Question

MEC311 Term Test, 2019w 2. 145%) This problem is about using work-energy and impulse-momentum principles. You must answer according to the notations and coordinate systems set up for you Answers based on other coordinate sysfem or notations will not be marked. Consider a sticky ball of weight Ws 0.1 [lb] located on an incline of angle 0-30-deg. The ball is initially placed on top of a compressed linear spring of spring constant k 10 [lb/ft]; see figure. It is released from rest and hit a triangular block W 2 [lb] held by a stop at a distance d-1 [ft] up the incline. Assume the flightpath of the stick ball is parallel to the incline (do not consider projectile motion) and, upon impact, it sticks to the block. Use the X-Y system with basis vectors i, j, respectively in the questions below. (a) [13/45] Suppose the spring was initially compressed by 0.5 [ft]. Use the work-energy principle to find the speed of the sticky ball right before it hits the wedge. X d (b) [16/45] This sub-question requires no calculation. You are to provide the vector impulse-momentum equaion for the sticky ball and the block together (so that the npact force becomes internal force). Consider the initial state to be right berore the impact, and the final state to be right after the impact. To write it down properly, denote s Vs1i as the velocity of k stop 0 20 the sticky ball right before the impact, = Vi, as the velocity of the sticky O ball and the block together right after the impact. Also, let N Nj be the normal force between the block and the incline, and f be the impact force between the sticky ball and the block. Hint: you need the free-body-diagram for the sticky ball and the block. (c) [6/45] Based on your result in (b), find the velocity reason(s) for your approach. = Vi right after the impact. You must explain the (d) 110/451 Assume the impact lasted 0.001 sec. Find the impact force on the sticky ball. Hint: Considering the ball and the block as one system, the impact force becomes an internal force and will not appear in any equation You must therefore consider the sticky ball alone. You should (again) have a free-body-diagram to help writing down the vector impulse-momentum equation in order to solve for the impact force

Answer 1

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