PHYC 2009 Question 5 [6 13 19 marks] (a) A jumbo jet of mass 2.7 x 10 kg is crui

Question

PHYC 2009

Question 5 [6 13 19 marks] (a) A jumbo jet of mass 2.7 x 10 kg is cruising at a constant speed of 720 km/hour (200 m/s), heading due west as can be seen in the diagram below Unknowingly, a small bird is flying due east at 1.0 m/s on a collision course with the jet. The bird is 30 cm long, and has a mass of 1.0 kg. After the collision, the pilot notices that the bird is stuck now to the front of the airplane. Unfortunately, the bird appears to be squashed rather flat. (i) How long does it take for the jet to squash the bird? (ii) Calculate the average force exerted by the plane on the bird during this time period. (iii What is the average force exerted by the bird on the plane during this time period? (b) An 8.00 cm diameter solid 400 g sphere is released from rest at the top of a 2.1 m long, 25o incline. It rolls, without slipping, to the bottom. (i) How much work is done by the gravitational force on the sphere between the time it is released and the time it reaches the bottom of the incline? (ii) What is the speed of the centre of mass of the sphere at the bottom of the incline? (iii) What is the sphere's angular velocity at the bottom of the incline? (iv) What is the acceleration of the centre of mass of the sphere as it travels down the slope? Take the moment of inertia ofa solid sphere of mass Mand radius R to be MR

Explanation / Answer

a) i) time taken = 0.3/(199.99) =   1.5 ms

    ii) average force exerted by plane on bird   = 27000/(1.5 * 10-3) = 1.8 * 107 N

    iii)   average force exerted by bird on plane = 198.99/(1.5 * 10-3) = 132660 N

b)   i)    work done =    0.4 * 9.8 * sin25 * 2.1

                              = 3.48 J

     ii) speed of centre of mass =    sqrt(1.428 * 9.8 * sin25 * 2.1)

                                                   = 3.524 m/sec

iii) angular velocity = 3.524/0.04   = 88.1 rad/sec

iv)   acceleration of centre of mass = 9.8 * sin25 = 4.141 m/sec2

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