Significant Figures
In science, all numbers known to limited precision, do not give more
figures than that
Only give the significant figures
Example 1: 201 means we do not know decimals, so 3
significant figures
200 significant figures unclear
Significant
Four Equations for Constant ax
1.
vfx vix = axt
2.
x = (vfx+vix)t
3.
x = vixt + ax(t)2
(Quadratic Theorem?)
4.
vfx2 vix2 = 2axx (vfx can be + or -)
Each equation relates 4 of the 5 variables x, t, vix, vfx and ax
Problems give 3, ask for 4th (then 5th pt
An object has negative acceleration ax. Its velocity is:
A.
Negative
B.
Positive
C.
Zero
D.
Zero, but just instantaneously
E.
We cannot say
Example of Finding ax
ax = slope of vx-t
= vx/t (m/s2)
With x and vx, vx =
slope of x-t plot, x =
area under vx-t p
Dimensional Analysis
Can often use dimensions to check validity of a formula (L: length, M:
mass, T: time)
Example 1: can 4r2 be the volume of a sphere?
Volume = cubic meters or L3, (area = L2)
But has dimensions of L2, so no, is not volume
Example 2: can
Average acceleration aav,x vx/t
ax = slope of vx-t plot, rate of change of vx
ax positive, vx increasing (no info about vx itself)
ax = 0, vx = constant (ditto)
ax negative, vx decreasing (ditto)
Example of Finding ax
ax = slope of vx-t
= vx/t (m/s2)
With
Adding and Subtracting Vectors
Define magnitude +ve length, size
Consider adding vector to itself
Would like A + A = 2A, so:
: vector with same direction, k times mag.
Define
so that
Equal (size) but opposite (direction)
So
Components
The x and y compone
Scientific Notation
Starting off
Based on a formula, how do quantities change if parameters change?
Example: how does the area of a square change (A = a 2) if the side is
doubled?
a 2a, A ?
Framework Method: substitute 2a for a
A (2a)2 = 4a2 = 4A
SO: area
Position and Displacement
Consider object (thing) moving along straight line
Choose x axis / line
Choose positive direction (x increasing)
Choose origin (point where x = 0)
Must make these choices to proceed
Good to draw or sketch this (arrow for directio
Moving on: Acceleration
If we break the plot up into
very thin vertical strips t
wide, the area of each strip (vx t) is the displacement x during that time
interval
Adding all displacements up, displacement = area under vx-t curve
x-t plot vx, vx-t plot x
Free Fall
Free fall refers to an object released and falling all by itself, just by
gravity (e.g. neglecting air resistance)
By experiment, free fall occurs with a constant downward
acceleration of 9.80 m/s2
Close to earth, independent of position, motion