- #1
Mr Davis 97
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Homework Statement
Masses M1 and M2 are connected to a system of strings and pulleys as shown. The strings are massless and inextensible, and the pulleys are massless and frictionless. Find the acceleration of M1.
Homework Equations
Newton's 2nd Law of motion
The Attempt at a Solution
So here is my line of reasoning. We have four objects with which we can use Newton's second law to derive relationships which will get us an explicit expression of the acceleration of block 1.
Newton's law for block 1:
##T_1 - m_1 g = m_1 a_1##
Newton's law for block 2:
##T_2 - m_2 g = m_2 a_2##
Newton's law for pulley with block 2:
##T_1 - 2T_2 = 0##
##T_1 = 2T_2##
Next, if we combine the equation for block 1 with the equation for block 2, and if we assume ##a_1 = a_2##, then we get,
##\displaystyle a_1 = \frac{g(2m_2 - m_1)}{m_1 - 2m_2}##
However, this is not the correct expression, because we must have that if M1 = M2 then ##\displaystyle a_1 = \frac{g}{5}##
Where am I going wrong with my reasoning?