Barron's 2nd Edition PT1 Q30

Barron's Book

30) This question asks us to find the speed of the mass at the lowest point of the circle. The object travels in circular motion, which means that the net force in the y-direction will be equal to the centripetal force.

Where F[c] is centripetal force, m is mass v is speed, r is radius of the circular path, and F[Net] is the net force

We also know that the net force is equal to the sum of forces acting on an object. Our next step is to draw out the force diagram for all forces in the y-direction.

Where v is speed, T is tension, and F[g] is gravitational force

Please keep in mind that v(speed) in the diagram above is not a force, but is drawn to clarify the motion of the object.

Finally, we need to sum the forces, equate to centripetal force, and solve for the speed(v) at this point.

Where F[Net] is net force, F[c] is centripetal force, T is tension force, F[g] is gravitational force, m is mass, g is acceleration of gravity, v is speed, and r is radius of circular path

Answer: B