3.
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A fairground ride consists of a cabin \(C\) that travels in a horizontal circle with a constant angular speed about a fixed vertical central axis. The cabin is attached to one end of each of two rigid arms, each of length 5 m . The other end of the top arm is attached to the fixed point \(A\) at the top of the central axis of the ride. The other end of the lower arm is attached to the fixed point \(B\) on the central axis, where \(A B\) is 8 m , as shown in Figure 2.
Both arms are free to rotate about the central axis.
The arms are modelled as light inextensible rods.
The cabin, together with the people inside, is modelled as a particle.
The cabin completes one revolution every 2 seconds.
Given that the combined mass of the cabin and the people is 600 kg ,
- find
- the tension in the upper arm of the ride,
- the tension in the lower arm of the ride.
In a refined model, it is assumed that both arms stretch to a length of 5.1 m .
- State how this would affect the sum of the tensions in the two arms, justifying your answer.