cahier physique - physics workbook

ACTIVITY 1: length of a line on a screen versus distance projector

Here is a line:

This line is projected on the screen. You will find out if there is a relationship between the distance projector-screen and the length of the line on the screen

step1: Place the projector at about 210cm (2 meters + 10cm) from the screen. Measure the distance from the feet of the cart to the screen. Measure the length of the line segment as it appears on the screen Record the data in the table below.

x= distance projector - screen (cm)	y = length of line segment on screen (cm)
200	_____________
210	_____________
220	_____________
230	_____________
240	_____________
250	_____________
260	_____________
270	_____________
280	_____________
290	_____________

step2: Repeat step1 using nine other locations of the projector.
the independent variable is __________________, the dependent variable is _________________________

step3: Use a graph paper. Trace the x-axis and the y-axis. Find the right scales.
Example: x-axis : 1 unit = 200cm y-axis: 1 unit = 1cm
plot the dots. Label the axis. Title the graph. don't connect the dot.
With a ruler trace the best fit line going through (0,0)

step4: Find the slope = rise / run = __________
Find the relationship between y (distance from projector) and x (length of the line)
y = _____ x. What kind of relationship is this ? ____________
if x = 265cm , y = __________ (according to your equation).
Check if this is true ? (move the projector to 265cm and measure the line)

ACTIVITY 2: 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. 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 = ______

step3: Suppose the relationship between y and x linear. y = mx
that is (mass in grams) = m x (length in cm). the mass of the wire is proportional to the length of the wire. Using the points form the table (x1, y1) and (x2,y2) solve for m.
y = ____ x. or (mass in grams) = _____ x (length in cm)
step4: Measure the length of the middle wire. x = ____ cm. Use your equation to predict the mass of the wire y_predicted= _____g.
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)
The slope m = d/t.
What is the unit m ? what physical quantity m represent ?
(what is distance over time?)

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 = ____________.

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)
substitute m in y = mx + b.
Solve for b using y2 = mx2 + b or y1 = mx1 + b

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) n, there is not 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.