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
v2 =
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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