Question

Calculate the acceleration of an Atwood machine if one of the two weight is four times as heavy as the other. What is the tension in the string if the lighter of the bodies has a mass of 3.0 kg ? Find also the time for this mass to cover a distance of 0.45 cm .

Answer 1

$mg-T=-ma$

$4mg-T=4ma$

We get

$T=mg+ma$

$4mg-mg-ma=4ma\to a=\frac{3}{5}g=5.9(m/s^2)$

$T=mg+ma=3\cdot9.81+3\cdot 5.9=47.13(N)$

And finally

$h=at^2/2\to t=\sqrt{2h/a}=\sqrt{2\cdot0.45\cdot10^{-2}/5.9}\approx0.04(s)$