Question

Is this anywhere correct?
F(t_2-t_1)=m(V_2-V_1)
N(s_2-s_1)=(kg)(m/s_2-m/s_1)
(kg)((m/s)^2)(s_1)=(kg)(m/s_1)
not homogeneous?

Answer 1

@jim_thompson5910 can you help me? :)

Answer 2

What are you trying to show again?

Answer 3

I need to determine whether or not the original equation is dimensionally homogeneous.

Answer 4

So the original equation is F(t_2-t_1)=m(V_2-V_1)

Answer 5

correct?

Answer 6

yes

Answer 7

t_2 and t_1 are times in seconds

so t_2 - t_1 is a time in seconds

Answer 8

So

F(t_2-t_1)=m(V_2-V_1)

becomes

F(seconds - seconds)=m(V_2-V_1)

which becomes

F(seconds)=m(V_2-V_1)

Answer 9

Same idea with V_2 and V_1, but these are velocities in m/s

V_2-V_1

m/s - m/s

m/s

Note: m and s are NOT variables, they are units, so m/s is NOT a variable...it's a unit

So we get

F(seconds) = m(m/s)

Do you see how I'm getting all this?

Answer 10

yes, I understand that. Then, F= (kg)(m/s)^2... So,
(kg)(m/s)^2(s)=(kg)(m/s)

right?

Answer 11

Units for force

F = Newtons

F = kg*(m/s^2)

t_2 and t_1 = seconds (s)

V_2 and V_1 = m/s

m = kg

Sadly there are two 'm' terms here, one for meters and one for mass...hopefully that's not too confusing
--------------------

F(t_2-t_1)=m(V_2-V_1)

F(seconds) = kg(m/s)

(kg*(m/s^2))(seconds) = kg(m/s)

(kg*(m/s^2))(s) = kg(m/s)

kg*m/s = kg*m/s

So the dimensions match

Answer 12

Oops, I meant to write "Units" instead of "units for force", but you get the idea

Answer 13

(kg*(m/s^2))(s) = kg(m/s)

kg*m/s = kg*m/s

how'd you go front that to that?

Answer 14

The s^2 in the denominator and the 's' in the numerator on the left side multiply and one pair of 's' terms cancel

So

(1/s^2)*(s/1) = 1/s

Answer 15

That's how

(kg*(m/s^2))(s)

simplifies to

kg*m/s

Answer 16

oh okay gotcha.

and one more I did, but I'm unsure if it's correct...
F=mV
(kg*(m/s^2))=(kg*(m/s))
not homogeneous?

Answer 17

no it's not, the left side has a s^2 in the denominator but the right side only has 's' in the denominator

so it's not homogeneous

Answer 18

okay, so yay got one right lol! thanks for the help. greatly appreciated.

Answer 19

you're welcome