16 Questions
What is the composition of a proton?
two up quarks and one down quark
Which formula is dimensionally consistent with an expression yielding a value for velocity?
at
What is the dimension of the constant A in the relation x = Av?
time
What are the units of a speed of 5 knots in the SI system of units?
m/s
Which equation is not dimensionally correct?
v = a/t
What are the dimensions of the constants b and c in the equation x = bt³ + ct⁴?
L/T³, L/T⁴
What is the relationship between the units of area and volume?
Both a and b are correct
What is the purpose of dimensional analysis?
To ensure mathematical expressions have consistent units
What is the standard meter defined in terms of since 1983?
the distance light travels in a certain fraction of a second
What is the standard definition for the second based on since 1967?
a characteristic frequency of the cesium-133 atom
What are the other two basic quantities used in mechanics to derive additional quantities, along with mass?
length and time
What do the prefixes p, n, and G represent?
10^-12, 10^-9, and 10^9
What is the value of the ratio M/m of the prefixes M and m?
10^9
How many seconds are in one year and one day, respectively?
3.16 × 10^7, 86 400
What particles are found in the nuclei of atoms?
protons and neutrons
When was the existence of the neutron confirmed?
in 1932
Study Notes
Standards of Length, Mass, and Time
- Since 1983, the standard meter has been defined in terms of the distance light travels in a certain fraction of a second.
- Since 1967, the standard definition for the second has been based on the characteristic frequency of the cesium-133 atom.
- In mechanics, the three basic quantities used to derive additional quantities are mass, length, and time.
- The prefixes p, n, and G represent 10^-12, 10^-9, and 10^9 respectively.
- The ratio M/m of the prefixes M and m has a value of 10^9.
The Building Blocks of Matter
- The nuclei of atoms contain protons and neutrons.
- The existence of the neutron was confirmed in 1932.
- The proton contains two up quarks and one down quark.
Dimensional Analysis
- Velocity can be expressed as at, where a is acceleration and t is time.
- The expression v/x is dimensionally consistent with an expression that would yield a value for time^-1.
- If the displacement of an object, x, is related to velocity, v, according to the relation x = Av, the constant A has the dimension of time.
- The speed of a boat in 5 knots can be expressed in the SI system of units as m/s.
- The equation t = x/v is dimensionally correct, but v = a/t is not.
- If an equation relating position, x, to time, t, is given by x = bt^3 + ct^4, the dimensions of b and c are L/T^3 and L/T^4 respectively.
Test your understanding of the fundamental units of length, mass, and time, including their definitions and prefixes.
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