Gioncoli 4th ed chap4 q59, tension

[Idoubt]

Homework Statement

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Homework Equations

The Attempt at a Solution

I assumed to meet the condition, there can be no vertical acceleration so if i assume the string of mass m_B to make an angle theta with the vertical, then if T is tension,

Tcos(theta) = m_Bg ...1
Tsin(theta) =m_Ba_x...2Since the 2 masses are relatively at rest then their acceleration (horizontal ) should be equal

so T = m_Aa_x...3

eq 2\3 gives sin(theta) = m_B\m_A

solving eq 3 and 1 i get a_x=gtan(theta)

also

m_ca_c=F-T-Tsin(theta)

and m_Ca_C=F-(m_A+m_B)a_x

But I can't find a way to get rid of a_C

Is there something wrong with my approach or reasoning?

 

[tiny-tim]

Hi Idoubt!

But I can't find a way to get rid of a_C

No, that's fine …

a_C is a_X ​

 

[SammyS]

m_A does not move relative to m_C, so a_C = a_x .

 

[Idoubt]

Doh ! *slaps myself*... *twice*...*moans in agony*...

gotta remember to read questions properly before diving in

thx guys