Thursday, August 16, 2012

Working With Units/Confirming Equations - August 16th, 2012


Working with units/confirming equations

Quantity
Letter used in equations
unit
Length, distance
d
m (meter)
Time
t
s (second)
Mass
M
kg (kilogram)
velocity
v
m/s
acceleration
a
m/s2
Force
F
N (Newton)
Energy, work
W
J (joule)
power
P
w (watt)
Frequency
f
Hz

Using the above chart and dimensional analysis, determine if the following equations are valid:

d = vt + at2/2 à d(m) = v(m/s)*t(s) + a(m/s2)*t2(s2)/2 = m+m/2 VALID
W = vt à W(J) = v(m/s)*t(s) = m/s2 NOT VALID
P = Wt àP(w) = W(J)*t(s) NOT VALID
P = Fv àP(w) = F(N)*v(m/s) VALID
W = Fd à W(J) = F(N)*d(m) VALID
v = at à v(m/s) = a(m/s2)*t(s) VALID
t = W/P à t(s) = W(J)/P(w) = W(Nm)/P(Nm/s) = s Valid
W = Pt à W(J) = P(w)*t(s) = P(J/s)*t(s) VALID
v= 2ad à v2(m2/s2) = 2*a(m/s2)*d(m) VALID
W = Mv à W(J) = m(kg)*v(m/s) NOT VALID
a = vt à a(m/s2) = v(m/s)*t(s) NOT VALID
P = Mv/t à P(w) = m(kg)*v(m/s)/t(s) = kgm/s2 NOT VALID
t = square root of (d/a) à t(s) = sqrt[d(m)/a(m/s2)] = s VALID
v2 = W/M à v2(m2/s2) = W(J)/m(kg) VALID
F = Ma à F(N) = m(kg)*a(m/s2) VALID
P = Fd/t à P(w) = F(N)*d(m)/t(s) VALID
w= Mv2/2 à j/s = (kg)(m2/s2)/2 = 2kgm2/s2 VALID
v= d*f à m/s = m*1/s = m/s VALID
f= a*t2 à 1/s = m/s2 * s2 = m NOT VALID


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