Unit Conversion
The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
All Rights Reserved -- Fair Use Encouraged
Discussion
Dimensional Analysis
Factor-Label Method
Summary
- Blah blah dimensional analysis blah blah.
- When quantities are multiplied, divided, or raised to a power their units are likewise multiplied, divided, or raised to a power.
- Quantities may be added or subtracted only if they have the same unit.
- Blah blah factor label method blah blah.
- multiply by a ratio equal to one with the intent of canceling the original unit(s)
Problems
practice
- A 20 km long, 8 m wide, two-lane highway is to be paved with a
4 cm thick layer of asphalt. A fleet of three dumptrucks is to be employed,
each with an empty mass of 20 metric tons and a carrying capacity of
20 m3. Asphalt with a density of 0.72 g/cm3 will
be used. Determine …
- the total volume of asphalt needed,
- the number of dumptruck loads required, and
- the gross mass of each truck.
- Answer it.
- Determine which of the following expressions are dimensionally consistent.
v2 = 2ax x = vt + ½ at3 tan θ = v x - Answer it.
- Write something else.
- Answer it.
- Write something completely different.
- Answer it.
algebraic
☞ For each of the following problems let a [m/s2], v [m/s], and x [m].
- Determine the SI unit of each of the following quantities.
v2 ax at2 2 2π√ x a - Determine which of the following expressions are dimensionally consistent.
v = xt x = vt t = vx x = at + ½ at2 x = vt + ½ at3 v2 = 2ax2 t = v x t = √ 2x a t = √ v2 ax tan θ = x y tan θ = y x [one more] - Determine the SI units of the constants C1 and C2 so
that the following expressions are dimensionally correct.
x = C1 + C2t x = C1t + ½ C2t2 v = C1t + C2t2 x = C1 sin (2πC2t) v = ½ C1e−C2t [one more] - In the formula below the symbol U is measured in kgm2/s2 and x stands
for length. What are the units of k?
U = ½kx2
- In the formula below the symbol T is measured in seconds
and l stands for length. What are the units of g?
T =2π √ ℓ g - Given the following equations:
with the following units:v = x a = v P = W F = ma W = Fx t t t
derive the unit for P.x meters [m] t seconds [s] m kilograms [kg] - Given the following equations:
with the following units:v = kx U = ½kx2 U = mgh
derive the unit for g.x, h meters [m] m kilograms [kg] F [kgm/s2]
Resources
- conversion calculators
- dictionaries/encyclopedia
- A Dictionary of Units Frank Tapson, University of Exeter
- mars climate orbiter
- Mars Climate Orbiter Team Finds Likely Cause Of Loss, NASA
- Oregon Students Have NASA's Number,The Oregonian
- Schoolkid Blunder Brought Down Mars Probe, New Scientist
| Another quality webpage by Glenn Elert |
 |
home | contact bent | chaos | eworld | facts | physics |