Some one me with the derivation

  • Thread starter lioric
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    Derivation
In summary, we discussed a problem involving light pulleys and a frictionless cord. We derived an expression for the acceleration of block 2 as a function of the mass of block 1. The final expression is a2=m2g/(4m1+m2).
  • #1
lioric
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Homework Statement


In figure, the pulleys and the cod are light, all surfaces are frictionless, and the cord does not
stretch.
a) How does the acceleration of block 1 compare with the acceleration of block 2?
The mass of block 2 is m2 = 1.3 kg. Derive an expression for the acceleration of the
block having mass m2 as a function of the mass of block 1, m1.


Homework Equations


mg-T=m2a2
T=m1a1=m12a2



The Attempt at a Solution



The first one (a) i have done.
Which is that due to the pulley the acceleration of a2=1/2 a1

Can some one help me with the b part
 

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  • #2


Hi lioric. Is there supposed to be a diagram to accompany this?
 
  • #3


sorry i was in a rush and forgot
now its there
 
  • #4


This is what i got for the derivation. But something is not right
 
  • #5


Mass 2 equation
The pulley give 2 tensions so 2T
m2g-2T=m2a2

Mass 1 equation

T=m1a1
since a2 = 1/2a1
a1= 2a2

T=m12a2

substitute mass 1 equation in mass 2 equation as T

m2g-2(2m1a2)=m2a2
m2g-4m1a2=m2a2

make subject a2

-4m1a2-m2a2=-m2g
change negative sign by multiplying by -1

4m1a2+m2a2=m2g

a2(4m1+m2)=m2g

a2=m2g/4m1+m2

But i feel that this is not right.
 
  • #6


lioric said:
In figure, the pulleys and the cod are light, all surfaces are frictionless, and the cord does not stretch.
It's cog, not cod.
mg-T=m2a2
That equation is not correct. What are all the forces on m2?
 
  • #7


m2 would have gravity and tension
 
  • #8


haruspex said:
It's cog, not cod.
I believe it's c-o-r-d
 
  • #9


ok enough about the "CORD"

m2 would have gravity and tension those are the forces on M2

so what's next?
 
  • #10


lioric said:
The pulley give 2 tensions so 2T
m2g-2T=m2a2
That's better (your post crossed with mine).
a2=m2g/4m1+m2
Looks ok to me, if parentheses inserted:
a2=m2g/(4m1+m2). What bothers you?
 
  • #12
lioric said:
It shows the answer where g is out side a bracket. mine is in the numerator
The two are equivalent.
 
  • #13
ok thank you
 

1. What is derivation in science?

Derivation in science refers to the process of obtaining a scientific result or theory from basic principles and assumptions. It involves using logical reasoning and mathematical equations to derive a conclusion or formula.

2. Why is derivation important in scientific research?

Derivation plays a crucial role in scientific research as it allows scientists to understand the underlying principles and mechanisms behind a phenomenon or theory. It also helps in verifying the validity of existing theories and predicting new outcomes or results.

3. How do scientists perform a derivation?

Scientists use a combination of mathematical equations, logical reasoning, and experimental data to perform a derivation. They start with a set of known principles and assumptions and use them to derive a conclusion or formula through logical steps and mathematical calculations.

4. Can derivations be proven wrong?

Yes, derivations can be proven wrong if there are errors in the assumptions or mathematical calculations used. This is why scientists often verify their derivations through experimental data and peer review before accepting them as valid.

5. How is derivation different from deduction?

While derivation and deduction both involve using logical reasoning to arrive at a conclusion, they differ in their starting points. Derivation starts with basic principles and assumptions, while deduction starts with accepted facts or observations. Additionally, derivation is used to obtain a new result or theory, while deduction is used to draw conclusions from existing knowledge.

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