Answer
(a) $T=3508.4N$
(b) $v=14.85m/s$
Work Step by Step
(a) The tension in the cable $T$ is made up of 2 forces:
- The horizontal centripetal force $F_c$ that always points to the center of the circle.
- The vertical component of $T$ that supports the chair and occupant's weight $W$, which we call $T_y$
From the given angle, we have $T_y=T\cos60$
Since there is no vertical acceleration, $$T_y=W$$ $$T\cos60=179\times9.8=1754.2N$$ $$T=3508.4N$$
(b) Since $F_c$ is the horizontal component of $T$, $F_c=T\sin60=3038.4N$
We have the mass of a chair and its occupant $m=179kg$. From the figure, we can find the radius of the circle $r=15m\sin60=13m$.
$$v=\sqrt{\frac{F_cr}{m}}=14.85m/s$$
