can anyone explain how to make equations in atwood machine
explain with examples
for 11th class student
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Answers
don't know dear sorry for taking free point
Atwood machine
The Atwood machine (or Atwood's machine) was invented in 1784 by the English mathematician George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics.
Illustration of the Atwood machine, 1905.
The ideal Atwood machine consists of two objects of mass m1 and m2, connected by an inextensible massless string over an ideal massless pulley.[1]
Both masses experience uniform acceleration. When m1 = m2, the machine is in neutral equilibrium regardless of the position of the weights.
Contents
Equation for constant accelerationEdit
The free body diagrams of the two hanging masses of the Atwood machine. Our sign convention, depicted by the acceleration vectors is that m1 accelerates downward and that m2 accelerates upward, as would be the case if m1 > m2
An equation for the acceleration can be derived by analyzing forces. Assuming a massless, inextensible string and an ideal massless pulley, the only forces to consider are: tension force (T), and the weight of the two masses (W1 and W2). To find an acceleration, consider the forces affecting each individual mass. Using Newton's second law (with a sign convention of {\displaystyle m_{1}>m_{2}}) derive a system of equations for the acceleration (a).
As a sign convention, assume that a is positive when downward for {\displaystyle m_{1}} and upward for {\displaystyle m_{2}}. Weight of {\displaystyle m_{1}} and {\displaystyle m_{2}} is simply {\displaystyle W_{1}=m_{1}g} and {\displaystyle W_{2}=m_{2}g}