A fairground ride consists of four carriages connected to a central vertical pole, as shown in the following view from above.

Question 39

A fairground ride consists of four carriages connected to a central vertical pole, as shown in the following view from above.

A motor rotates the central pole about its axis. This results in the four carriages each moving along a circular path.

The distance from the middle of each carriage to the centre of the pole is 3.20 m. When they are moving, each carriage experiences an air resistance force of 85.0 N. Assume that there are no other significant resistive forces.

Which torque does the motor need to apply to the pole to keep the system rotating at constant maximum speed?

A 5.44 N m                 B 272 N m                  C 544 N m                  D 1090 N m

Reference: Past Exam Paper – March 2019 Paper 12 Q12

Solution:

Answer: D.

Consider one carriage.

Distance from the middle = 3.20 m

Air resistance experienced by 1 carriage = 85.0 N

To keep a carriage rotating at constant speed, a force equal to the air resistance must be applied.

Torque = F × d

Torque to keep one carriage rotating = 85 × 3.2 = 272 Nm

This is the torque on one carriage. The system consists of 4 carriages.

Total torque = 4 × 272 = 1088 Nm