# 1.2 Physical quantities and units  (Page 6/18)

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(1) Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong units as follows:

which are obviously not the desired units of km/h.

(2) Check that the units of the final answer are the desired units. The problem asked us to solve for average speed in units of km/h and we have indeed obtained these units.

(3) Check the significant figures. Because each of the values given in the problem has three significant figures, the answer should also have three significant figures. The answer 30.0 km/hr does indeed have three significant figures, so this is appropriate. Note that the significant figures in the conversion factor are not relevant because an hour is defined to be 60 minutes, so the precision of the conversion factor is perfect.

(4) Next, check whether the answer is reasonable. Let us consider some information from the problem—if you travel 10 km in a third of an hour (20 min), you would travel three times that far in an hour. The answer does seem reasonable.

Solution for (b)

There are several ways to convert the average speed into meters per second.

(1) Start with the answer to (a) and convert km/h to m/s. Two conversion factors are needed—one to convert hours to seconds, and another to convert kilometers to meters.

(2) Multiplying by these yields

$\text{Average speed}=\text{30}\text{.}0\frac{\text{km}}{\text{h}}×\frac{1\phantom{\rule{0.25em}{0ex}}\text{h}}{\text{3,600 s}}×\frac{1,\text{000}\phantom{\rule{0.25em}{0ex}}\text{m}}{\text{1 km}}\text{,}$
$\text{Average speed}=8\text{.}\text{33}\frac{\text{m}}{\text{s}}\text{.}$

Discussion for (b)

If we had started with 0.500 km/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m/s.

You may have noted that the answers in the worked example just covered were given to three digits. Why? When do you need to be concerned about the number of digits in something you calculate? Why not write down all the digits your calculator produces? The module Accuracy, Precision, and Significant Figures will help you answer these questions.

## Nonstandard units

While there are numerous types of units that we are all familiar with, there are others that are much more obscure. For example, a firkin is a unit of volume that was once used to measure beer. One firkin equals about 34 liters. To learn more about nonstandard units, use a dictionary or encyclopedia to research different “weights and measures.” Take note of any unusual units, such as a barleycorn, that are not listed in the text. Think about how the unit is defined and state its relationship to SI units.

Some hummingbirds beat their wings more than 50 times per second. A scientist is measuring the time it takes for a hummingbird to beat its wings once. Which fundamental unit should the scientist use to describe the measurement? Which factor of 10 is the scientist likely to use to describe the motion precisely? Identify the metric prefix that corresponds to this factor of 10.

The scientist will measure the time between each movement using the fundamental unit of seconds. Because the wings beat so fast, the scientist will probably need to measure in milliseconds, or ${\text{10}}^{-3}$ seconds. (50 beats per second corresponds to 20 milliseconds per beat.)

One cubic centimeter is equal to one milliliter. What does this tell you about the different units in the SI metric system?

The fundamental unit of length (meter) is probably used to create the derived unit of volume (liter). The measure of a milliliter is dependent on the measure of a centimeter.

## Summary

• Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.
• Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four fundamental units.
• The four fundamental units we will use in this text are the meter (for length), the kilogram (for mass), the second (for time), and the ampere (for electric current). These units are part of the metric system, which uses powers of 10 to relate quantities over the vast ranges encountered in nature.
• The four fundamental units are abbreviated as follows: meter, m; kilogram, kg; second, s; and ampere, A. The metric system also uses a standard set of prefixes to denote each order of magnitude greater than or lesser than the fundamental unit itself.
• Unit conversions involve changing a value expressed in one type of unit to another type of unit. This is done by using conversion factors, which are ratios relating equal quantities of different units.

## Conceptual questions

Identify some advantages of metric units.

## Problems&Exercises

The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

1. $\text{27}\text{.}\text{8 m/s}$
2. $\text{62}\text{.}\text{1 mph}$

A car is traveling at a speed of $\text{33 m/s}$ . (a) What is its speed in kilometers per hour? (b) Is it exceeding the $\text{90 km/h}$ speed limit?

Show that $1\text{.}\text{0 m/s}=3\text{.}\text{6 km/h}$ . Hint: Show the explicit steps involved in converting $1\text{.}\text{0 m/s}=3\text{.}\text{6 km/h.}$

$\frac{\text{1.0 m}}{s}=\frac{1\text{.}\text{0 m}}{s}×\frac{\text{3600 s}}{\text{1 hr}}×\frac{1 km}{\text{1000 m}}$

$=3\text{.}\text{6 km/h}$ .

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)

length: $\text{377 ft}$ ; width: ; .

What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)

Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

$8\text{.}\text{847 km}$

The speed of sound is measured to be $\text{342 m/s}$ on a certain day. What is this in km/h?

Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

(a)

(b) $\text{40 km/My}$

(a) Refer to [link] to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?

please guys help, what is the difference between concave lens and convex lens
convex lens brings rays of light to a focus while concave diverges rays of light
Christian
for mmHg to kPa yes
Matthew
it depends on the size
Vincent
a lens which diverge the ray of light
rinzuala
concave diverges light
Matthew
thank you guys
Vincent
A diverging lens
Yusuf
What is isotope
Yusuf
each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. "some elements have only one stable isotope
Karthi
what is wire wound resistors?
What are the best colleges to go to for physics
I would like to know this too
Trevor
How do I calculate uncertainty in a frequency?
Calculate . ..
Olufunsho
What is light wave
What is wave
Sakeenah
What is light
Sakeenah
okay
True
explain how neurons communicate feed and stimulate
Jeff
Great science students
Omo
A wave is a disturbance which travels through the medium transferring energy from one form to another without causing any permanent displacement of d medium itself
OGOR
Light is a form o wave
OGOR
Neurons communicate by sending message through nerves in coordination
OGOR
What are petrochemicals, give two examples
OGOR
light has dual nature, particle as well as wave. when we want to explain phenomena like Interference of light, then we consider light as wave.
Lalita
what is it as in the form of it or how to visualize it or what it contains
Matthew
particles of light are like small packets of energy called photons, and flow or motion of photons is wave like
Lalita
light is just the energy of which photons emit
Matthew
the wave is how they travel
Matthew
photons do not emitt energy, they are energy. They are massless particles.
Lalita
a wave is a disturbance through the medium. Have you ever thrown a stone in still water? the disturbance produced travels in form of wave, the wave produced by throwing stone in still water are circular in nature.
Lalita
a photon does contain mass when in motion. it doesnt contain mass when at rest
Matthew
when would it ever be at rest
Bob
a wave is a disturbance of which energy travels
Matthew
that's darkness. darkness has no mass because the photons within in aren't moving or producing energy
Matthew
Hi guys. Please I've been trying to understand the concept of SHM, but it's not been really easy, could someone please explain it to me or suggest a site I could visit? Thank you.
Odo
Matthew
effective mass of photons only comes into picture when we consider it accelerating in gravitational field, mass of photon has no meaning as it is always travelling with speed of light and is never at rest. with that high speed, Energy and momentum are equivalent. and darkness is absense of photons.
Lalita
darkness is absense of light. not the presence of 'resting photons'. photons are never at rest.
Lalita
photons are present in darkness but don't give off any light because they are stationary with no mass or energy. once a force makes them move again they will gain mass and give off light
Matthew
this theory is presented in Einsteins theory of special relativity
Matthew
A.The velocity Vo for the streamline flow of liquid in a small tube depends on the radius r of the tube,the density and the viscosity iter of the liquid .use the dimensional analysis to obtain an expression for the velocity . B.Given that Vo =r square ×p all over 4×iter ×l
True
A.The velocity Vo for the streamline flow of liquid in a small tube depends on the radius r of the tube,the density (rho)and the viscosity (iter)of the liquid. Use the method of dimensional analysis to obtain an expression for the velocity . B.Given that Vo =r square x p all over 4 x iter x l
True
Matthew, photons ARE light. there is no such thing as a photon that isn't moving. in fact the speed they move at is called C (for constant) in physics. through a vacuum they always travel at this speed no matter what. they can not slow down; except in another medium.
The reason why a photon can go at this speed is BECAUSE it had no mass. nothing can go this speed or faster because it needs to have no mass or negative mass. that's why it's called the constant.
when a photon hits something that is opaque, this is the only way to "stop"it. it isn't merely stopped but absorbed and turned into heat energy, then the remaining energy is reflected in different wavelengths. that reflection is what we call color. the darker something is, the less photons are ther
e. complete blackness is the absolute absence of photons altogether. I believe what you're referring to is not speed, but wavelength, which is indirectly proportional to the amount of energy a particular photon is made up of.
in order for a photon to have zero wavelength, it must (at least theoretically) have infinite energy.
about mass: you may have photons confused with electrons. elections have a mass so small that people say they are without mass, but they do. it is called electron mass or Me-.
you may also be getting electrons and photons confused because of the cherenkov effect. that is what happens when a particle travels faster than light IN THAT PARTICULAR MEDIUM. I emphasize that because no other particle besides photons can go the speed of c.
when a particle goes faster than light in a particular medium, a blue light is emitted, called cherenkov radiation. this is why nuclear reactors glow blue.
nuclear reactors release so much energy that when they emit electrons, those electrons are given enough energy to go faster than light in that medium (in this case water), releasing blue light. if you put the reactor in air or a vacuum, this effect wouldn't happen because the speed of light in air
is very close to c, which is the universal speed limit. I'd you did go faster than c, time would go backwards and you would have infinite theoretical mass and probably spagghettify, like with a black hole.
*if
*electrons
light waves can travel through a vacuum, and do not require a medium. In empty space, the wave does not dissipate (grow smaller) no matter how far it travels, because the wave is not interacting with anything else.
Salim
Please is there any instructional material for sounds Waves, Echo, light waves
Salami
how far there is hot topic that is boarding me now
Abraham
linear motion
Ahmed
kinematic
Abraham
Akinsanya
kinematic
Emma
kinematics disscuss the motion without cuases ...
ghulam
wow I like what am seeing here I need someone to brush me up in physics in fact I'll say I know nothing
Godslight
How does the Geiger tube works
pls he do we find for tension
tension is equal to the weight of the object. so for example if something weighs 45 Newtons then the tension in the Rope holding it is 45 Newtons. and because it is in equilibrium if the object is 45N and there are three ropes holding it there would be 15 N of tension in each to equal the weight
Shii
does that work for you?
Shii
tnx
Belinda
very correct
Kudzy
A prankster applies 450 V to an 80.0 µF capacitor and then tosses it to an unsuspecting victim. The victim’s finger is burned by the discharge of the capacitor through 0.200 g of flesh. What is the temperature increase of the flesh? Is it reasonable to assume no phase change?
what is mass
the quantity of matter that a body contains, as measured by its acceleration under a given force or by the force exerted on it by a gravitational field.
Aliyu
I agree wth aliyu shuwa
Nikita
correct
Jalil
or in easier terms the amount of stuff in an object (stuff meaning whatever element or material that makes the object heavy) the object composition
Shii
an object's resistance to change in motion?
Kudzy
your mass never changes but your weight changes based on the gravitational pull of a system or planet. your mass is just the amount of matter with a certain object
Matthew
please can someone help, why a bats can fly in the night without heating anything, how does he managed an see in darkness?
Vincent
...hit an obstacle and has bounced back.
Odo
Hi Vincent. From what I can remember and what I've learnt, bats do not have a good eye sight and so they make use of waves, when they send out waves and they do not return back to them, they realise that the site is free of obstacles but if it sends a wave and it returns back, it means it hit an
Odo
obstacle and bounced back
Odo
So bats make use of waves in place of eye sight. I think but confirm from a few sites .
Odo
they us echolocation to make a sort of mental map. many sea animals use the same method. this can also be compared to sonar which works in the same way
Matthew
y is atom d smallest particle
yes
Lajpat
its a question Lajpat Rai
EDWIN
Google Quantum Physics or refer to the text
Shii
atoms are considered the smallest unit of matter. it is further divided into three subatomic particles: protons, neutrons, and electrons.
Arshiya
what's the dimensions of moment of inertia?
what is the same conditions
what is important property of thermistor
Naveedkhan
a horizontal force of 10n is applied to a 4.0kg block that is at rest on a perfectly smooth, level surface.find the speed of the block and how far has it gone after 6.0s.
10n/4.0kg=2.5m/s^2 v=6.0sx2.5m/s^2= 15m/s (15m/s x 15m/s x 2)÷ (2.5m/s^2 )= 180m
could yoy guve me formula
Denz
v=u+at, a=F/m=10/4, t=6, u=0, so v=15m/s, v2-u2=2as, so s=45m
praveen
a=F/m. 10n/4kg =2.5m/s^2 a=v/t but v=at = 2.5m/ s^2×6s=15m/s v^2=2as. but s=v^2/2a =15^2÷(2×2.5^2)=45m
Thank yoy guys. i'm having a bad time on our Physics class We're now studying work energy theorem can someone interested teaching me?
Denz
what is resistance of copper wire length
Naveedkhan
what is acceleration
is the rate of change of displacement
caramen
velocity
Naveedkhan
rate of change of velocity called acceleration
Nikita
is the rate of change in velocity with time taken
Anyebem
an unbalanced force
Matthew
EDWIN
M/S2
Achmet
Achmet
Aliyu
how quickly velocity changes over a time interval (period)
Shii