# Unit Analysis – An offshoot of Dimensional ```SPH3U: Physics Math Part C and D
PART C: Create The Unit
Determine the scientific (SI) units of the following quantities:
1.
volume (length x width x height)
2.
acceleration (velocity/time)
3.
density (mass/volume)
4.
force (mass &times; acceleration)
8.
electric field (force/charge) – charge is in
Coulombs (C)
9.
work (force &times; distance)
10. energy (e.g., gravitational potential energy = mgh
= mass &times; gravitational acceleration &times; height)
5.
charge (current &times; time)
6.
pressure (force/area)
7.
(volume)2
11. square root of area
PART D: Formulas and Dimensional Analysis
1.
2.
Given mv = Ft, where m is mass, v is speed, F is force, and t is time, what are the units of each side of the equation? Is
Given x = xo + vot + &frac12;at2, where x is the final position, t is the time, xo is the initial position, vo is the initial speed,
and a is constant acceleration, what are the units of each side of the equation? Is the equation dimensionally correct?
3.
Given P =
, where P is pressure,  is density, g is gravitational acceleration, and h is height, what are the units
of each side of the equation? Is the equation dimensionally correct?
4.
Given H = mC, where H is in joules, m in kilograms, and  in kelvin, what are the SI units of C?
Physics Math Assignment
PART C:
1. m3
2. m/s2
3. kg/ m3
4.
kg  m
or N
s2
5. As
6.
kg  m
kg
2
 m =
2
s
m  s2
7. m6
kg  m
C  s2
kg  m 2
9. Nm or
s2
kg  m 2
10.
s2
8. N/C or
11. m
PART D:
kg  m
s
1. YES,
2. YES, m
3. NO,
4.
kg
kg

2
ms
m  s2
J
kg  K
or N/m2
```