In 2019, the International Committee for Weights and Measures adopted a new set of definitions for the fundamental units of the SI system. The three important base units in classical mechanics are the unit of time (s), the unit of length (m), and the unit of mass (kg). These three units are derived from three physical constants in the new SI system: Quantity Symbol Units Transition Frequency of Cesium 133 Av Planck's Constant s-1 kg - m?/s m/s h Speed of Light Use dimensional analysis to determine the combination of these three parameters that will define the base units of the SI system. (a) What combination of h, c, and Av defines a second? (b) What combination of h, c, and Av defines a meter? (c) What combination of h, c, and Av defines a kilogram?

Classical Dynamics of Particles and Systems
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ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.36P
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In 2019, the International Committee for Weights and Measures adopted a new set of definitions for the fundamental
units of the SI system. The three important base units in classical mechanics are the unit of time (s), the unit of length
(m), and the unit of mass (kg). These three units are derived from three physical constants in the new SI system:
Quantity
Symbol Units
Transition Frequency of Cesium 133 Av
s-1
kg - m?/s
m/s
Planck's Constant
h
Speed of Light
Use dimensional analysis to determine the combination of these three parameters that will define the base units of
the SI system.
(a) What combination of h, c, and Av defines a second?
(b) What combination of h, c, and Av defines a meter?
(c) What combination of h, c, and Av defines a kilogram?
You only need to find the combination of h, c, and Av that has the right units. Your answer should not involve any
numerical values.
Transcribed Image Text:In 2019, the International Committee for Weights and Measures adopted a new set of definitions for the fundamental units of the SI system. The three important base units in classical mechanics are the unit of time (s), the unit of length (m), and the unit of mass (kg). These three units are derived from three physical constants in the new SI system: Quantity Symbol Units Transition Frequency of Cesium 133 Av s-1 kg - m?/s m/s Planck's Constant h Speed of Light Use dimensional analysis to determine the combination of these three parameters that will define the base units of the SI system. (a) What combination of h, c, and Av defines a second? (b) What combination of h, c, and Av defines a meter? (c) What combination of h, c, and Av defines a kilogram? You only need to find the combination of h, c, and Av that has the right units. Your answer should not involve any numerical values.
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