Question

Determine whether or not each of the following equations is dimensionally homogeneous. Show your work.
a) F=ma
b) F=m(V^2/R)
c) F(t_2-t_1)=m(V_2-V_1)
d) F=mV

I have no idea how to solve this.

Answer 1

what is dimension of F?

Answer 2

? Idk. All I know is the F= force(N)

Answer 3

Ma M = kg a = m/s^2

Dimmenssional Formula = [MLT^-2]

Answer 4

F is the product of mass and acceleration. Acceleration is measured in meters per second squared, that is, Length per time squared.
So, the dimensional formula of F is
F=M * L/ T^2 or expressed as \[F=[MLT ^{-2}]\]

Answer 5

similarly work out for each side, if in any case the dimensional formuae do not match, it is NON HOMOGENEOUS, else it is homogeneous

Answer 6

I am so confused... can someone take it [SLOW] LOL.. please :/

Answer 7

umm, okk, what r the units of m and a?

unit of F is N which is equalt to kgm/s2

Answer 8

m=kg
a=m/s^2

Do I just write:
F=ma
N=(kg)(m/s^2)
(kg)(m/s^2)=kg(m/s^2)
which means they are equal.....?
is that what I do?

Answer 9

um yes, but in a different way lol

unit of F is kgm/s2

so its dimensional formula wil be : [F] =[ M L T^-2 ]

Answer 10

[F] =[ M L T^-2 ]

wth is that^? lol can you explain that.

Answer 11

similarly, dimensional formula for ma will be : [ma] =[ M ] [ L T^-2 ] = [ M L T^-2 ]

both r same, so dimensionally homogeneous

Answer 12

well, u replace kg by M, m by L and s by T

thats all

ans use square brackets lol

Answer 13

why do you replace it? do you have to?

Answer 14

yes, thats called DIMENSIONAL ANALYSIS lol

Answer 15

can u do it n show me for the b part?

Answer 16

I'll try....

Answer 17

F=m(V^2/R)
N=(kg)((m/s^2)/(m))

[F]=[M][....

I'm stuck there.

Answer 18

You don't necessarily have to change units to M,L,T (mass, length, and time), but you do need to break everything down into fundamental units so you have a consistent basis for comparison.

Answer 19

Well, I understand the units and comparing them. But, once I start changing it to M,L,T.. that confuses me!

Answer 20

B isn't homogeneous is it?

Answer 21

it is.

well as cliff said u can use untis only if that how u r taught in school?

no need to convert then

jus check if both sides have same untis

Answer 22

F=m(V^2/R)
N=(kg)((m/s^2)/(m))
(kg)(m/s^2)=(kg)((m/s^2)/(m))

How is that equal on both sides? Or did I do something wrong?

Answer 23

Check this part:
V² = ( m/s ) ² = m²/s²

Answer 24

but there is still a (m) left...? both (kg) cancel out and both (m/s)^2 cancel out.. there is a (m) left?

Answer 25

(kg)(m/s²)=(kg)((m²/s²)/(m))
= kg * m/s²

Answer 26

Does it look equal now?

Answer 27

how did you go from
=(kg)((m²/s²)/(m))
=kg * m/s²

? there is 3 (m)
m^2 and m

Answer 28

m²/ m = m

Answer 29

oh you simplified!