A particle of mass 1.2 kg is attached to one end of a light inextensible string of length 2 m . The other end of the string is fixed to a point \(O\) on a smooth horizontal surface. With the string taut, the particle moves on the surface with constant speed \(8 \mathrm {~ms} ^ { - 1 }\) in a horizontal circle with centre \(O\).
Find the angular velocity of the particle about \(O\).
Calculate the tension in the string.
The diagram below shows a woman standing at the end of a diving platform. She is about to dive into the water below.
The woman has mass 60 kg and she may be modelled as a particle positioned at the end of the platform which is 10 m above the water.
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When the woman dives, she projects herself from the platform with a speed of \(7.8 \mathrm {~ms} ^ { - 1 }\).
Find the kinetic energy of the woman when she leaves the platform.
Initially, the situation is modelled ignoring air resistance. By using conservation of energy, show that the model predicts that the woman enters the water with an approximate speed of \(16 \mathrm {~ms} ^ { - 1 }\).
Suppose that this model is refined to include air resistance so that the speed with which the woman enters the water is now predicted to be \(13 \mathrm {~ms} ^ { - 1 }\). Determine the amount of energy lost to air resistance according to the refined model.