Question

A $10kg$ block is pulled on the vertical plane along a frictionless surface in the form of an arc of a circle of radius $10m$. The applied force is of $200N$ as shown in the figure. If the block started from rest at $A$, what is the velocity at $B$?

Answer 1

Surface is smooth, which means no less in energy due to friction.

length $CB=10\times sin{60}^{\circ }=\frac{10\sqrt{3}}{2}=5\sqrt{3}lengthCA=10-10cos{60}^{\circ }=10-5=5changeinKE=networkdone\frac{1}{2}m{v}^2=-mg\left(AC\right)+200\left(CB\right)\frac{1}{2}m{v}^2=-100\times 5+200\times 5\sqrt{3}m{v}^2=(-500+1000\sqrt{3})\times 2\therefore v^2=246.6\therefore v=15.69\simeq 15.7\frac{m}{s}$