A uniform, thin rod hangs vertically at rest from a frictionless axle attached to its top end. The rod has a mass of 0.780 kg and a length of 1.54 m. (Assume a coordinate system where the +y-direction is up and the +x-direction is to the right. The rod is free to swing about the axle in the x- y plane.) (a) You take a hammer and strike the bottom end of the rod. At the instant the hammer strikes, the force it applies to the rod is (15.71) N. What is the acceleration (in m/s²) of the rod's center of mass at this instant? (Express your answer in vector form.) m/s² a = (b) What is the horizontal force (in N) that the axle exerts on the rod at this same instant? (Express your answer in vector form.) F = N (c) The rod then returns to hanging at rest. You again strike the rod with the hammer, applying the same force, but now you strike it at its midpoint. What now is the acceleration of the center of mass (in m/s²) at the instant of impact? (Express your answer in vector form.) m/s² a = (d) What is the horizontal force (in N) that the axle exerts on the rod when the rod is struck at the midpoint? (Express your answer in vector form.) F = N (e) You wish to find a point on the rod where you can strike it with the hammer so that the axle exerts no horizontal force on the rod. How far (in m) is this point from the top of the rod? This point is called the center of percussion. m
A uniform, thin rod hangs vertically at rest from a frictionless axle attached to its top end. The rod has a mass of 0.780 kg and a length of 1.54 m. (Assume a coordinate system where the +y-direction is up and the +x-direction is to the right. The rod is free to swing about the axle in the x- y plane.) (a) You take a hammer and strike the bottom end of the rod. At the instant the hammer strikes, the force it applies to the rod is (15.71) N. What is the acceleration (in m/s²) of the rod's center of mass at this instant? (Express your answer in vector form.) m/s² a = (b) What is the horizontal force (in N) that the axle exerts on the rod at this same instant? (Express your answer in vector form.) F = N (c) The rod then returns to hanging at rest. You again strike the rod with the hammer, applying the same force, but now you strike it at its midpoint. What now is the acceleration of the center of mass (in m/s²) at the instant of impact? (Express your answer in vector form.) m/s² a = (d) What is the horizontal force (in N) that the axle exerts on the rod when the rod is struck at the midpoint? (Express your answer in vector form.) F = N (e) You wish to find a point on the rod where you can strike it with the hammer so that the axle exerts no horizontal force on the rod. How far (in m) is this point from the top of the rod? This point is called the center of percussion. m
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter13: Rotation Ii: A Conservation Approach
Section: Chapter Questions
Problem 45PQ: A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an...
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Transcribed Image Text:A uniform, thin rod hangs vertically at rest from a frictionless axle attached to its top end. The rod has a mass of 0.780 kg and a length of 1.54 m. (Assume a coordinate system where the +y-direction is up and the +x-direction is to the right. The rod is free to swing about the axle in the x-
y plane.)
(a) You take a hammer and strike the bottom end of the rod. At the instant the hammer strikes, the force it applies to the rod is (15.71) N. What is the acceleration (in m/s²) of the rod's center of mass at this instant? (Express your answer in vector form.)
m/s²
a =
(b) What is the horizontal force (in N) that the axle exerts on the rod at this same instant? (Express your answer in vector form.)
F =
N
(c) The rod then returns to hanging at rest. You again strike the rod with the hammer, applying the same force, but now you strike it at its midpoint. What now is the acceleration of the center of mass (in m/s²) at the instant of impact? (Express your answer in vector form.)
m/s²
a =
(d) What is the horizontal force (in N) that the axle exerts on the rod when the rod is struck at the midpoint? (Express your answer in vector form.)
F =
N
(e) You wish to find a point on the rod where you can strike it with the hammer so that the axle exerts no horizontal force on the rod. How far (in m) is this point from the top of the rod? This point is called the center of percussion.
m
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