Two Pulleys with two acceleration and two tensions (Diagram included)

AI Thread Summary
The discussion revolves around a physics problem involving two masses connected by strings and pulleys, where the goal is to calculate the tensions (T1 and T2) and accelerations of the blocks. The coefficient of friction between the upper block and the table is 0.32, and the user has derived initial equations but is unsure about their approach. Key equations include the relationships between tensions and accelerations, with suggestions made to substitute variables to simplify the problem. The user received guidance on how to proceed with the calculations by eliminating variables. This collaborative effort aims to clarify the solution process for the given physics scenario.
Wara
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pulley

Homework Statement


Two masses are attached together by means of light inextensible strings and light frictionless pulleys as shown in the diagram. The system is released and the upper block slides along the table. The coefficient of friction between this block and the table is 0.32. Calculate the magnitude of the tensions (T1 and T2) and accelerations while the blocks are acceleration.
http://content.screencast.com/users/Waraa/folders/Snagit/media/bc6a12fc-dd79-4db6-91a4-1057f75aca6e/03.10.2012-15.11.45.png

Homework Equations


(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1

The Attempt at a Solution


T1 = 113.7N
T2 = 196N

(1) + (2) + (3) + (4)
m1a1 + m2aa + 2T1 + 2a2 = T1 - μmg + m2g - T2 + T2 + a1
2a2 = T1 - μmg + m2g + a1

I'm stuck right there. Am I even doing it right?
 
Last edited by a moderator:
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Wara said:

Homework Statement


Two masses are attached together by means of light inextensible strings and light frictionless pulleys as shown in the diagram. The system is released and the upper block slides along the table. The coefficient of friction between this block and the table is 0.32. Calculate the magnitude of the tensions (T1 and T2) and accelerations while the blocks are acceleration.
http://content.screencast.com/users/Waraa/folders/Snagit/media/bc6a12fc-dd79-4db6-91a4-1057f75aca6e/03.10.2012-15.11.45.png


Homework Equations


(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1


The Attempt at a Solution


T1 = 113.7N
T2 = 196N

(1) + (2) + (3) + (4)
m1a1 + m2aa + 2T1 + 2a2 = T1 - μmg + m2g - T2 + T2 + a1
2a2 = T1 - μmg + m2g + a1

I'm stuck right there. Am I even doing it right?
Hi Wara! :wink:
Wara said:
(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1

Fine so far! :smile:

ok, now you should substitute for a2 and T2 from (3) and (4) into (2):

(1) m1a1 = T1 - μmg
(2) m2a1/2 = m2g - 2T1​

then eliminate T1 :wink:
 
Last edited by a moderator:
tiny-tim said:
Hi Wara! :wink:


Fine so far! :smile:

ok, now you should substitute for a2 and T2 from (3) and (4) into (2):

(1) m1a1 = T1 - μmg
(2) m2a1/2 = m2g - 2T1​

then eliminate T1 :wink:

Thank you so much.
 
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