A thin rod has length L and total mass M lies along the x axis. (a) Suppose the rod is uniform. Find the position of the center of mass with respect to the left end of the rod in terms of L, M, and ?̂. (b) Now suppose the rod is not uniform but has a linear mass density that varies with the distance x from the left end according to the relation: ? = ? ?ଷ ?ଷ where λ0 is a constant and has SI units of kg/m. The total mass of the rod is still M. Find λ0 and the position of the center of mass with respect to the left end of the rod. Express your answer in terms of some or all of the following: L, M, and ?̂.
A thin rod has length L and total mass M lies along the x axis. (a) Suppose the rod is uniform. Find the position of the center of mass with respect to the left end of the rod in terms of L, M, and ?̂. (b) Now suppose the rod is not uniform but has a linear mass density that varies with the distance x from the left end according to the relation: ? = ? ?ଷ ?ଷ where λ0 is a constant and has SI units of kg/m. The total mass of the rod is still M. Find λ0 and the position of the center of mass with respect to the left end of the rod. Express your answer in terms of some or all of the following: L, M, and ?̂.
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter9: Linear Momentum And Collisions
Section: Chapter Questions
Problem 9.12CYU: Check Your Understanding Suppose you have a macroscopic salt crystal (that is, a crystal that is...
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A thin rod has length L and total mass M lies along the x axis.
(a) Suppose the rod is uniform. Find the position of the center of mass with respect to the left end of the
rod in terms of L, M, and ?̂.
(b) Now suppose the rod is not uniform but has a linear mass density that varies with the distance x from
the left end according to the relation:
? =
?
?ଷ ?ଷ
where λ0 is a constant and has SI units of kg/m. The total mass of the rod is still
M. Find λ0 and the
position of the center of mass with respect to the left end of the rod. Express your answer in terms of
some or all of the following: L, M, and ?̂.
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