# Three weights and two pulley system

## Homework Statement

The goal is to find the tension in the strings and acceleration of each block. M1=8 kg, m2=1 kg, and m3= 2 kg. This is a study problem so not really homework but im having trouble finding anything quite like this problem.

m1g-t1=m1a1
t2-m2g=m2a2
m3g-t2=m3a3
t1=2r2
a2=a1+a'
a3=a'-a1

## The Attempt at a Solution

Initially i used a=((8-3)/(3+8))9.8 to figure out a1 giving me its acceleration of -4.455 m/s^2, I initially tried plugging this into the formulas given and that would give incredibly high values for a2 and a3 and a high value for the tension. So i tried using it as a positive for the right side of the system moving up. which actually gave me the tension i verified with calculators(ive spent hours on this now and beating my head into the wall.). From there i used this value to try and determine the rest, however a' never matchs for a2 and a3 and the equations for body 2 and 3 never work out. I also attempted to figure out the acceleration of m2 and m3 on their own and then use that acceleration plus a1 and that didnt work either. At this point I'm completely lost, I didnt have any issues with my homework but this is really bugging me that i cant figure this one out.

#### Attachments

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I can't understand what you did here. What is a? How did you find it's value? I think what you need to do here is solve the equations simulataneously. You have six equations and six variables. Proceed stepwise by eliminating one variable at a time. Should be doable.

I can't understand what you did here. What is a? How did you find it's value? I think what you need to do here is solve the equations simulataneously. You have six equations and six variables. Proceed stepwise by eliminating one variable at a time. Should be doable.
a isnt given, have to find a of each block so theres a1, a2, and a3. also have to find the tension in each string. To find a1 which is the acceleration downward of block 1 and upward of pulley 2 i took the mass of block 1(8kg) and subtracted the other two blocks(1 kg and 2 kg) then divided by the total weight(the pulleys and strings are weightless for this example.) giving .455 then multiply by g for acceleration 1 giving 4.455 m/s^2(both rounded.) I then plugged this into equation 1 to give me a tension of 42.76N. given the equations this would then make t2 21.38N, plugging this in to find a2 giving me 11.58 m/s^2. put this into the equation for a2 gives a' of 7.125 m/s^2. plug this into the a3 equation would give a a3 of 2.67m/s^2. The problem run into is if i plug t2 into the equation for m2/a3 it gives an a3 of -.891 m/s^2 which doesnt match or if i plug in the a3 i solved for it would give a t2 of 14.26 which causes t2 to not match and thats my frustration. I tried to solve for acceleration of m2 and m3 the same way i did m1, then add and subtract a1 depending which direction they are moving but i had the same problem where they dont match. So either the equations i was given are wrong or i am doing something massively wrong.

TSny
Homework Helper
Gold Member
Initially i used a=((8-3)/(3+8))9.8 to figure out a1
This is an incorrect equation for a1. You cannot lump m2 and m3 together and treat them as one mass when finding a1. To help see this, consider the case where m2 → 0. It should be fairly intuitive what the accelerations of a1 and a3 would be in this case. But would your method of finding a1 give you what you would expect in this case?

Note that your attachment lists 6 equations for 6 unknowns. So, you already have enough equations to find everything.

Then im completely lost then I have attempted to solve without using that to solve for a1 first and i cannot for the life of me isolate any single variable. Homework didnt have anything like this, nor did we do anything in class like this, and the tutors at school are even lost. was hoping to get it figured out by office hours on tuesday =/

never mind i finally got it, i kept trying to solve t2 in terms of t1 and substituting that and it became rediculously convoluted. Finally just subbed in 2t2 for t1 and was able to isolate so looks like a1=4.9 m/s^2, a2=9.8 m/s^2, a3=0 m/s^2, t1= 39.2N, t2= 19.6N, a'= 4.9 m/s^2

TSny
Homework Helper
Gold Member