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What are the SI base units of length, mass, and time?

Short Answer

Expert verified
The SI base units are meter (m) for length, kilogram (kg) for mass, and second (s) for time.

Step by step solution

01

Identify SI Unit of Length

The SI base unit of length is the meter, symbolized by \( m \).
02

Identify SI Unit of Mass

The SI base unit of mass is the kilogram, symbolized by \( kg \).
03

Identify SI Unit of Time

The SI base unit of time is the second, symbolized by \( s \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Meter
The SI base unit for measuring length or distance is the meter, denoted as \( m \). A meter was originally defined as one ten-millionth of the distance from the equator to the North Pole along a meridian passing through Paris. Today, it is more precisely defined by the distance light travels in a vacuum in \( 1/299,792,458 \) seconds. This definition links the unit of length to the speed of light, which is one of the most constant and precisely measurable natural phenomena.

When it comes to practical applications, meters are everywhere. From the height of a doorframe to the length of a sports field, understanding how a meter translates into something tangible can help you better grasp the concept of length in the physical world.
Kilogram: The Mass Standard
Moving on from length to mass, we encounter the kilogram, symbolized by \( kg \). It is the SI base unit for mass, not weight, which is a force. Originally, the kilogram was defined by a platinum-iridium alloy cylinder known as the 'International Prototype of the Kilogram' stored in France. In 2019, the definition was revised to align with physical constants, specifically the Planck constant. Now, the kilogram is defined using the Planck constant, which is a quantity that allows scientists to use the Kibble balance, an extremely precise weighing machine, to define an object's mass.

The concept of mass is fundamental in physics as it's a measure of the amount of matter in an object. Mass affects how objects move and interact with gravitational forces. It's crucial to differentiate between mass and weight since weight is dependent on gravity, and mass is the same regardless of where you are in the universe.
The Second: SI Base Unit of Time
Lastly, the second (\( s \)) is the SI base unit of time, an aspect of measurement that is crucial to our understanding of the world around us. The second has a fascinating history of definition: it was initially based on the Earth's rotation cycle and later on the orbital period around the Sun. With advancements in technology, the definition evolved, and now the second is determined by the vibrational frequency of cesium atoms in an atomic clock.

The frequency, specifically 9,192,631,770 vibrations, represents one second and provides us with a highly reliable and precise standard. Atomic clocks have such high precision that they will not lose or gain a second for millions of years. Time regulates our lives, from the cycles of natural phenomena to the precision needed in scientific experiments and technological applications, thereby making the understanding of the second indispensable.

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Most popular questions from this chapter

The first atomic bomb was detonated on July 16,1945 at the Trinity test site about \(200 \mathrm{mi}\) south of Los Alamos. In 1947 , the U.S. government declassified a film reel of the explosion. From this film reel, British physicist G. I. Taylor was able to determine the rate at which the radius of the fireball from the blast grew. Using dimensional analysis, he was then able to deduce the amount of energy released in the explosion, which was a closely guarded secret at the time. Because of this, Taylor did not publish his results until 1950. This problem challenges you to recreate this famous calculation. (a) Using keen physical insight developed from years of experience, Taylor decided the radius \(r\) of the fireball should depend only on time since the explosion, \(t,\) the density of the air, \(\rho,\) and the energy of the initial explosion, \(E .\) Thus, he made the educated guess that \(r=k E^{a} \rho^{b} t^{c}\) for some dimensionless constant \(k\) and some unknown exponents \(a, b,\) and \(c .\) Given that \([\mathrm{E}]=\mathrm{ML}^{2} \mathrm{T}^{-2}\) determine the values of the exponents necessary to make this equation dimensionally consistent. (Hint: Notice the equation implies that \(k=r E^{-a} \rho^{-b} t^{-c}\) and that \([k]=1\) ) (b) By analyzing data from high-energy conventional explosives, Taylor found the formula he derived seemed to be valid as long as the constant \(k\) had the value \(1.03 .\) From the film reel, he was able to determine many values of \(r\) and the corresponding values of \(t .\) For example, he found that after \(25.0 \mathrm{ms}\), the fireball had a radius of \(130.0 \mathrm{m}\). Use these values, along with an average air density of 1.25 \(\mathrm{kg} / \mathrm{m}^{3},\) to calculate the initial energy release of the Trinity detonation in joules (J). (Hint: To get energy in joules, you need to make sure all the numbers you substitute in are expressed in terms of SI base units.) (c) The energy released in large explosions is often cited in units of "tons of TNT" (abbreviated "t TNT"), where 1 t TNT is about 4.2 GJ. Convert your answer to (b) into kilotons of TNT (that is, kt TNT). Compare your answer with the quickand-dirty estimate of \(10 \mathrm{kt}\) TNT made by physicist Enrico Fermi shortly after witnessing the explosion from what was thought to be a safe distance. (Reportedly, Fermi made his estimate by dropping some shredded bits of paper right before the remnants of the shock wave hit him and looked to see how far they were carried by it.)

Certain criteria must be satisfied if a measurement or observation is to be believed. Will the criteria necessarily be as strict for an expected result as for an unexpected result?

(a) How many significant figures are in the numbers 99 and \(100 . ?\) (b) If the uncertainty in each number is 1 , what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers: significant figures or percent uncertainties?

(a) What is the relationship between the precision and the uncertainty of a measurement? (b) What is the relationship between the accuracy and the discrepancy of a measurement?

Consider the physical quantities \(m, \quad s, \quad v, \quad a\) and \(t\) with dimensions \([m]=M,[s]=L,[v]=L T^{-1}\) \([a]=\mathrm{LT}^{-2},\) and \([t]=\mathrm{T} .\) Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a) \(F=\) \(m a ;(\mathrm{b}) K=0.5 \mathrm{mv}^{2} ;(\mathrm{c}) p=m v ;(\mathrm{d}) W=m a s ;(\mathrm{e}) L=m v r\)

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