ME 562 Advanced Dynamics Summer 2010 HOMEWORK # 1 Assignment Due: 06/09/2010 Q1. Problem 1-1: Forces P and Q are applied to a particle of mass m . The magnitudes of these forces, P and Q, are constant but the angle between their lines of action can be varied, thereby changing the total force, and hence the acceleration of the particle. Suppose that the magnitudes of these forces are such that the maximum possible acceleration is three times as large as the minimum possible acceleration. Now, the forces are arranged at an angle such that the acceleration attained by the particle is the mean of the maximum and minimum accelerations. Find the angle between the forces. Q2. Problem 1-3: Consider a triad of vectors (not necessarily unit vectors) e 1 , e 2 , and e 3 . Let them be represented in terms of the Cartesian basis i , j , and k as: 1 1 2 3 2 1 2 3 3 1 2 3 , , . e l i l j l k e m i m j m k e n i n j n k (a) Find the three equations that must be satisfied by the coefficients 1 2 3 1 2 3
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