What is the tension in part GH?

[Chestermiller]

on 1kg left side,
a=T-T'-g
on 1 kg right side,
a=-T+g
on 2kg right side,
2a=-T-T'+2g

This is not what I get. Using the symbols and diagram in your post #8, I corresponding equations get are:

$$a=T-5g-g$$
$$a=T'-T+g$$
$$2a=-T'+2g$$

Do you see where T is not acting on the 2 kg mass, only T'?
Do you see where T' is acting on the 1 kg mass on the right?
Do you see where T' is not acting on the 1 kg mass on the left, but 5g is (the force exerted by the spring)?

 

[Suyash Singh]

This is not what I get. Using the symbols and diagram in your post #8, I corresponding equations get are:

$$a=T-5g-g$$
$$a=T'-T+g$$
$$2a=-T'+2g$$

Do you see where T is not acting on the 2 kg mass, only T'?
Do you see where T' is acting on the 1 kg mass on the right?
Do you see where T' is not acting on the 1 kg mass on the left, but 5g is (the force exerted by the spring)?

oh ok i understand now

1 kg mass on left,
T up, 5g down ,g down
a=T-5g-g

1 kg on right,
2g down , 1g down, T up
a=2g+g-T

2 kg right,
T' up,2g down
2a=-T'+2g

second equation is not matching

 

[Chestermiller]

1 kg on right,
2g down , 1g down, T up
a=2g+g-T

2g down , 1g down, T up
No. T' down, 1g down, T up

 

[Suyash Singh]

2g down , 1g down, T up
No. T' down, 1g down, T up

a=T'+g-T

 

[Chestermiller]

a=T'+g-T

Good. Now, add the three equations together. What do you get?

 

[Suyash Singh]

Good. Now, add the three equations together. What do you get?

4a=T-5g-g+T'+g-T-T'+2g
4a=-6g+3g
a=-3g/4

 

[Suyash Singh]

4a=T-5g-g+T'+g-T-T'+2g
4a=-6g+3g
a=-3g/4

from equation 1
a=T-6g
T=-3g/4+6g
T=21g/4