2. The Strenuis Ardua is intended to have a mass m = 100 × 106 kg and be propelled forward by a constant force F = 106 N

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2 The Strenuis Ardua Is Intended To Have A Mass M 100 106 Kg And Be Propelled Forward By A Constant Force F 106 N 1 (144.33 KiB) Viewed 9 times

2 The Strenuis Ardua Is Intended To Have A Mass M 100 106 Kg And Be Propelled Forward By A Constant Force F 106 N 2 (110.21 KiB) Viewed 9 times

2. The Strenuis Ardua is intended to have a mass m = 100 × 106 kg and be propelled forward by a constant force F = 106 N as shown in Fig. Q2a. AA 0000 000 F Figure Q2a: Cruise ship Strenuis Ardua being propelled forward. For questions (i)-(iii) consider the vertical plane and model the ship as a particle. (i) Draw the free-body diagram of the ship including a generic drag force FD. (ii) During the initial design an engineer assumed that the drag was constant and equal to F₁ = 3 × 105 N. Derive an expression for the speed of the ship as a function of time and calculate its value after 25 minutes under this assumption. (iii) At a later stage in the design the drag was assumed to be equal to FD = bv, where v is the ship's velocity and b is a constant. Derive an expression for the speed of the ship as a function of time under this assumption, and calculate what its value will be after 25 minutes if b - 105 kg s-¹. You may make use of the following identity: "X1 1 [²²a = -dx --lna - cx| C [10 marks] a cx == [4 marks] [5 marks]
In a port manoeuvre, when the forward thrust force is zero, two tugboats turn the Strenuis Ardua by pushing its sides, as shown in Fig. Q2b. (Top view) F₁ L L G Ft Figure Q2b: The Strenuis Ardua in the horizontal plane with tugboat forces acting on the sides. The force exerted by each tugboat is equal to F₂ = 3 × 105 N and it is always perpendicular to the ship centreline c-c (i.e., the forces rotate with the rotating body). The distance between the lines of action of Ft and the centre of mass of the ship G is L = 60 m while the radius of gyration of the ship with respect to G is kg = 80 m. (iv) Neglecting any form of drag and friction, calculate how long it takes to rotate the ship by 90° in the horizontal plane, starting from rest. The angular speed does not have to be zero once it has turned through 90°. [6 marks]