- Question 3 A Nonuniform Bar Of Mass M And Length L Is Pin Supported At P From A Block Which Moves On A Horizontal Track 1 (179.41 KiB) Viewed 12 times
Question 3. A nonuniform bar of mass m and length L is pin supported at P from a block which moves on a horizontal track, as shown in Figure 3 below. The coefficients of static and dynamic frictions between the block and the track are denoted by μs and µk. The bar has a radius of gyration k about point G; the distance from centre of mass G and point P is d. Neglect the mass of the block. A horizontal force F is applied to the bar at point P while it is at rest in the position shown in Figure 3 below. Assuming the force F is large enough to cause the block to slide, immediately after the force F is applied: [4 marks] (a) Draw the free-body-diagram of the rod showing all the forces acting on it. [8 marks] (b) Obtain an expression for the angular acceleration of the rod in the fixed frame A (AB, with B denoting the rod) in terms of a3 unit vector. (c) Obtain an expression for the acceleration of point P in the fixed frame A in terms of unit vectors of A. [14 marks] (d) Obtain an expression for the acceleration of point Q in the fixed frame A in terms of unit vectors of A, and compare its magnitude to that of [6 marks] point P. Total: [32 marks] Note: Expressions obtained in parts (b), (c), and (d) must be in terms of some or all of the following parameters: F, L, M, 9, and m (g is the acceleration due to gravity). Neglect the mass of the block in your calculations. Use the table below for the magnitudes of kc and d in terms of L. A P āz a₁ Last digit of your KG d student number 0, 1, 2 0.2L 0.7L 3,4 0.3L 0.65L 5,6 0.25L 0.75L 7,8,9 0.35L 0.6L Suggested time: 45 minutes. az d G Q Figure 3