Solution: Formula for XCM for a continuous object (rather than points): √ x(dm) XCM Sdm Plug in for dm: fx(A+Bx)dx XCM √(A+Bx)dx Integrate from x = 0 to x = L: XCM = Clean up: AL²+BL +. 3 AL+B12 XCM 3A+2BL 6A+3BL L CM of Baseball Bat The "linear density" (mass per unit length) of a baseball bat increases with distance x from the thin end according to the function: λ(x) = A + Bx A small piece of the bat with length dx has a mass of dm = x(x)dx. The bat has a length of L. The CM is a distance of XCM away from the handle. 7 A B 0.457kg m 1.36 kg m² ☑ (no answer) Correct Answer: 0.511 L 0.861m XCM m 8 A B L XCM kg kg 1.32- 0.869m 0.512m m m² ☑ (no answer) Correct Answer: 0.498
Solution: Formula for XCM for a continuous object (rather than points): √ x(dm) XCM Sdm Plug in for dm: fx(A+Bx)dx XCM √(A+Bx)dx Integrate from x = 0 to x = L: XCM = Clean up: AL²+BL +. 3 AL+B12 XCM 3A+2BL 6A+3BL L CM of Baseball Bat The "linear density" (mass per unit length) of a baseball bat increases with distance x from the thin end according to the function: λ(x) = A + Bx A small piece of the bat with length dx has a mass of dm = x(x)dx. The bat has a length of L. The CM is a distance of XCM away from the handle. 7 A B 0.457kg m 1.36 kg m² ☑ (no answer) Correct Answer: 0.511 L 0.861m XCM m 8 A B L XCM kg kg 1.32- 0.869m 0.512m m m² ☑ (no answer) Correct Answer: 0.498
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter8: Rotational Motion
Section: Chapter Questions
Problem 90A
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