Deriving Equation: g = aave(M + m / m)

[vrobins1]

I am supposed to derive this equation: g=a_ave(M + m / m)

It gives me two pairs of equations:
T₁-F_r = Ma₁
mg-T₁= ma₁

and

T₂ + F_r = Ma₂
mg - T₂ = ma₂It also says, "hint: for the first pair of equations, eliminate the unknown tension. Do the same for the second pair of equations. In this new pair of equations, eliminate the unknown force of kinetic friction F_r.

So I tried just canceling out the T in the first set of equations, leaving me with
-F_r = Ma₁ and mg = ma₁, but that doesn't seem right. I am mostly just confused on how to "derive an equation". I'm just looking for a little direction--do I set them equal to each other? I'm just confused on what it's asking, I've never done a problem like this before and have been trying to understand it forever! Any help would be greatly appreciated. Thanks!

 

[danago]

I am supposed to derive this equation: g=a_ave(M + m / m)

It gives me two pairs of equations:
T₁-F_r = Ma₁
mg-T₁= ma₁

and

T₂ + F_r = Ma₂
mg - T₂ = ma₂


It also says, "hint: for the first pair of equations, eliminate the unknown tension. Do the same for the second pair of equations. In this new pair of equations, eliminate the unknown force of kinetic friction F_r.

So I tried just canceling out the T in the first set of equations, leaving me with
-F_r = Ma₁ and mg = ma₁, but that doesn't seem right. I am mostly just confused on how to "derive an equation". I'm just looking for a little direction--do I set them equal to each other? I'm just confused on what it's asking, I've never done a problem like this before and have been trying to understand it forever! Any help would be greatly appreciated. Thanks!

When it says to cancel the T's out, it doesn't mean to literally pretend they never existed. To eliminate the T's from the first two equations, re-write them so that the T's are isolated in both equations.

Now it should be obvious that if A=C and B=C, then A=B. Use the exact same idea with the equations, and see if you can work from there.

 

[vrobins1]

Thanks that helped, I think I got it now!