cahier physique - physics workbook

ACTIVITY 1: Using a graph to predict and estimate the mass of an object

you will be given a plate scale , wire, wire cutter.
step1: cut 3 wires. 1 between 5 and 8cm, 1 between 13 and 16cm and 1 between 20 and 28cm.

step2: Put the (13/16cm) on the side (don't use it yet) . Measure the length of the smallest and the longest wires using a ruler. report the measures in a data table. (below). Using the scale, find the mass (g) of the small and the long wires. report in the table.

length in cm x	mass in grams y
x1 = ____	y1 ________
x2= ___	y2 = ______

The independent variable is _________________ , the dependent variable is _______________________
step3: Suppose the relationship between y and x linear: y = mx m is a constant = slope of the graph length vs grams
In that case, the mass of the wire is proportional to the_________________.
Using the points form the table (x1, y1) and (x2,y2) find the slope m.
hint: remember? m =( y2- y1) / (x2 -x1 )
So y = ____ x or (mass in grams) = _____ x (length in cm)

step4: Measure the length of the middle wire. (the one you didn't use).
x = ____ cm. DON'T SCALE IT YET.
Use your equation to predict the mass of the wire y_predicted= _____g. (use y = mx, you already have m).

Check your prediction. Use the scale to weight the wire. y_calculated = _________g.

step5: Compute the relative error = |y_{calculated -}y_{predicted| /} (y_calculated) = _________________
multiply by 100 to get the %error = ____________ %.If it is below 5% , you did a great job. below 10% it is good. above, something went wrong.
Note that you take the absolute value of the difference between the y values. SO the %error is always >0.

GOING FURTHER

1) Consider the linear relationship y = mx . We also say that y is directly proportional to x and m is the constant of proportionality. If we graph y vs x, the slope is m. Using this fact, fill the blanks:

A) If the distance d (meters) (covered by a car) is directly proportional to the time t (seconds) (to cover that distance) we write: d = ________. ____ is the constant of proportionality (or slope)

What is the unit m ? what physical quantity m represent ?
(m= change in y / change in x = change in distance / change in mass. What units do you get with this ration?)

B) If the mass M (g) of an object is proportional to the volume V (cm³) of the object we write:
M = __________. The constant of proportionality (slope) m' = ___ / ____.
What is the unit of m ? what physical quantity m represent ?
(what is mass over volume ? check google ..)

C)You remember that weight (N) = mass (Kg) x 9.8. We say that the weight is ____________
to the mass and 9.8 is the ___________ of ______________.
The units for 9.8 is m/s/s. 9.8 is an __________, the acceleration due to gravity.

D) If the stress F (newtons) applied to a spring is proportional to the stretch X (meters):
F = ___ X. The constant of proportionality m = ___ / ____ m is called the spring constant.

E) If the pressure P (newtons per square meter) in a liquid is proportional to the depth H (meters) we write:
P = ____________. So if the depth is multiplied by 2 the pressure is ____________________.

2) The velocity of sound V in dry air increases as the temperature increases T.
The velocity V is the dependent variable y and the temperature T the independent variable x.
At 40 degrees (x1= 40) sounds travels at at a rate of about 355m/s (y1 = 355)
At 49 degrees (x2=49) sounds travels at about 360m/s (y2=360).
A) WRite the linear equation for the velocity V of sounds based on the temperature T.
Call the speed y and the temperature x.
hint: write y = mx + b. y is the velocity and x is the temperature. you need to find the slope m and the y-intercept b.
slope = m = ( y2 - y1 ) / (x2 - x1) - use the 2 points you are given.
substitute m in y = mx + b.
Solve for b using y2 = mx2 + b or y1 = mx1 + b

y = ____ x + _______

B) Use the equation to estimate the velocity of sound at 60 degrees.
(hint: plug x=60 in the equation y = mx + b, and solve for y)

3) The number y=C of calories a person burns performing an activity varies directly with the time x= t (in minutes) the person spends performing the activity. A 160 pounds person can burn 73 Calories (y1 = 73) by dancing for 20 minutes (t1=20).
A) Find the linear model that gives C (calories) as a function of t (time) .

hint: the model is y = mx . b=0 because if the person is not active at all (t=0) , there is no calorie (t=0) burnt
use x=20 and y = 73 to solve for m. (73 = m20)

B) In this case, the number of calories y burnt is proportional to the __________________________________________

C) Use your model to estimate how long a 160 pounds person should dance to burn 438 calories.

hint. Use the model y = mx (you already soved for m). y = 438. solve for x.

4) The weight of a person's skin is related to body weight by the equation s = 1/16 w, where s is skin weight and w is body weight.
A) Does this equation show a linear relationship between the skin's weight s and the body weight ?
The skin's weight is proportional to ____________________
B) If a person calculates skin weight as s= 9 _3/4 lb , what is the person's body weight w ?

hint: plug s = 9 _3/4 lb in s = 1/16 w. Solve for w.