Question A1 [20 marks] The figure shows a solid cylinder of radius r = 10 cm and mass m = 8 kg as it rolls off a sloped

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Question A1 20 Marks The Figure Shows A Solid Cylinder Of Radius R 10 Cm And Mass M 8 Kg As It Rolls Off A Sloped 1 (64.86 KiB) Viewed 13 times

Question A1 [20 marks] The figure shows a solid cylinder of radius r = 10 cm and mass m = 8 kg as it rolls off a sloped roof. The cylinder starts from rest and rolls without slipping a distance L = 6 m down the roof, which is inclined at angle 8 = 30°. costo === (a) [2 marks] Show that the gravitational potential energy of the cylinder is reduced by APE = 235.2 J between when it starts rolling and and when it leaves the roof. (b) [4 marks] Use the principle of conservation of mechanical energy to show that the speed of the cylinder as it leaves the roof is 6.3 m/s. (Hint: for a solid cylinder, I = =/mr²) (c) [2 marks] What is the velocity vector of the centre of mass of the cylinder as it leaves the roof? Use the coordinate system shown in the diagram For the questions below, use a value of H = 5 m for the height of the edge of the roof. (d) [4 marks] Calculate the time interval between the cylinder leaving the roof, and it hitting the ground. (e) [4 marks] At what distance horizontally from the roof's edge does the cylinder hit the ground? Assume the ground is level. (f) [2 marks] Is the moment of inertia of a hollow cylinder (with the same mass m as the solid cylinder) larger or smaller as compared to a solid (uniform) cylinder? Explain why? (g) [2 marks] Would a hollow cylinder of the same mass hit the ground further away or closer to the house? Explain why this is?