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x + √x √xx X Submit Previous Answers Request Answer * Incorrect; Try Again; 3 attempts remaining The correct answer does not depend on: la Part B n(n+1) + n(n — 1)(n-2) 21 3! What does your result become for ar? (Hint: Use the power series (1+z)"=1+nz+ Express your answer in terms of the gravitational constant G and some or all of the variables m, p, a, and r. 2Gmp P- Submit Previous Answers ✓ Correct IXI x.10% 2³+...(|z|< 1).)

x + √x √xx X Submit Previous Answers Request Answer * Incorrect; Try Again; 3 attempts remaining The correct answer does not depend on: la Part B n(n+1) + n(n — 1)(n-2) 21 3! What does your result become for ar? (Hint: Use the power series (1+z)"=1+nz+ Express your answer in terms of the gravitational constant G and some or all of the variables m, p, a, and r. 2Gmp P- Submit Previous Answers ✓ Correct IXI x.10% 2³+...(|z|< 1).)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A narrow uniform rod has length 24. The linear mass density of the rod is p, so the mass m of a length of the rod is pl. Part B n(n-1)(n-2)³+... (|z| < 1).) n(n+1) 2! 2² + 3! What does your result become for ar? (Hint: Use the power series (1+z)" = 1+nz+ Express your answer in terms of the gravitational constant G and some all of the variables m, p, a, and r. 2Gmp F= Submit Previous Answers ✓ Correct Part C For a > r, what is the gravitational field g = Fg/m at a distance from the rod? Express your answer in terms of the gravitational constant G and some or all of the variables m, p, a, and r. 2Go q= Submit Previous Answers ✓ Correct Part D Consider a cylinder of radius and length L whose axis is along the rod. As in part C, let the length of the rod be much greater than both the radius and length of the cylinder. Then the gravitational field is constant on the curved side of the cylinder and perpendicular to it, so the gravitational flux through this surface is equal to gA, where A = 2TTL is the area of the curved side of the cylinder. Calculate this flux. Write your result in terms of the mass M of the portion of the rod that is inside the cylindrical surface. Express your answer in terms of the gravitational constant G and variable M. IVD ΑΣΦ C $g =
Transcribed Image Text:A narrow uniform rod has length 24. The linear mass density of the rod is p, so the mass m of a length of the rod is pl. Part B n(n-1)(n-2)³+... (|z| < 1).) n(n+1) 2! 2² + 3! What does your result become for ar? (Hint: Use the power series (1+z)" = 1+nz+ Express your answer in terms of the gravitational constant G and some all of the variables m, p, a, and r. 2Gmp F= Submit Previous Answers ✓ Correct Part C For a > r, what is the gravitational field g = Fg/m at a distance from the rod? Express your answer in terms of the gravitational constant G and some or all of the variables m, p, a, and r. 2Go q= Submit Previous Answers ✓ Correct Part D Consider a cylinder of radius and length L whose axis is along the rod. As in part C, let the length of the rod be much greater than both the radius and length of the cylinder. Then the gravitational field is constant on the curved side of the cylinder and perpendicular to it, so the gravitational flux through this surface is equal to gA, where A = 2TTL is the area of the curved side of the cylinder. Calculate this flux. Write your result in terms of the mass M of the portion of the rod that is inside the cylindrical surface. Express your answer in terms of the gravitational constant G and variable M. IVD ΑΣΦ C $g =
A narrow uniform rod has length 2a. The linear mass density of the rod is p. so the mass m of a length of the rod is pl. Part A A point mass is located a perpendicular distance 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 I- and y-components of the force on the point mass, and integrate from a toa 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, a, and r. IVE ΑΣΦ ? a xa Xb √x xx x b IXI F= Submit Previous Answers Request Answer X Incorrect; Try Again; 3 attempts remaining The correct answer does not depend on: la Part B n(n+1)2 + n(n−1)(n−2) 1+nz+ T³ +... (|1| < 1).) What does your result become for a r? (Hint: Use the power series (1+x)" 2! 3! Express your answer in terms of the gravitational constant G and some or all of the variables m, p, a, and r. 2Gmp Previous Answers Submit ✓ Correct X.10" X
Transcribed Image Text:A narrow uniform rod has length 2a. The linear mass density of the rod is p. so the mass m of a length of the rod is pl. Part A A point mass is located a perpendicular distance 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 I- and y-components of the force on the point mass, and integrate from a toa 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, a, and r. IVE ΑΣΦ ? a xa Xb √x xx x b IXI F= Submit Previous Answers Request Answer X Incorrect; Try Again; 3 attempts remaining The correct answer does not depend on: la Part B n(n+1)2 + n(n−1)(n−2) 1+nz+ T³ +... (|1| < 1).) What does your result become for a r? (Hint: Use the power series (1+x)" 2! 3! Express your answer in terms of the gravitational constant G and some or all of the variables m, p, a, and r. 2Gmp Previous Answers Submit ✓ Correct X.10" X
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