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Nina N.
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Physics (Newtonian Mechanics)
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Question:

A plane, which is flying horizontally at a constant speed Vo and at a height h above the sea, must drop a bundle of supplies to a castaway on a small raft. (a) Write down Newton's second law for the bundle as it falls from the plane, assuming you can neglect air resistance.

Nina N.

When the bundle falls, the only force acting on it at the time is gravity, since we are not taking into account air resistance. Therefore the force in the y direction = Fy= -mg. Since there is no horizontal movement, the x force Fx = 0. The net force on the bundle is F = -mgj or in vector form ( 0 , -mg ). From Newton's second law we have mx'' = ( 0 , -mg ) which simplifies to x'' = ( 0 , -g ).

Basic Math
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Question:

Solve initial value problem for y(t) by Laplace Transformation. y' + 5.2y = 0, y(0)=1

Nina N.

1) Apply Laplace transform to differential equation with Linearity property so we get: L(y') + 5.2L(y) = L(1) The resulting transform of that equals (sY - y(0)) + 5.2Y = 1/s.* 2) Factor out the 'Y' term to get Y(s + 5.2) = 1/s, and then solve for Y to get: Y = 1/( s(s + 5.2) ) 3) Use partial fractions to break up the fraction into 1/( s(s + 5.2) ) = A/s + B/(s+2) which then simplifies to 1 = [A(s+2)]/s + (Bs)/(s+2). Simplifying again -> 1 = [(As + 2A) + Bs] / [ s(s+2) ] 4) Set the coefficients of the terms of the same order to then solve for A and B, so we obtain: A + B = 0 (for order of 1 terms) and 2A = 1 (for order of zero term) so then you get A = 1/2, and thus B = -1/2. 5) Plug the A and B terms back into the first partial fraction you made: Y = (1/2)/s + (-1/2)/(s+2) or Y = 1/(2s) - 1/2(s+2). 6) These terms are now in a manageable form to take the inverse Laplace transform of each of them to be in the form: L^-1(Y) = L^-1 [ 1/(2s)] - L^-1[ 1/2(s+2) ]. Taking the inverse laplace transform* we get: y(t) = (1/2)t - (1/2)e^-2t which is the final solution to the initial value problem. *Laplace transforms and inverse Laplace transforms are generally determined from a provided table of given transforms.

Mechanical Engineering
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Question:

The cable will fail when subjected to a tension of 2kN. Determine the largest vertical load P the frame. http://mgh-images.s3.amazonaws.com/9780133918922/714361-7-10IP1.png

Nina N.

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