Question

[2] (Use the discussed Energy methods) A 2-Ib. (weight) block, initially at rest at position A on a specially designed track shown in the figure is released Track AB is a circular arc, and BC is a straight horizontal track. After passing the object flies horizontal distance d until himing the pround Assume that there's no friction between the block and the curved track AB. The kinetic friction coefficient is a = 0.3 between the block and the horizontal tack BC imore the effect of air-resistance. The gravity acceleration =322 Please answer the following questions: (1) Find the velocity vector of the block when it is about to hit the ground (at D) for the first time. Use the Cartesian unit vectors i and for the final answer (25 pts) (b) Find the time taken for the block travels from B to C. You must use one of the Energy method to solve it. (15 pts) (C) Please draw v. Vs. X, and . x curves approximately in the paph shown below. You don't need to denote include exact values of velocities in the graph (5 pts) • Energy methods discussed: Principle of work and Energy Conservation of Energy, Principle of Impulse and Momentum, Theory of Impact

Answer 1

a) From A to B, Potential energy at a (sel to B) = Kinetic Energy at B. » mgh= mv's v= regn >> Vo = 12x92-22447 = 16.05 fils from B to C, Frictional force f= en N= mg. os f= ung = 0.3x2 = 0.6dbf Energy dissipated by friction = KE lost > 0-6X 4ft= kE lost >Ź mereve) = 214 m= 2 » v²= 2x2.4032-24 16.052 7 V = 13.43 ft/s → From, a to D there is no aceleration in x-direction. So, a does not change: P.E lost = K E gained a mgh = 12 m v ang h=4ft * Voy a ragn = 16:05 ft/s to so, velocity at Das Vc + 16-051 Vy = 13:43 ; – 16.05j ft/s) 32.2 2 ti

- by using Principle of momentum 1 Free (P) = (mu) ).m from B to c. Froce is constant=f=0.6 lbf => 0-b= m de meeste => 0.6+32.2 dt = adv Integrate => 0.6823 2 sat affect = 2 [Ve-ve] o).= 2 [16.05–13.43] , t= 0.27 gec 0.6x32.2

A-B Var Vy = 0 at A ; Vy =0 at B Vo Keeps on increasing direction vy increases then reduces y dineer direction. C-DIVE Const P vyzo a o B -c Va reduces due to friction. . Vy=const (0) y always to one Vor always > tve c-D Vy increases de I togravity