Some one me with the derivation

[lioric]

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

 

[NascentOxygen]

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

 

[lioric]

sorry i was in a rush and forgot
now its there

 

[lioric]

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

 

[lioric]

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.

 

[haruspex]

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?

 

[lioric]

m2 would have gravity and tension

 

[NascentOxygen]

It's cog, not cod.

I believe it's c-o-r-d

 

[lioric]

ok enough about the "CORD"

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

so what's next?

 

[haruspex]

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?

 

[lioric]

Look at this

https://docs.google.com/viewer?a=v&...xNx2tl&sig=AHIEtbQYTiDtrIkEvdaF2EveiVHB_EJn2g

It shows the answer where g is out side a bracket. mine is in the numerator

 

[haruspex]

It shows the answer where g is out side a bracket. mine is in the numerator

The two are equivalent.

 

[lioric]

ok thank you