cahier physique - physics workbook

INTRODUCTION
y = m x + b is the equation of the line .
m is the slope and b is the y-intercept (intersection between the line and the y-axis)

PROCEDURE
you need: a beaker , a ruler an a plate scale.
step1: Fill the beaker to a height of 2 cm. Measure the mass of the beaker water. (grams)
report the values in the table below.

step2: repeat step1 for a height = 4cm, 8cm, 10cm, 12cm. Fill the table,

x= height of water (cm)	y= mass of beaker + water (g)
2	_______________________
4	_______________________
8	_______________________
10	_______________________
12	_______________________

ANALYSIS

1) Use a graph paper. plot the points (x,y). Label the axis and give a title to the graph. Do not connect the dots.

2) trace the best fit line. The line DOES NOT go through zero.
Find the slope of the line and the y- intercept. Use the graph below and the definitions to help you.
slope = ______ g/cm y-intercept = _________ g (for x = 0, no water)

Trace a triangle like on the picture.
the slope = m = rise/run
or slope = (height/base)
In the example, slope = 0.3333...

the y-intercept is the intersection
between the line and the y-axis.
In the example:
y-intercept = 1.7 (about)
The y-intercept is the value of y
for which x=0.

On your graph, slope =m= ______ g/cm
On your graph, y-intercept = b = _______ g
What does the y-intercept represent ? _________________________

Find the mass of the empty beaker using the scale b' = ___________g.
Is this number close to your y-intercept ?
(The y-intercept is the mass of the beaker (for x=0, no water). )

3) Find the equation of the line y = mx + b (y is the mass of the beaker, x is the height of water)
m is the slope and b the y-intercept

4) using your equation predict the mass if the height of water is x= 6cm. y = _____ g .
Check your prediction: Fill the beaker with water to a height of 6cm. Find the mass = _________
DO you get the same value ? _____________

GOING FURTHER

1) Ten students each did a different number of jumping jacks and then recorded their heart rates. Find and graph a line of best fit for the data. How is heart rate related to exercise,

x values =Jumping Jacks	0	5	10	15	20	25	30	35	40	45
y values = Heart Rate (beats/min)	78	76	84	86	93	90	96	92	100	107

TO answer the question you need to find the equation of the best fit line. You can use your TI.

2) A) Is there a linear relationship between the x= total fat (g) and the total calories ?
If the answer is yes, find the best fit line. (follow the same step)
source: http://www.regentsprep.org/regents/math/algebra/AD4/linefitcalc.htm
you can use the above website to follow the same steps as before.

Sandwich	Total Fat (g)	Total Calories
Hamburger	9	260
Cheeseburger	13	320
Quarter Pounder	21	420
Quarter Pounder with Cheese	30	530
Big Mac	31	560
Arch Sandwich Special	31	550
Arch Special with Bacon	34	590
Crispy Chicken	25	500
Fish Fillet	28	560
Grilled Chicken	20	440
Grilled Chicken Light	5	300

The linear relationship is y (calories) = ____ x (fat) + _____
So , each time the fat is increased by 1 g, the calories are increased by _____ (slope)

B) Predict the total calories based upon x= 25 grams of fat. y = _________.