Question 791452
In physics class problems cords have no mass, and there would be no friction of the cord at the hole either.
The centripetal acceleration of the air puck, {{{a[c]}}}, in {{{"m /"}}}{{{s^2}}}, is
{{{a[c]=v^2/r}}} with
{{{v}}}= linear velocity of the puck, and
{{{r}}}= radius of the trajectory of the puck
The centripetal force, {{{F[c]}}}, that keeps the air puck in that steady circular motion is the mass of the puck times the centripetal acceleration:
{{{F[c]=(0.23kg)(v^2/"1.1 m")}}}
That centripetal force is the weight of the 1.1kg mass suspended from the end of the cord, which is equal to that mass times the acceleration of gravity, {{{g=9.81m}}}{{{"/"}}}{{{s^2}}}, so
{{{(0.23kg)(v^2/"1.1 m")=(1.1kg)*9.81m}}}{{{"/"}}}{{{s^2}}}
{{{v^2=(1.1kg/"0.23 kg")}}}{{{(1.1m)(9.81m)/s^2=51.6091}}}{{{m^2}}}{{{"/"}}}{{{s^2}}}
So, {{{v=sqrt(51.6091)}}}{{{"m/s"=7.18}}}{{{"m/s"}}}