Question

Represent each of the following units as a combination of primitive

dimensions where M=mass, L=length, T=time. As an example, miles per hour would
correspond to [L/T].

a. kilometer
b. quart
c. pascal
d. watt
e. newton
f. horsepower

Answer 1

a. unit of length: [L]

b. unit of volume: [
`L^3`]

c. unit of pressure:
`P=(F)/(A) \equiv([MLT^(-2)])/([L^2])`
`[ML^(-1)T^(-2)]`

d. unit of power:
`N.m.s^(-1)\equiv [ML^2T^(-3)]`

e. unit of force:
`[kg.m/s^2]\equiv [MLT^(-2)]`

f. unit of power:
`N.m.s^(-1)\equiv [ML^2T^(-3)]`

Force:
`F=m.a=m.(v)/(t)=m.(x)/(t)/ t`

Power:
`P=(W)/(t)=(F.x)/(t)`

where:

F = force

A = area

W = work

t = time

a = acceleration

v = velocity

x = displacement