Country : India
Assignment Task:

TASK:

Classical Mechanics Study

1. Using conservation of momentum, show that the final velocity of a rocket is related to its initial velocity, exhaust velocity, initial mass and final mass as follows: ???????? = ???????????? ln ????0 ???? + v0

2. Calculate the amount of work done by a force ????? = ????1 sin ???? ????? + ????2???? ???? ????? over the quarter circle path shown in the figure. P is at position (2.0, 2.0). ????1 ????2

3. A frictionless object with mass ????0 is connected to two springs with spring constants ????1 and ????2 respectively. If the object is moved a distance ????0 from the equilibrium position of the springs and released from rest at ???? = 0, what is the equation for the position as a function of time?

4. A boulder with mass ????0 is dropped from a stationary hovering helicopter from a height of ?0. Assuming that the quadratic air drag term dominates, what if the velocity of the boulder as a function of time? Take the downward direction to be positive. The following integral might be helpful: ∫ ???????? 1−???? 2 = atanh ???? 1. Show that: ???? cos ???????? + ???? sin ???????? = ???? cos(???????? − ????)

NOTE: Just writing equations is insufficient you need to use words to explain what you are doing. x x = 0 2. A cart is connected to a spring and oscillates due to a motor that applies a force: ???????????????????????? = 2 cos(2 ????) ????. In addition to the spring force there is a damping force: ???????????????????????????????? = −2 ???????? ???? ????. The cart has a mass of 2 kg and the spring has a spring constant of ???? = 18 ???????? ???? 2 . A) After waiting for ???? ? 1/???? what is the amplitude and phase angle of the position as a function of time? You can leave your answer as a fraction.

B) If you wanted to make the amplitude a maximum without changing the driving force how much mass would you add to the cart? You can leave your answer as a fraction.

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  • Uploaded By : Pearl
  • Posted on : June 08th, 2019

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