Two masses m1 and m2 are connected by a string over a frictionless pulley of negligible mass. The masses are released from rest. Air resistance is negligible.Mass m2 accelerates downwards at g2 . What is m1m2 ?
Question
Two masses m1 and m2 are connected by a string over a frictionless pulley of negligible mass. The masses are released from rest. Air resistance is negligible.Mass m2 accelerates downwards at g2 . What is m1m2 ?
Solution
The problem involves two masses m1 and m2 connected by a string over a frictionless pulley. The acceleration due to gravity is represented by g. When the system is released from rest, mass m2 accelerates downwards at an acceleration g2.
The force acting on m2 is its weight, which is m2*g. This force is causing the acceleration of the entire system. Therefore, we can write the equation of motion for m2 as follows:
m2*g = (m1 + m2)*g2
We are asked to find the ratio m1/m2. To find this, we can rearrange the above equation:
m1/m2 = g/g2 - 1
So, the ratio of m1 to m2 is equal to the ratio of the acceleration due to gravity to the acceleration of m2, minus 1.
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