(a) Consider two objects with equal mass m, which are connected by a long rope, passing over two pulleys which are at di

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A Consider Two Objects With Equal Mass M Which Are Connected By A Long Rope Passing Over Two Pulleys Which Are At Di 1 (44.85 KiB) Viewed 47 times

(a) Consider two objects with equal mass m, which are connected by a long rope, passing over two pulleys which are at distance L. The rope is inextensible and has no mass, and the pulley is frictionless and massless as well. Another object of mass M hangs from the rope exactly in the middle between the objects. When the system is at equilibrium, the rope makes an angle a to the vertical from both sides, as sketched below. i. Sketch the diagram of forces acting on the three masses. ii. Calculate the angle a when the system is at equilibrium. What happens when M> 2m? ii. Calculate the distance from the initial position (a = 90°) of the central object to its final equilibrium position along the vertical. Express the distance as a function of L. M and m only and show that it is L/2 when M = V2m. m (b) A dive-bomber releases a bomb at a height of 200 m above the ground, while it travels downwards with a speed of 100 m/s at an angle of 30° below the horizontal i. When does the bomb hit the ground? ii. What is the horizontal distance travelled by the bomb when it hits the ground?