A-Level Kinematics of uniform circular motion and centripetal acceleration: worked solution

Question

A fairground ride uses a spinning circular platform 10.0 m across. A child in a seat can be treated as a 60 kg mass hanging from the end of a 3.00 m light rope. As the platform spins, the rope settles at an angle θ of 30.0° to the vertical. Ignore air resistance. (a) In the space below, draw a labelled free-body diagram for child A together with the seat, treating the child and seat as a single 60 kg mass.

Treating the child + seat (60 kg) as a single point mass, only two forces act (air resistance ignored): - Weight W = mg, acting vertically downward from the mass. - Tension T in the rope, acting along the rope, directed up and inward toward the top of the rope, at 30.0 degrees to the vertical. The horizontal component of T (T sin30) provides the centripetal force; the vertical component (T cos30) balances the weight.