2 A fairground ride consists of raising vertically a bench with people sitting on it, allowing the bench to drop and then bringing it to rest using brakes. Fig. 2 shows the bench and its supporting tower. The tower provides lifting and braking mechanisms. The resistances to motion are modelled as having a constant value of 400 N whenever the bench is moving up or down; the only other resistance to motion comes from the action of the brakes.
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\caption{Fig. 2}
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On one occasion, the mass of the bench (with its riders) is 800 kg .
With the brakes not applied, the bench is lifted a distance of 6 m in 12 seconds. It starts from rest and ends at rest.
- Show that the work done in lifting the bench in this way is 49440 J and calculate the average power required.
For a short period while the bench is being lifted it has a constant speed of \(0.55 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Calculate the power required during this period.
With neither the lifting mechanism nor the brakes applied, the bench is now released from rest and drops 3 m .
- Using an energy method, calculate the speed of the bench when it has dropped 3 m .
The brakes are now applied and they halve the speed of the bench while it falls a further 0.8 m .
- Using an energy method, calculate the work done by the brakes.