The Maths and Science Thread - Collection of Problems and Facts

[Varun]

Hmmmm.... I got it!

 

[Abhas]

Was that a question or a challenge?! lol I thought it was a challenge.. I just made this stuff up.
If you were after an 'theoretical' solution, I'm not sure this is it.

Anyway, it proves the point, and seems logical to me, so yeah

 

[King Cricket]

Prove Newton's first law of motion from his second law of the same.

Let's see who does this first.

 

[Neo95]

Prove Newton's first law of motion from his second law of the same.

Let's see who does this first.

I will try to prove it in the best way that I can.

This proof is not a perfect proof.

We will first state the respective laws

1st Law

An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

2nd Law

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

i.e in simple words F(net)=m*a.

To prove-The first law is a corollary(i.e direct consequence)

Proof-
Let us consider a book(Shiv Sena's Book) of mass 'm' that is simply lying on a table.It has force being acted upon by the atmosphere "F1" in a particular direction and equal force "F2" gravitational attraction force in the opposite direction.

Now by concept of vectors
F1=-F2-----(1)

Fnet=F1+F2=F2-F2=0

Using the formula Fnet=ma
ma=0 we know 'm' has some value so we can safely say that a=0 and a=0 only for bodies at rest.

Now King Cricket pushes the book off the table due to his digust with those Marathi chauvinists.

So King Cricket applies some force F3>F1 on the book and it falls of the table
Here Fnet=F1+F2+F3=F3.

Again from 2nd law we can conclude due to action of an unbalanced force on the book ,state of the book changed from rest to motion.

Hence proved

 

[Varun]

Prove Newton's first law of motion from his second law of the same.

Let's see who does this first.

Easy

2nd Law of Motion : F= ma
Let F = 0 (Since the forces are balanced) and m be a constant other than 0.
Then, 0 = ma, and from this a = 0.
Am I wrong ?

 

[King Cricket]

Am I wrong ?
__________________

Nope. Both of you are right. But I guess Neo over-complicated it a bit.

 

[ste_mc_efc]

I think you are mistaken. That's base units you are talking about

proper = base for those like me!

although in one uni module I have to use cm^-1, as a standard. Which bugs me.

 

[Brook]

Actually Neo didn't prove it generally, only for the case he specifies.

 

[Neo95]

Actually Neo didn't prove it generally, only for the case he specifies.

Yes but then you could apply the same logic for the general proof.

 

[Brook]

Also really you can't prove it, they're just a set of axioms anyway.

 

[Varun]

Also really you can't prove it, they're just a set of axioms anyway.

Science and Maths are just like this. If you go deeper and deeper, then you realize that it's all assumptions.
I love Science for that thing.

 

[Brook]

Science and Maths are just like this. If you go deeper and deeper, then you realize that it's all assumptions.
I love Science for that thing.

I agree, at the very least maths. Start off with a series of rules (the axioms) and everything just comes from them.

 

[Varun]

A tricky one :cool:


Bill 75 /-

three friends went to a hotel.the bill was Rs 75/-

each one contributed Rs.25/-.

the waiter took the bill to the cashier.

the cashier was happy & decided to give them a discount of Rs.5/- & said the waiter to return them Rs.5/-.

but he was confused how to distribute Rs 5 among 3 persons.

he kept Rs 2 in his pocket & gave one rupee to each one of the 3 persons.

so 1st each one contributed 25 Rs now as they are given 1 rupee back their contibution reduces to Rs 24.

they all contributed rs 24 that is 24x3=72 & 2 rupees are in the waiters pocket.

the total becomes 74 but they paid rs 75.

where is the remaining 1 rupee?.

 

[Abhas]

Each man pays 25, therefore, 25x3=75,
They get back 1 each, therefore their contribution = 24x3 = 72

the cashier gets 75. but gives 5 discount. Thus, 75-5 = 70
The waiter keeps 2 for himself.

70+2 = 72.

Abhas added 0 Minutes and 57 Seconds later...

The 2 in the waiter's pocket in your question was already included in the initial contribution of 25. it is just being added twice.

 

[Kshitiz_Indian]

Yeah I've had that one come to me as an SMS many times. Funny how people find it to be tricky, its just elementary thinking, its easy to spot that something is being added twice.