(Circular motion) Many types of bird can be seen flying in circles without flapping their wings, often because they have found a region of rising air, such as a thermal. This type of flight is called soaring. The wings of soaring birds generate a lift force L (generally directed upwards) even when they aren't flapping, that counteracts the weight force W acting on the bird. To fly in a circle the bird will bank, i.e. tilt the inner wingtip downwards and the outer wingtip upwards. The lift force L generated by a banking bird is in the direction shown in the figure below - it is tilted from the vertical by the angle of bank and therefore has a horizontal component that causes the bird to turn. The forces acting on a banking bird are shown in the figure below, where the bird is flying horizontally out of the page towards the reader, in a path that is curving to the reader's left. The angle of bank O is also shown in the figure. Notes: (i) Referring to the above figure, the horizontal and vertical components of the lift force L are L sin and L cos 0 respectively. (ii) The centripetal force Fc, mass m and speed v for an object moving in constant circular motion: Fc = (iii) At moderate speeds (neither too slow or too fast), the lift force L generated by a bird with wing area A travelling at speed v in a fluid of density p is given by L = CLpv?A, where CL is the coefficient of lift of the bird's wings, and depends only on the shape and orientation of the wings. In the following questions, a bird of mass m, with wings of area A and coefficient of lift L is soaring at a speed v, at an angle of bank 0, through air of density p. (a) Which of the following is the best estimate for the radius of the path the bird is moving along?: 2mv2 B 2mv- 2m 2m CLPA sine CLPA COS O CLPA sin 0 D CLPACOS O [4 marks] In the following question, the bird (with mass m = 2.5 kg as shown the above figure, soaring at an angle of bank ( and generating a lift force L) is travelling at constant speed 10 ms in a horizontal circular path. As long as the bird is flying fast enough, there is one angle of bank 0 that maintains vertical equilibrium and maintains horizontal flight. (b) Which of the following is the best estimate for the angle of bank 0 of the bird, if it is travelling fast enough to generating a lift force of 40N: A 20 B 30 C 40 D 50 [5 marks]