Chapter 1: Unit, Physical Quantities and vectors

The U.S. National Institute of Science and Technology (NIST) maintains several accurate copies of the international standard kilogram. Even after careful cleaning, these national standard kilograms are gaining mass at an average rate of about 1μg/year when compared every 10 years or so to the standard international kilogram. Does this apparent change have any importance? Explain.

If the mass of the kilogram standard changes, then the mass of actual kilogram changes as well. And it will cause issues if those are use to create future kilogram object

SI

International System. Standard unit use in the scientific world. Aka Metric system

Q1.9 Three archers each fire four arrows at a target. Joe's four arrows hit at points 10 cm above, 10 cm below, 10 cm to the left, and 10 cm to the right of the center of the target. All four of Moe's arrows hit within 1 cm of a point 20 cm from the center, and Flo's four arrows hit within 1 cm of the center. The contest judge says that one of the archers is precise but not accurate, another archer is accurate but not precise, and the third archer is both accurate and precise. Which description applies to which archer? Explain.

Joe is accurate but not precise (the average position of his arrows are in the bullseye, but none of the arrows are close together), Moe is precise but not accurate (all of his arrows are grouped closely together, but none are close to the bullseye), and Flo is both accurate and precise. Matt Parker has a great video explaining the difference.

How many correct experiments do we need to disprove a theory? How many to prove a theory? Explain.

Only one correct experiment is needed to disprove a theory, and no finite number of correct experiments can prove a theory. However, a large amount of correct experiments can be used as evidence to support a theory within a range of validity.

Range of validity

Range of condition in which the theory is valid

Unit

Reference standard use in measuring quantity

Theory

an explanation of natural phenomena based on observation and accepted fundamental principles

Accuracy

how close it is likely to be to the true value

unit prefix

nano : 10^-9 micro : 10^-6 mili : 10^-3 centi : 10^-2 kilo : 10^3

Order of magnitude estimate

rough but reasonable approximation, often use when accurate input data is not avalible

Dimensionally consistent

two terms can only be added or equated only if they have the same unit

Error

An indicates the maximum difference there is likely to be between the measured value and the true value

Uncertainty

An indicates the maximum difference there is likely to be between the measured value and the true value

Precision

Ex: If a watch can give you the time 12:35:56 it is very precise but a clock that can tell time only with hour and minutes can be accurate by less precise

Experimental science

Trying to find pattern in in observe phenomena of nature.

Significant figures

Number of meaningful digits

Physical quantity

Number that is used to describe a physical phenomenon quantitatively

Physics

Science concerned with nature and properties of physical entities, matter and energy.

Particle (free body)

Simple representation of object. Use to ignore size and shape of object

Model

Simplified version of a physical system that would be too complicated to analyze in full detail

Operational definition

Some physical quantities are so fundamental that we can define them only by describing how to measure them. Such a definition is called an operational definition Ex: measuring a distance by using a ruler

Suppose you are asked to compute the tangent of 5.00 meters. Is this possible? Why or why not?

This is not possible. The tangent function is a trigonometric function that takes an angle as an input. Since 5.00 meters is a quantity of length, this is not a valid input. They need to dimensionally consistent to be operated on