given. Only answer of odd question numbers are given.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey OK

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge i wanted to ask you a question that was really means centripetal acceleration? i defines that its acceleration is towards center but , as an example if earth rotates at the centripetal acceleration of 9.8 m/s^2 then will earth exert force to us towards space or towards earth itself ?

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge You can find the solutions of this book here

satvik pandey - 5 years ago

Log in to reply

Simply find the accelerations of A and B. Then find the time (t) that A will require to cover distance 'h' then use equations of motion to find the distance covered by B in time 't'.

satvik pandey - 5 years ago

Log in to reply

The main problem is I don't know to find acceleration in like this arrangement of pulley

Yogesh Ghadge - 5 years ago

Log in to reply

fig fig

Always try to draw the FBDs first.

Can you setup two equations for block A and B using newton's second law?

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey I got it thank you . Can you tell me how you post diagram in comment box

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge Please refer to this note. I think there is a similar problem on brilliant also.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey I have got that wrong so I asked you. And see I have framed equipment like this F-2T=0 T=F/2 taking block b as system a=T/m a=F/2m Thus acceleration of block A a=F/4m because acceleration of block B is twice than A .is this correct

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge Equipment is wrong word there should be eq

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge I don't understand what is 'F' in your equation.

Refer to diagram:

For Block A

4mg2T=4ma 4mg-2T=4ma............(1)

For block B

Tmg=ma1T-mg=ma_{1}................(2)

Also 2a=a12a=a_{1} .................(3)

Now you have 3 equations and 3 variables. Just find the values of a and a1a_{1}

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey F refers to the downward force of block A

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge So F=4mg.

But you wrote F-2T=0. Block A is not in equilibrium.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey See in first condition before Block B is released they both are in equilibrium

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge I have done by different point of view but our result is same 2a=a1

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge This eq. is just the part of whole solution. I have made 3 eq earlier. By solving those equations you will get the exact values of the accelerations of the A and B.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey But try to understand I make an sequence of finding T first then the acceleration and the tension in the rope is equal in every period of time so it doesn't matter if I take the period before motion or after

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge I think we are approaching to the problem in different ways.

Can you find time period in which block A covered distance 'h'.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey T=0.4s

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge i got same too. :)

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey We both think in different ways but have same direction

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge Yeah! Vector having different magnitude but same direction. :D

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey Satvik when do you get time to do all this stuff .when I was in class 10 in didn't get time to do this. What is the board of your school

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge I am in CBSE board. Well I have started studying mechanics when I was in class 9. I have studied most part of the mechanics in summer vacations.

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey Is CBSE board better than SCC board

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge I don't know what is SCC board. What is the board of your school?

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey SSC

Yogesh Ghadge - 5 years ago

Log in to reply

@Satvik Pandey satvik i want to ask you about writing comments. In my comments all the words are one behind the other I use enter to start the sentence from new line the but when i click post the words again come one behind the other so how do you write your comment so nicely

Yogesh Ghadge - 5 years ago

Log in to reply

@Yogesh Ghadge To start a new line you need to press enter key two times.

satvik pandey - 5 years ago

Log in to reply

@Yogesh Ghadge Here we have to consider the period in which the blocks are in motion

satvik pandey - 5 years ago

Log in to reply

@Satvik Pandey @satvik pandey You in class 11th right?

Abhineet Nayyar - 5 years ago

Log in to reply

@Satvik Pandey a comes out to be g/4 and a1=g/2

Abhineet Nayyar - 5 years ago

Log in to reply

@Abhineet Nayyar Correct. :)

satvik pandey - 5 years ago

Log in to reply

Is the answer 40 cm.?????

Abhineet Nayyar - 5 years ago

Log in to reply

No its 60 cm

Yogesh Ghadge - 5 years ago

Log in to reply

Could you prove your statement?

Guiseppi Butel - 5 years ago

Log in to reply

@Guiseppi Butel Yes I can

Yogesh Ghadge - 5 years ago

Log in to reply

@Guiseppi Butel I and satvik has discussed it's solution below you can refer to that. And if you still have doubt after reference then ask me I will clear the doubt

Yogesh Ghadge - 5 years ago

Log in to reply

Yes its 60cm

Kirti Prajapati - 1 year, 4 months ago

Log in to reply

I agree with you.

Guiseppi Butel - 5 years ago

Log in to reply

The answer is got to be 40...Wait i'm gonna post a solve!!

Abhineet Nayyar - 5 years ago

Log in to reply

@Abhineet Nayyar Sorry, Abhineet. I was thinking about the static situation. If A is lowered 20 cm then B will end up at 40 cm higher. I wasn't thinking about the accelerations involved.

Guiseppi Butel - 5 years ago

Log in to reply

You may also use the Mechanical Energy Conservation Law and have in mind that displacement h of body A will correspond to displacement 2h of body B and that every moment B body speed is twice that of body A. Then you can find B body speed (v) at the instant body A sticks the ground. You will easily get that v^2=2gh. And the maximum height will be 2h+h=3h.

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...