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Two weights with masses m(1) and m(2) ar...

Two weights with masses `m_(1) and m_(2)` are suspended from a thread slung over a pulley (Fig.). Find the acceleration of the system `a_(1)` the tension of the thread F and the force `F_(p)` acting on the pulley's axis. Neglect the mass of the thread and of the pulley and friction.

Text Solution

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The correct Answer is:
`a="g"(m_(2)-m_(1))/(m_(2)+m_(1)), F=(2m_(1)m_(2)g)/(m_(2)+m_(1)), F_("pres")=2F`.
Let.s direct the y-axis vertically downwards. The equation of motion may be written as follows:
`-F+m_(1)g = -m_(1)a, -F+m_(2)g = m_(2)a`
where F is the tension of the string. Solving the system, we obtain the acceleration and the tension.
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