ENGINEERING PHYSICS - EXAMPLE 30.1 : Two viruses a and b with masses of Ma and Mb are moving at velocities of Va and Vb respectively, facing towards each other and collide. After collision both masses of Ma and Mb disappear. (a) Find the total momentum available for both a and b. Hint : momentum = mass x velocity = M x V. (b) Guess the total energy E generated from the disappearance of a and b. Let c to be the velocity of light. Hint : E is equal to M c square.
ENGINEERING PHYSICS - ANSWER 30.1 : (a) Momentum of a = Ma x Va. Momentum of b = Mb x Vb. Total momentum of a and b = Ma x Va + Mb x Vb. (b) After mass disappearance : Energy of a = Ma x c x c. Energy of b = Mb x c x c. Then E = Ma x c x c + Mb x c x c = (Ma + Mb)(c x c). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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Question 55 - The differential equation is 3 dy / dt + 2y = 1 with y(0) = 1. (a) The Laplace transformation, L for given terms are : L (dy / dt) = sY(s) - y(0), L(y) = Y(s), L(1) = 1 / s. Use such transformation to find Y(s). (b) The initial value theorem states that : When t approaches 0 for a function of y(t), it is equal to a function of sY(s) when s approaches infinity. Use the initial value theorem as a check to the answer found in part (a).
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