How do I write a Newtons 2nd law equation without using numbers?

Question

Heres a crappy diagram of what the problem looks like:
<---[12kg]----[20kg]----[16kg]

Three boxes are tied together and are pulled forward on a frictionless surface by a rope with a tension of Ft=12N.

a) Write Newtons 2nd law equation for the horizontal forces on each box individually. (No numbers allowed)


If someone could write one of these, or all of them so I can see what to do, a few people have written them for me but they keep putting numbers in them and I dont know how to take them out.

Answer 1

Just dont put the numbers in, define your masses, m1 m2 m3, and the forces Ft1 Ft2 and so on

Answer 2

Call the force exerted by the rope between the 12 and 20 kg masses T1 and the force exerted by the rope between the 20 and 16 kg masses T2. Then Newton's second law for the forces acting on the 12 kg mass would be

12N-T1 = 12a

Newton's second law and the 20 kg mass would be

T1-T2 = 20a

And Newton's second law and the 16kg mass would be

T2 = 16a

Now, you have three equations with three unknowns. So you can solve to find T1, T2, and a.

Answer 3

Newton's second law: Fnet=ma

For 16 kg box: T1=ma

For 20 kg box: T2-T1=ma

for 12 kg box: T3-T2=ma

Answer 4

Force on left mass = Ft - force of tension in string between the two masses on the left

Force on Middle = Force of tension between two masses on left subtract the force tension between the two masses on the right

Etc