Difficulty with this Problem involving a Pully and Cart

[haruspex]

Hm... Okay, they actually do make a lot of sense! My only question is, for the m_1a=m_1g-T_1 equation, what would a be? Because isn't the acceleration of the weight dependant on gravity?

Yes, that's the m₁g term, but it is partly countered by the tension in the string.

 

[i_love_space_and_eng]

Yes, that's the m₁g term, but it is partly countered by the tension in the string.

Alright... so how would we go on to find the "a" without the T1 and T2?

 

[haruspex]

Alright... so how would we go on to find the "a" without the T1 and T2?

You need one more equation, a simple relationship between a and α.

 

[i_love_space_and_eng]

Okay, so this is what I set up.
I(a/r)= ((m1g-m1a)-m2a)R
Does that look correct? I substituted a/r for α .

 

[Chestermiller]

What is I in terms of the mass M and radius R of the pulley?

 

[i_love_space_and_eng]

What is I in terms of the mass M and radius R of the pulley?

It will be 6.125*10^-5kgm^2

 

[Chestermiller]

It will be 6.125*10^-5kgm^2

Please provide it algebraically.

 

[i_love_space_and_eng]

I=(2/5)mr²

 

[haruspex]

I=(2/5)mr²

So combine the three equations in #32 with those in #39 and #43.

 

[i_love_space_and_eng]

Okay so I plugged it all in and got this:
(2/5)m(r^2)(a/r)=(((m1g)-(m1a))-(m2a))R
I plug in all the correct numbers but the issue is I still get the wrong answer. Did I write my equation correctly? Should I be getting the right answer and I am probably doing a math error?

 

[haruspex]

Okay so I plugged it all in and got this:
(2/5)m(r^2)(a/r)=(((m1g)-(m1a))-(m2a))R
I plug in all the correct numbers but the issue is I still get the wrong answer. Did I write my equation correctly? Should I be getting the right answer and I am probably doing a math error?

Your equation looks right. First simplify it, then post that and your calculation steps.

 

[Chestermiller]

Okay so I plugged it all in and got this:
(2/5)m(r^2)(a/r)=(((m1g)-(m1a))-(m2a))R
I plug in all the correct numbers but the issue is I still get the wrong answer. Did I write my equation correctly? Should I be getting the right answer and I am probably doing a math error?

Those should be capital R's on the left side of the equation, since they are the radius of the pulley. They should also then cancel with the R on the right hand side of the equation. Please provide you algebraic results for a (i.e., in terms of algebraic variables).