Newtons 3rd Law (Ropes, Pulley)

[PhysicsNoob76]

Homework Statement

A 2.5 kg mass is attached to a 3.5 kg mass by a light string that passes over a friction-less pulley. The masses are released.

a) What is the magnitude of the acceleration of the masses?
b) What is the tension in the string?

Homework Equations

(I think) Ft - mg = ma

The Attempt at a Solution

I drew 2 free body diagrams for both the weights and they both have Fg and Ft on the y.

On this 6th line, starting with (2.5)(a)... I made it so that Ft2 = Ft2
My answer was suppose to be 6.54 m/s in the work I showed because the acceleration of the bigger weight will accelerate negatively. So ignore the minus sign for my answer to a =
I think I've done the best I could, but my answer is still wrong, not sure why.

 

[lewando]

The magnitude of the acceleration will be the same, but in opposite directions.

 

[PhysicsNoob76]

The magnitude of the acceleration will be the same, but in opposite directions.

Yeah, I knew that, I should have included that too. I need actual with with the question though.

 

[lewando]

You have 2 equations, 2 unknowns (one needs fixing-- one of the masses should be accelerating upwards-- use "a", the other, downwards-- use "-a"). Solve for a.

 

[PhysicsNoob76]

You have 2 equations, 2 unknowns (one needs fixing-- one of the masses should be accelerating upwards-- use "a", the other, downwards-- use "-a"). Solve for a.

I've done some changes, but I am still getting it wrong...

 

[lewando]

Since the heavier one is accelerating downward, replace "a" in line 2 with "-a". Try again.

 

[PhysicsNoob76]

Since the heavier one is accelerating downward, replace "a" in line 2 with "-a". Try again.

Ohhhhhhh, thank youuuuuuuuuuuuu. I re-did my whole thing and now it works!