Part A A narrow uniform rod has length 2a. The linear mass density of the rod is p, so the mass m of a length 1 of the r

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Part A A Narrow Uniform Rod Has Length 2a The Linear Mass Density Of The Rod Is P So The Mass M Of A Length 1 Of The R 1 (70.38 KiB) Viewed 81 times

Part A A narrow uniform rod has length 2a. The linear mass density of the rod is p, so the mass m of a length 1 of the rod is pl. A point mass is located a perpendicular distance r from the center of the rod. Calculate the magnitude of the force that the rod exerts on the point mass. (Hint: Let the rod be along the y-axis with the center of the rod at the origin, and divide the rod into infinitesimal segments that have length dy and that are located at coordinate y. The mass of the segment is dm = pdy. Write expressions for the r- and y- components of the force on the point mass, and integrate from -a to ta to find the components of the total force). Express your answer in terms of the gravitational constant G and some or all of the variables m, p, q, and r. EVO AEO ? F = Submit Request Answer Part B What does your result become for a >>r? (Hint: Use the power series n(n+1) (m - 1)(m - 2) (1+x)" = 1+nr+ -2° +... (0 <1).) 2! 3! Express your answer in terms of the gravitational constant G and some or all of the variables m, p, a, and r. -12 + IVA| ΑΣφ ? F= Submit Request Answer P Pearson