Question

In a lab experiment a light flexible string is wrapped around a solid cylinder with mass M = 9.50 kg and radius R. The cylinder rotates with negligible friction about a stationary horizontal axis. A mass m = 3.00kg is tied at the free end of the string and release and the mass moves downward. Find the magnitude of the acceleration of the object of mass m.

Answer 1

Answer:$3.79 m/s^2$

Explanation:

Given

Mass $M=9.5 kg$

$m=3 kg$

Net Force is equivalent to $\sum F=ma$

with tension T in the string    

For mass $m$

$mg-T=ma$

$T=mg-ma--------1$

For cylinder

$T\cdot R=I\times \alpha$

I for solid cylinder is $\frac{2}{5}MR^2 , and \alpha =\frac{a}{R}$

thus $T=\frac{Ma}{2}----2$

Substitute the value of T we get

$\frac{Ma}{2}=mg-ma$

$a(\frac{M}{2}+m)=mg$

$a=\frac{mg}{\frac{M}{2}+m}$

$a=3.79 m/s^2$