HW#1b
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1. Can dimensional analysis determine whether the area of a circle is πr2 or 2πr2?
no
Because the factor of 2 is dimensionless. πr2 and 2πr2 both have the same dimension, which
is length square. That is the dimension of area. When dimension is correct, dimension
analysis can not tell whether a constant like 2 should be there or not.
Which of the following equations are dimensionally consistent?
v2 = 2ax Left side units: (m/s)2 ; Right side units: m/s2* m = (m/s)2
Both sides have dimension velocity square.
t = a/v
Left side units: s; Right side units: (m/s2)/(m/s)=1/s ;
Left side Dimension ---time can not be equal to right side dimension ----1/time.
v = at2 Left side units: m/s; Right side units: (m/s2)*s2=m ;
Left side Dimension --velocity can not be equal to right side dimension --length
v = at Left side units: m/s ; Right side units: m/s2*s = m/s
Both sides have dimension velocity.
HW#1b
4. (a) What is the area of a circle of radius 14.37 m?
(b) What is the area of a circle of radius 3.8 m?
5.
In the second example, Anew =( ¾)2 Aold.
Anew = 9/16 Aold.
It is 16/9 times smaller. 1.78 times less in area.
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HW#1b
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HW#1b
340*7=2380 (m)
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