Calc II physics problems.

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Math 1152 Written Homework 1 - Page 7 Spring 2022 5. [20 pts] Read the following problem carefully! The amount of work, W. required to move a particle of mass M a vertical distance 0' above its starting height is given by the formula: W=Mgd . A heavy rope is 15 m long and has a constant (linear) density of p = 2kg/m. The rope hangs over the edge of a 25 m building. as shown below: The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length, Ay. Calculate Ay. Ay= B. Find the mass, M2, of the middle segment of the rope. C. The y values of the bottom of each segment of rope are indicated above. Find the values yo, yl, and y; and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y;: D. Find the distance d2 the middle segment must be moved to reach the top of the building. A E. Find the approximate the work, W2 required to move the middle segment to the top of the building by using the given formula. For computational convenience. take g = 10 m/sz. Math 1152 Written Homework 1 - Page 8 Spring 2022 Problem 5 continued. . .. II. (The Exact Work) To compute the exact work required to pull the whole rope to the top of the building, slice the rope into many segments of equal length. Ay. One such segment, centered at a height y, is shown on the figure below: A. Find the mass, AM. of the indicated segment of the rope. Leave your answer in terms of Ay. AM: By approximating that the segment is a particle located at height y: B. Find the distance d 2 dog that the segment must be moved to reach the top of the building in terms of y. d(y) = C. Find the approximate the work. AW required to move the segment to the top of the building by using the formula given in the beginning of the problem. For computational convenience, take g = 10 m/s2 and leave your final answer in terms of y and Ay. AW: D. Set up, but do not evaluate an integral that would give the work required to pull the entire rope up to the top of the building. 1This is just notation that the distance will depend on the height y where the segment is found