Physics 1050
Laboratory #2 Acceleration of Falling Objects
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Acceleration of Falling Objects
Freely falling objects are those whose motion is only under the
influence of gravity. When up is taken as the positive direction,
objects fall with a constant downward acceleration a of
ay = −g = −9.81m/s2 .
The motion of objects in free-fall obeys the kinematics equations
governing one-dimensional motion, but with the acceleration always
equal to the above constant.
€
The displacement in the y-direction is given by
y f = y i + v yi t +
1
2
ay t 2
= y i + v yi t − 1 2 gt 2
where yf and yi are the final and initial positions in the y-direction, vyi is
the initial velocity in the y-direction and t is the time.
€
The instantaneous velocity, v, may be found as the slope of the
tangent to a displacement versus time graph at any point. In relation
to other kinematics variables, instantaneous velocity is given by
v yf = v yi + ay t
= v yi − gt .
Plotting one kinematics variable versus another allows you to see
these relationships, as well as to find constants such as the
acceleration due to
€gravity and initial velocity.
Physics 1050
Laboratory #2 Acceleration of Falling Objects
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Interpreting Graphical Results:
To draw physical meaning from graphical results, it is necessary to
compare the physics equations relating the plotted variables to the fit
results.
As given on the previous page, the vertical displacement of an object
in free fall is given by
y f = y i + v yi t − 1 2 gt 2
which may be rewritten as
€
y f = − 1 2 gt 2 + v yi t + y i
A plot of y vs t will be fit to a quadratic form:
€
y = at 2 + bt + c .
The coefficients in each of the two forms must be compared to
determine which physical quantity is represented by a.
€
Similarly, velocity of an object is given by
v yf = v yi − gt
which is rearranged to give
€
v yf = −gt + v yi .
A plot of v vs t will be fit to the linear form
€
v = mt + b .
Comparing the two equations indicates the physical meaning of the
parameters m and b.
€
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Physics 1050
Laboratory #2 Acceleration of Falling Objects
Prelab Questions
These questions need to be completed before entering the
lab.
Show all workings.
Attach this sheet to your workbook.
Markers
Initials
Prelab 1
For a falling ball which bounces, draw the expected shape of the vertical position
vs time graph.
Prelab 2
From the position vs time graph of an object moving with constant acceleration,
how could you find the instantaneous velocity?
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Physics 1050
Laboratory #2 Acceleration of Falling Objects
Name and Student Number:
___________________________________
Date:
___________________________________
Partner:
___________________________________
Part I:
Introduction
Part II:
Apparatus
Part III:
Data Acquisition
Part IV:
Data Analysis (Falling Ball)
CHECKPOINT: Have an instructor check your graphs and initial.
QUESTION 1:
Attach your printed graph to the following page.
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Physics 1050
Laboratory #2 Acceleration of Falling Objects
Attach graph to this page.
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Physics 1050
QUESTION 2:
QUESTION 3:
QUESTION 4:
QUESTION 5:
Laboratory #2 Acceleration of Falling Objects
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Physics 1050
TABLE 1:
Laboratory #2 Acceleration of Falling Objects
Fit parameter for position versus time graph.
Value
Uncertainty
Expected value of
parameter A
Units
N/A
Automatic fit parameter A
QUESTION 6:
QUESTION 7:
TABLE 2:
Slope of velocity versus time graph.
Value
Slope
QUESTION 8:
Uncertainty
Units
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Physics 1050
TABLE 3:
Laboratory #2 Acceleration of Falling Objects
Mean and standard deviation from acceleration vs time
graph
Mean
Standard
Deviation
Number of
Samples
Standard
Error
Acceleration
QUESTION 9:
Part V:
Data Acquisition and Analysis (Falling Balloon)
TABLE 4:
Fit parameter for position versus time graph.
Value
Automatic Fit parameter A
QUESTION 10:
Uncertainty
Units
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Physics 1050
Part VI:
Laboratory #2 Acceleration of Falling Objects
Summary
QUESTION 11:
QUESTION 12:
QUESTION 13:
Return to the lab manual:
Staple graphs to the reverse
of this page.