# 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?

Calculate the Newton's the weight of a 2.5 Kilogram of melon. What is its weight in pound?
calculate the tension of the cable when a buoy with 0.5m and mass of 20kg
what is displacement
it's the time rate of change of distance
Mollamin
distance in a given direction is diplacement
Musa
Distance in a spacified direction
you shouldn't say distance,displacement and distance are two different things .distance can be lopped curved but displacement is always in a straight line so you can't use distance to define it. displacement is the change of position in a specified direction.
Joshua
Well stayed josh👍
Joshua
well explained
Mary
what is the meaning of physics
to study objects in motion and how they interact or take part in the natural phenomenon of the universe.
Phill
an object that has a small mass and an object has a large mase have the same momentum which has high kinetic energy
The with smaller mass
how
Faith
Since you said they have the same momentum.. So meaning that there is more like an inverse proportionality in the quantities used to find the momentum. We are told that the the is a larger mass and a smaller mass., so we can conclude that the smaller mass had higher velocity as compared to other one
Mathamaticaly correct
Mathmaticaly correct :)
I have proven it by using my own values
Larger mass=4g Smaller mass=2g Momentum of both=8 Meaning V for L =2 and V for S=4 Now find there kinetic energies using the data presented
grateful soul...thanks alot
Faith
Welcome
2 stones are thrown vertically upward from the ground, one with 3 times the initial speed of the other. If the faster stone takes 10 s to return to the ground, how long will it take the slower stone to return? If the slower stone reaches a maximum height of H, how high will the faster stone go
30s
how can i calculate it's height
Julliene
is speed the same as velocity
no
Nebil
in a question i ought to find the momentum but was given just mass and speed
Faith
just multiply mass and speed then you have the magnitude of momentem
Nebil
Yes
Consider speed to be velocity
it worked our . . thanks
Faith
Distinguish between semi conductor and extrinsic conductors
Suppose that a grandfather clock is running slowly; that is, the time it takes to complete each cycle is longer than it should be. Should you (@) shorten or (b) lengthen the pendulam to make the clock keep attain the preferred time?
I think you shorten am not sure
Uche
shorten it, since that is practice able using the simple pendulum as experiment
Silvia
it'll always give the results needed no need to adjust the length, it is always measured by the starting time and ending time by the clock
Paul
it's not in relation to other clocks
Paul
wat is d formular for newton's third principle
Silvia
okay
Silvia
shorten the pendulum string because the difference in length affects the time of oscillation.if short , the time taken will be adjusted.but if long ,the time taken will be twice the previous cycle.
discuss under damped
resistance of thermometer in relation to temperature
how
Bernard
that resistance is not measured yet, it may be probably in the next generation of scientists
Paul
Is fundamental quantities under physical quantities?
please I didn't not understand the concept of the physical therapy
physiotherapy - it's a practice of exercising for healthy living.
Paul
what chapter is this?
Anderson
this is not in this book, it's from other experiences.
Paul
am new in the group
Daniel
Sure
What is Boyce law
Boyles law states that the volume of a fixed amount of gas is inversely proportional to pressure acting on that given gas if the temperature remains constant which is: V<k/p or V=k(1/p)