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Answer the marked (*) questions using complete solutions. 1. A uniform wooden planck of length L = 6.0 m and mass M = 90 kg rests on top of two sawhorses separated by D = 1.5 m, located between equal distances from the center of the planck. You try to stand on the right-hand end of the planck. If the planck is to remain at rest, what should be your mass? Solution: From the diagram shown below, imagine the planck as a point mass centered on its center 3.0 m 1.5 m of mass (point O). We then have two masses: planck and you. Let your mass be M. The origin x = 0 is at the center. (90 kg)(0 m) + (M)(3 m) 90 kg + M XCM = To establish equilibrium, set the center of mass to the tip of the right sawhorse. Therefore, xCM = 0.75 m. 3M 0.75 = 90 kg + M We get M = 30 kg. Question 2.* Now, let the origin x = 0 be at the tip of the right sawhorse. Show that the resulting mass does not depend on the arbitrary choice of origin.

Answer the marked (*) questions using complete solutions. 1. A uniform wooden planck of length L = 6.0 m and mass M = 90 kg rests on top of two sawhorses separated by D = 1.5 m, located between equal distances from the center of the planck. You try to stand on the right-hand end of the planck. If the planck is to remain at rest, what should be your mass? Solution: From the diagram shown below, imagine the planck as a point mass centered on its center 3.0 m 1.5 m of mass (point O). We then have two masses: planck and you. Let your mass be M. The origin x = 0 is at the center. (90 kg)(0 m) + (M)(3 m) 90 kg + M XCM = To establish equilibrium, set the center of mass to the tip of the right sawhorse. Therefore, xCM = 0.75 m. 3M 0.75 = 90 kg + M We get M = 30 kg. Question 2.* Now, let the origin x = 0 be at the tip of the right sawhorse. Show that the resulting mass does not depend on the arbitrary choice of origin.

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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Answer Question 2 using details from Number 1:

Answer the marked (*) questions using complete solutions. 1. A uniform wooden planck of length L = 6.0 m and mass M = 90 kg rests on top of two sawhorses separated by D = 1.5 m, located between equal distances from the center of the planck. You try to stand on the right-hand end of the planck. If the planck is to remain at rest, what should be your mass? Solution: From the diagram shown below, imagine the planck as a point mass centered on its center 3.0 m 1.5 m of mass (point O). We then have two masses: planck and you. Let your mass be M. The origin x = 0 is at the center. (90 kg)(0 m) + (M)(3 m) XCM 90 kg + M To establish equilibrium, set the center of mass to the tip of the right sawhorse. Therefore, xCM 0.75 m. 3M 0.75 = 90 kg + M We get M = 30 kg. Question 2.* Now, let the origin x = 0 be at the tip of the right sawhorse. Show that the resulting mass does not depend on the arbitrary choice of origin.
Transcribed Image Text:Answer the marked (*) questions using complete solutions. 1. A uniform wooden planck of length L = 6.0 m and mass M = 90 kg rests on top of two sawhorses separated by D = 1.5 m, located between equal distances from the center of the planck. You try to stand on the right-hand end of the planck. If the planck is to remain at rest, what should be your mass? Solution: From the diagram shown below, imagine the planck as a point mass centered on its center 3.0 m 1.5 m of mass (point O). We then have two masses: planck and you. Let your mass be M. The origin x = 0 is at the center. (90 kg)(0 m) + (M)(3 m) XCM 90 kg + M To establish equilibrium, set the center of mass to the tip of the right sawhorse. Therefore, xCM 0.75 m. 3M 0.75 = 90 kg + M We get M = 30 kg. Question 2.* Now, let the origin x = 0 be at the tip of the right sawhorse. Show that the resulting mass does not depend on the arbitrary choice of origin.
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