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Maths and Physics (Problems)


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AuthorMaths and Physics (Problems)
post 57

You need to clarify another condition: the rope is massless and unstretchable.
If you don't say that, the problem is a very hard one :p

so post 58 is correct, assuming those conditions!
Yea, sorry I forgot to mention those things.

G as a weight means weight and not mass..I was going to write "(in Newtons)" but figured people would guess it haha.

#58 is the right answer (making changes according to the wrong assumption :P)..can you explain how though? I was unable to interpret how the force is being applied or it's effect on the rope.

#59 - I wrote down the exact question, and weight indeed refers to force..it's only in chemistry that weight = mass hehe ^_^ But well, this is an illustration in a book and the solution says twice the weight. Just that the solution is rather weird and I wasn't able to understand it. But tell me -
The energy must be released when decelerating the distance l:
Why distance l? The distance should be equal to the height = nl.

#60 - Indeed it involves being able to see that the question can be written in the form (a-b)^2. What is your solution by Heron's Formula?
G as a weight means weight and not mass..I was going to write "(in Newtons)" but figured people would guess it haha.
If you ask a person about his weight, he is going to answer with a mass in kg. (Or if you ask a girl, it will be a slap in your face.) In fact, I would say that an overwhelming percentage of the word 'weight' refers to mass.


#58 is the right answer (making changes according to the wrong assumption :P)..can you explain how though? I was unable to interpret how the force is being applied or it's effect on the rope.
You naturally have assume (thanks Enano_) that all parts except the triangle are massless, the rope ideal, and the roof is fixed. If you pull at the rope with the force F, all parts of the rope will be subject to this force. There are 2 parts of the rope that is pulling the triangle up, so the total force is 2F.


Why distance l? The distance should be equal to the height = nl.
Each link of the chain is accelerating down from it's initial position at the height nl. When touching the table it is starting to decelerate. In real life this would involve lots of peaks when bouncing etc. However, the average deceleration can be assumed to be spread out the entire length of one link, l.

I have unfortunately made a very bad explanation concerning the falling chain. The energy is not conserved because of losses in the impact. The momentum is preserved during any impact. This solution explains it better. As you can see, the result stays the same.

This is the correct solution:
The velocity after falling from the height nl:
v = sqrt(2nlg)
The momentum right before impact is:
p = mv = m*sqrt(2nlg)
The momentum will be preserved during the impact. The length of the impact is l and the average acceleration a.
p = m*sqrt(2la)
Since p is equal in both cases we get:
m*sqrt(2nlg) = m*sqrt(2la)
sqrt(2nlg) = sqrt(2la)
2nlg = 2la
ng = a
The force needed to accelerate an object is f=a*m. This gives us:
ng = f/m
f = mng


#60 - Indeed it involves being able to see that the question can be written in the form (a-b)^2. What is your solution by Heron's Formula?
I stopped halfway and started thinking so I did not get an answer using that path. Today, I examined it more and I noticed that this equation with 3 variables does have infinite solutions, but funnily enough only one without complex numbers. This is the design of the problem that makes it possible to solve.
Move all parts of the equation to the left side. You now have a function f(a,b,c). You can now set constant values for b and c, and find the local minimum for f(a). After that, do the same for b and c. This is the answer to the problem. This approach will provide an answer to any similar problem that isn't based on whole numbers.
If you ask a person about his weight, he is going to answer with a mass in kg. (Or if you ask a girl, it will be a slap in your face.) In fact, I would say that an overwhelming percentage of the word 'weight' refers to mass.
Indeed, even many of those who have studied Physics in their life get confused. But my point is that this was a Physics question, posted in a Physics thread, to Physics people by a Physics person :P

Each link of the chain is accelerating down from it's initial position at the height nl. When touching the table it is starting to decelerate. In real life this would involve lots of peaks when bouncing etc. However, the average deceleration can be assumed to be spread out the entire length of one link, l.

Each link of the chain is accelerating down from it's initial position at the height nl. When touching the table it is starting to decelerate. In real life this would involve lots of peaks when bouncing etc. However, the average deceleration can be assumed to be spread out the entire length of one link, l.
I think we need to assume that there will be no bouncing. Thus I did the same as your first part - Change in momentum = m[sqrt(2gnl)] (Final momentum is 0).
However I didn't think of using conservation of momentum..thanks, I'll try with that now. When I get time I'll send you the photo of the solution, maybe it's wrong :)
Ok a very simple one:-
In how many ways can a student score exactly a total of 60 marks in 3 papers of 60 marks each? {Assume no negative marking system}
62 c 2

1891
good man, you remember this still:)
PR sir has taught us great:)
high five!
1. If you take a very long and resistant rope and put it around the Earth's equator (suppose it's a sphere and its diameter is 13,000 km) holding it tight, then you add 1 meter to this rope (so it won't hold the earth tight, there will be a small distance between the Earth and the rope) so as the distance between the rope and the earth in each point around the equator is equal (the distance between the Earth and the rope is evenly distributed around the equator), what will be the distance between the rope and the earth?

2. What are the exact times in a day in which the hour and the minute needles (I think that's what they are called) on a watch are superposed (one over the other)?

^^ These are not hard, but the first one has an interesting result and the second thing happens to me frequently as I don't see the hour needle and I'm trying to search it just to find it's under my minute needle :)
A man has 17 houses he decided to distribute them among his 3 children such that the eldest get half of them second one get one-third of the eldest one and the third one get one-thitd of the second one now tell how will he distribute them
Add 1 to 17 and solve it u will get 9,6,2 and the total sum will be 17
Add 1 to 17
why do we need to add 1 to 17?? why not minus one??
for ParaLeul:

1. The rope will be 1 meter away from earth. Circ = 2*Pi*R, so the increase in Circ is the same as an increase in R.

2. 24 times. For each hour, the two needles can coincide once.
2. 24 times. For each hour, the two needles can coincide once.

I believe the answer is 22, there is a certain trick to this question. I don't know why 22 though.

for Lord spiral-doom:
If you subtract one then you'll have 16, which is not divisible by 3 :P
I believe the answer is 22, there is a certain trick to this question. I don't know why 22 though.

They coincide at 11:59(23:59) and 12:00(00:00) separately.
I still believe in 24 :o)
Post 69, nr 1:
The rope will be 1/2/pi = 0.15915... meters over the equator. Funnily enough, the diameter of the sphere (in this case earth) does not matter.

Post 69, nr 2:
Lets say we start at 00:01. In 24 hours the long needle does 24 full turns. The short needle does 2 turns. They pass each other 24-2=22 times. However, if we start at 00:00 they are initially covering each other and does so again at the next 00:00. So the correct answer would be 23 times.

Post 70:
1/2 + 1/3 + 1/9 is not equal to 1. The last 1/18 of the property is unaccounted for. I suggest they sell all, share the money according to the will and donate the last 1/18 to charity. :)
1/2 + 1/3 + 1/9 is not equal to 1. The last 1/18 of the property is unaccounted for. I suggest they sell all, share the money according to the will and donate the last 1/18 to charity. :)

C'mon, where will the main live?? :P

Though the actual answer is that he later sells the remaining house.
Lol u can't get one third of 8
How many zeroes are there at the end of 50! (50 factorial) ?
12 zeroes
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