Question 6 (20 marks) Block A of mass 45 kg is attached to an inextensible cord...

 

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Question 6 (20 marks) Block A of mass 45 kg is attached to an inextensible cord that is wrapped on the inner rim of the compound drum B which has a combined mass moment of inertia I = 12 kgm², as shown in Figure 6.1. At the instant shown, block A has a downward velocity of 0.5 m/s. A tangential force P is applied at the outer rim of the compound drum B at time t = 2 seconds to bring the system to a stop as shown in Figure 6.2. A constant bearing friction torque t+= 18 Nm acts on the compound drum B throughout the motion. To = 600 mm- v₁ = 0.5 m/s --- A 45 kg Tr = 18 Nm Figure 6.1 001, 002 n = 300 mm To = 600 mm- V2 [Ans: (452.7 -22.5 v₂), 15.93 rad/s, 550.84 N] V₂ = 0 40₂ / 0 = 0 n = 300 mm T₁ = 18 Nm Figure 6.2 (a) Derive an expression for the cord tension at time t = 2 seconds, immediately before tangential force P is applied, using the Impulse-Momentum Method, with the aid of a free body diagram of block A. (5 marks) (b) Determine the angular velocity m2 of compound drum B at time t = 2 seconds, immediately before tangential force P is applied, using the Impulse-Momentum Method and the derived expression in part (a), with the aid of a free body diagram of compound drum B. (9 marks) (c) Determine the magnitude of tangential force P, knowing that compound drum B turns 1½ revolutions in coming to a stop subsequent to application of tangential force P, using the Work-Energy Method. (6 marks) Question 6 (20 marks) Block A of mass 45 kg is attached to an inextensible cord that is wrapped on the inner rim of the compound drum B which has a combined mass moment of inertia I = 12 kgm², as shown in Figure 6.1. At the instant shown, block A has a downward velocity of 0.5 m/s. A tangential force P is applied at the outer rim of the compound drum B at time t = 2 seconds to bring the system to a stop as shown in Figure 6.2. A constant bearing friction torque t+= 18 Nm acts on the compound drum B throughout the motion. To = 600 mm- v₁ = 0.5 m/s --- A 45 kg Tr = 18 Nm Figure 6.1 001, 002 n = 300 mm To = 600 mm- V2 [Ans: (452.7 -22.5 v₂), 15.93 rad/s, 550.84 N] V₂ = 0 40₂ / 0 = 0 n = 300 mm T₁ = 18 Nm Figure 6.2 (a) Derive an expression for the cord tension at time t = 2 seconds, immediately before tangential force P is applied, using the Impulse-Momentum Method, with the aid of a free body diagram of block A. (5 marks) (b) Determine the angular velocity m2 of compound drum B at time t = 2 seconds, immediately before tangential force P is applied, using the Impulse-Momentum Method and the derived expression in part (a), with the aid of a free body diagram of compound drum B. (9 marks) (c) Determine the magnitude of tangential force P, knowing that compound drum B turns 1½ revolutions in coming to a stop subsequent to application of tangential force P, using the Work-Energy Method. (6 marks)

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