cahier physique - physics workbook

PART1: LINEAR RELATIONSHIP

1) Read and complete: In Physics, the relationship between the experimental values is shown using a technique using graphing.
The independent variable x is always plotted along the x axis of the graph, and the dependent value y is plotted along the y axis of the graph.

Example: Say a car has an average speed of 40mph. Let's the time (in hr) be the independent variable x (also called the manipulated variable)
and the distance (mi) covered the depended variable y (or responding vaiable) . This means, the distance covered depends on the time.
40mph means : in 1 hour, you cover _________miles, in 2 hours you cover __________ miles, in 3 hours you cover ______miles...
call x the hours (independent variable) and y the miles (dependent variable).
Usually, the first thing to do is to build a (x,y) values table. Fill the following table:

x= time (h)	y= distance(mi)
1	__________
2	__________
3	__________
4	__________

Now it is easy to see the relationship between y (distance) and x (time). y = _____ x (or d = ___ t)
This is called a linear relationship. WE say y is proportional to x.

That is if the time is multiplied by 2, then the distance is multiplied by _________.
It is easy to plot the points on a graph. Since the relationship is linear, we trace a straight line through the points:
Plot the points (x,y). !! Give a title to the graph, label the axes,
think about the right scale. !!
You should use your own graph paper, in that case,trace the first quadrant as distance and time are positive.
GRAPH PAPER
The slope tells you about the steepness of the line.
slope = rise/run = change in y / change in x. In that case the slope = _______ mi/hr
The slope is a rate. It tells you by how much the speed increases every second.
The equation of the line is y = ___ x.

watch this movie in class. Choose the segment called: graphing relationships (10:59)
http://player.discoveryeducation.com/index.cfm?guidAssetId=BECB9850-FB39-4BCD-BBD0-16413F95F261
(ask me for login and password).
The movie tells about how graph can be used to derive relationships between
2 variables and the meaning of a slope.

2) REad and fill. In the previous case, the line go through (0,0) and the equation of the line is in the form y = m x
where m is the slope.
(In Math you call that the slope-intercept form).
It can be that the straight line does not go through (0,0)
Imagine you take Summer classes in an university. The registration fee is $500 (only paid once, independent of the number of credits you take) and then you pay $100 per credit. If you register and take no credit, you still pay $500.
If you take 1 credit, you pay _____ + ______ = ________
Instead, if you take 2 credits, you pay _______ + 2 (_______) = _____________
and so forth.
The independent variable x is the __________________ and the dependent variable y is ________________----
Fill the table :

x = number of credits	y = tuition
0	500
--------------	---------
-------------	--------
--------------------	---------

You see that the equation of the line that gives the relationship between the tuition (y) and the number of credits (x) is:
y = ____ x + _____. This is again a linear relationship.

Plot the points (x,y). !! Give a title to the graph, label the axes, think about the right scale. !!
(hint: along the y-axis 1 unit = 500 , along the x-axis 1 unit = 1 )
Trace a line through the points. The y-intercept is the intersection between the line and the y-axis.

GRAPH PAPER

The equation of the line is y = ______________. The slope is _________
(rise/run = change in y / change in x)
The slope tells you by how much the price increases each time you add one credit.
The y-intercept is ________. The y-intercept is where the line cross the y-axis.
( That is : x = 0 , in that case you just register and take no credit)
The equation of the line is y = ____ x + _____. The form is called slope-intercept.

3) do the following lab: labgraph1
you need bouncing balls.

In Physics, even if you expect a linear relationship between 2 variables, the graph will not be a perfect
line if the data are collected during an experiment. Some inaccuracy occurs because of human errors.
First you do a scatter plot. (plot the points). If you see a linear trend, the relation is linear. Trace your best fit line. Here is a nice video that shows you the idea:

4) Students are given a toy car to study uniform motion.
During the experiment they record the distance d(m)
covered by the car as well as the time t(s). Their measures are recorded below:

x= time (s)	y= distance (m)
1.0	0.32
2.0	0.80
3.0	0.95
4.0	1.18
5	1.6

A) The students try to find out if there is a relationship between the distance and the time. the time is the ____________ variable (independent ? dependent ?)
the distance is the __________ variable.

B) To find out what kind of relationship exist between the variables, you need to make a graph
(so get a graph paper). NEW: you can use your TI for this one. See this MOVIE to find out how !!
Trace the x-y axis - Find the right scale
(example: 1 unit on x-axis = 0.1 and 1 unit on y axis = 1 )
plot the points. Don't connect the dot. Label the axis. Give a title to your graph
Is this a linear relationship (does it look like a line ? )

C) Find the best fit line. don't connect the dots. go through (0,0)

D) Find the slope (see the lab for instructions). slope = _____ m/s

E) Can you find the relationship between y and x ? y = _____ x
since y is the distance and x the time, you can write d = _____ t.

F) the unit of the slope is m/s. The slope represent therefore the __________ of the car. (m/s or mph is the unit of _____)
The slope means that the car will cover ________ meters in one second.

5) lab fitting a line to a set (labgraph2) of data to make prediction

6) During an experiment, a student measured the mass of 10 cm³ of alcohol.
The student then measured the mass of 20cm³ of alcohol. In this way, the
data were collected: (if you know how to use the TI, use it, draw what you get on a separate paper)

x= volume (cm3)	y = mass (g)
0	0
10	8
20	16
30	24
40	32
50	40

A) plot the values given. Find the right scale and don't forget the label the axis. Give a title to your graph. Don't connect the dot.
(hint: 1 unit along x = 10 , 1 unit along y = 5 try)
B) trace the best fit line (going through the origin ). slope = ______g/cm³
The slope represents the ________ of alcohol. (mass per unit volume is the _______)
It means that 1 unit volume of 1 cm³ has a mass of ________
It means: each time you increase the volume by 1 cm³,
you increase the mass by __________.
C) Find the relationship between y (the mass) and x (the volume). y = ______ x.
D) CAn you use your equation to predict the mass of x= 35cm³ of alcohol ?
y = mass = __________. (hint: use the relation between y and x)

Learn how to find the best fit line and to use the TI to do the job for you:
labgraph3 -----

7) During a class demonstration, a physics instructor placed a 1kg mass on a horizontal table was nearly frictionless.
The instructor then applied various horizontal forces F to the mass and measured the acceleration a for each force applies.
The acceleration tells you by how much the speed increases every second.. That is how fast the mass get faster.
So the input x (or independent variable) is the force F (N) = x and the output
(or dependent variable ) is the acceleration a (m/s/s) = y. The results of the experiment are shown here:

x=force (N)	y=acceleration (m/s/s)
0	0
5	4.9
10	9.8
15	15
20	20.1
25	25
30	29.9

A) Graph acceleration vs force : plot the points. don't connect the dots. Don't forget to label the axis and to give a title to the graph. Find the best fit line. Not that I forced the y-intercept to be 0 because 0 force means 0 acceleration. (Newton's 1st law)
(you can use the TI if you know how)
B) Find the slope of the line. slope = _____ m/s²/ N
extra credits: a Newton = N = kg . m/s². Find now the new unit of the slope. (m/s²/ kg . m/s²)
The slope represent the inverse of ______, the unit is ________ in the SI system.

8) A) An experiment is done by students. They measure the weight (y) of different masses (x). They report their measures in the following table:

x= mass (kg)	y=weight (N)
0	0
5	50N
15	148N
20	203N
25	249N
30	303 N

Plot the points on a graph and trace the best fit line. don't forget to label the axes, give
a title ... (hint: 1 unit x = 5 and 1 unit y = 50 )

Estimate the slope of the line slope = _____N/kg
Is this number surprise you ?
On Earth, weight = mass x ________ ? (at sea level)
the equation of the line is therefore y = _______ x.
The slope represents the gravitational acceleration on EArth.

B) An astronaut conduct experiments on a distance planet to find the gravitational acceleration of the planet. His measurements are reported in the table:

x= mass (kilograms)	y= weight (newton)
0	0
15	106
20	141
25	179
30	216
35	249

Help the astronaut to find the acceleration of this new planet. Suppose the relationship between weight and mass is linear. y = m x. You are looking for m. (the slope of the line). Use your TI. Note that since the line go through (0,0), the y-intercept = 0. THat is b =0.
Your TI may find a small y-interecept (smaller than 1 in magnitude). Just ignore it. Use only the slope found by the TI.
so y = ____ x , the slope represent _________________________ on the planet. (see A)
Plot the points on a graph (it is ok if it not precise ). give it a title and label the axis.

10) During a unit in electricity, students built a circuit including a generator (like a variable battery) and a resistor. Using the generator they generate currents of different magnitudes (independent variable x) and record the tension (difference of voltage) across the resistor (dependent variable). They recorded the data collected in the following table.

y= Tension across the resistor (volts)	0	1.2	2.5	4.8	10.2	14.8	20.5	27.0
x= Current (amps)	0	.025	.05	.1	.2	.3	.4	.6

Find the relationship (linear) between the tension y and the the current x.
(you can use the TI). y = mx . you need to find the slope. if you use the TI you should get
b very small (in the 10^-4 order of magnitude) . b is actually 0. When x = 0, y = 0. (zero energy = zero current)
y = ____ x THAT IS TENSION (V) = __________ CURRENT (A) that is U = _____ I (U is the symbol for tension and I for current)
In Physics the symbol of a tension is U and the symbol for current is I.
The relationship is linear. U = R I. This is called Ohm's law/ R is the resistance of the circuit.
In your experiment R = ____ Ohms.

11) A number of different temperature scales have been devised, two popular choices being the Celsius (formly centigrade) and Fahrenheit scales. Historically, both scales where defined by assigning 2 temperature points on the scale arbitrary and then dividing the distance between them equally spaced intervals.

On a Fahrenheit scale, the water boils at 212F and freezes at 32F.
On a Celsius scale, the water boils at 100 C and freezes at 0C.
The relationship between Fahrenheit and Celsius is linear.
If you have Fahrenheit = y and Celsius = x then y = mx + b or F = mC + b/

A) Find the linear relationship between F and C using your TI or using algebra
hint: The line of F versus C contains the 2 points: (xvalues are the temperature in Celsius and yvalues are temperature in Fahrenheit. get it ? )
( x=0, y= 32 ) and (x = 100 , y =212) . you can either :
A) use the TI: Enter these 2 point in STAT EDIT then find the equation of the line. (follow the steps)
using STAT CALC .
B) use algebra. You can also plug (x1,y1) and (x2,y2) in y= mx + b to solve for m and b. (you have a simple system of 2 variables)
C) use geometry. or you can use the point-slope formula (y - y1) = m (x - x1). with (x1,y1) either one of the 2 points and m the slope , m= (y2-y1) / (x2 -x1)
First find the slope then plug the slope m and (x1,y1), any of the 2 points, into your formula.

you find F = ___ C + _____
Write the slope as a fraction = _______ .
to go from decimal to fraction using the TI: use the MATH key and then FRAC then ENTER ENTER )
so rewrite the formula with the slope as a ratio : F = ___ C + ________

B) An healthy person has an oral temperature of 98.6F . What would this reading on the Celsius scale?
hint: F = 98.6 solve for C using your equation found in A

C) A "time and temperature" sign on a bank indicate the outdoor temperature is - 20C.
Find the corresponding temperature on the Fahrenheit scale.

D) A room temperature in Europe is 19C , How much is that in F ?

12) In Physics we use another temperature scale called the Kelvin temperature scale. Named after the Scottish physicist Lord Kelvin.
A temperature of 300K is said "three hundred kelvins ". The kelvin is the SI base unit for temperature.
The relationship between kelvins and degrees Celsius is K = C + 273.15
Experiments with gases have shown that there is;w a lowest possible temperature. This temperature is defined to be the zero point on the Kelvin scale (=0 K ). This is referred as the absolute value. At that temperature, the atoms
(molecules) stop moving and electricity can circulate without any resistance.
On the Celsius scale, the absolute zero is ______ C
(hint use C= K + 273.15)
The ice point (water freezes, 0C) occurs at _________ K on the kelvin scale.

The surface temperature of Sun is 6000 K. How much is that is degrees Celsius ? ___________

13) Remember the pressure in 9th grade ?
each time you dive down about 33 feet (10 meters) the atmospheric pressure increase by 1 atmosphere.
1 atmosphere is the pressure exerted by the air above you or about 10 cars per square yards (10 tons per square meters).
In math you translate this fact by : P(d) = 1 + (d/33)
P is the ___________ in atmosphere, d is the ________ in feet.
P(0) = ___________ (does that make sense ? )
P(33) = _____________-
Find the pressure at 20ft, 30ft and 100 ft.

14) The function T(d) = 10d + 20 gives the temperature, in degrees Celsius, inside the earth as a function
of the depth d, in kilometers (1.5 km = 1 mile) . THe slope is _________ that means, each time the depth
increases by 1 km, the temperature by ___________. THe y-intercept is __________, meaning
if d = 0 (at the surface), the temperature is about _________ degrees (68F).
Find the temperatures at 5km, 20km, and 1000km

15) The function C(F) = 5/9 ( F - 32 ) determines the CElsius temperature that corresponds to F degrees Fahrenheit.
Find the Celsius temperature that corresponds to 62F, 77F and 23F.

PART2: non linear relation ships (in construction)

1) Some relationships are non linear. You will study them in Math. Among them: the quadratic functions ax²+bx +c (projectile motions),
inverse relationships 1/x (when on object is acted upon by a force, the acceleration is inversely proportional to the mass)
, inverse square law 1/x² ( the gravitational force is inversely proportional to the distance squared ...). .

2) Let's take an inversely propotional relationship.
The dominant color of a star depends on the temperature. A " cool " star is red and a " hot " star is blue.
In the middle, the star is yellow like our sun. Each color is associated to a wavelength. The Wien's law gives the
relationship between the peak wavelength and the temperature.
(wavelength in meters) x (temperature in kelvins) = constant.
or L x T = constant or L = constant / T
So when T increases, L ___________
Here is a table with wavelengths and corresponding temperatures.

L (in 10^-10m)	T (in kelvins)
3500	8300
4000	7300
4500	6400
5000	5800
5500	5300

A) plots these points and trace the best fit curve.
B) Find the constant of the law. (in 10^-10 m x kelvins)

C) so if you divide the wavelength (color) by 2 , the temperature is __________ by 2.
Why a violet-hot star has double the temperature of a red-hot star ?
(violet avelength is about 400 nm, red is up to 800 nm)

3) Also, there is another law (Stefan-Boltzamn law) that gives the energy produced by a star per unit area per unit second.
The energy (electromangetic radiations) E produced by a star per unit area and per second is proportional to the temperature
raised to the fourth power T⁴. Call s the constant or proportionality. The law is : ____ = __ x ____ (use E, T and s).
So if a star is twice as hot than another, it will produce _________ more energy.

5) more graphing

3) Here is an xerecice given for the regent exam in 9th grade. (NY state)
THe table below shows the relationship between the amount of aluminum in a given type of rock
and the energy needed to extract aluminum from that rock.

sample	aluminum content of ore (percent)	Energy needed to extract 1 ton of aluminum (thousands of KWh)
1	3	220
2	5	140
3	10	90
4	20	65
5	30	54
6	40	49
7	50	48

A) the iindependent variable (manipulated) is ___________, the dependent variable is ____________(responding)

B) as the % of aluminum in the ore increases, the energy to extract ______________

C) plot the points. Title the graph and the axis. Trace the best fit curve.

D) is it a direct or inverse relationship ?

E) ty to find the equation of the function that best fits the data. (hint: it is a power function y = a x^b )
use your TI to find a and b.

6) Consider the planets around the Sun. The forces acting on them is the gravitational force Fg.
This force is proportional to the product of the mass of the sun M and the mass of the planet m.
The constant of proportionality is the gravitational constant G =

gravitational constant = 6.67300 × 10^-11 m³ kg^-1 s^-2

It is also inversely proportional to the distance between the Sun and the planet d.

A) Try to write the formula for the force using m , M, G and d . Fg = ______ / _____
SHOW YOUR WORK

hint: is it GMmd ? Gd /Mm ? G Mm/d ? G / Mmd² ? GMm / d² ? Mm / Gd ?

B) Newton's second law says Fg = m a_c, m is the mass of the planet, a_c is the centripetal acceleration .
Even though the speed of the planet is constant, its direction changes so there is an acceleration.
This acceleration is equal to ac = V² / d . V is the orbital speed and d is the distance between the
planet and the Sun. In the formula Fg = m a_c Substitute ac by V² / d and Fg by its expression found in A.
Cross out the m. Isolate V² on one side of the equation. V²= ___ / ____ (use G, M and d).
Take the root square and find the expression of V = ______/ ______. (use G, M, d and

Is it a direct or inverse relationship ?

C) Using the relationship, find the orbital speed. The mass of the Sun is mass of the sun = 1.98892 × 10³⁰ kilograms

Fill the table

Planet	average distance from sun in m	orbital speed (m/s)
Mercury	58 000 000 000	=
Vernus	108 000 000 000	=
Earth	150 000 000 000	=
Mars	229 000 000 000	=
Jupiter	777 000 000 000	=
Saturn	1 429 400 000 000	=
Uranus	3 000 000 000 000	=
Neptune	4 500 000 000 000	=
Pluto	5 910 000 000 000	=

D) using a TI Plot the speed vs distance. You can have the distances in billions of meters
(you can choose the window to be: 4000<Y<40000 and 5000000000<X<6000000000000

gravitational constant = 6.67300 × 10-11 m3 kg-1 s-2

gravitational constant = 6.67300 × 10^-11 m³ kg^-1 s^-2