kissmeass78
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Determine whether or not each of the following equations is dimensionally homogeneous. Show your work.

AF=ma
BF=m(V^2/R)
CF(t_2-t_1)=m(V_2-V_1)
DF=mV

Verified Answer :

a and b are dimensionally homogenous but c and d aren't.

Force = N (newtons) = kg m/s^2

Therefore,

a) F = m a = kg m/s^2 (since m (mass) = kg and a (acceleration)= m/s^2) = kg m/s^2

b) F = m(v^(2)/r)= kg ((m/s)^(2)/m) = kg m/s^2 = kg m/s^2

c) F = m (v2-v1)= kg (m/s - m/s) = kg m/s  ≠ kg m/s^2

d) F= m v = kg m/s ≠ kg m/s^2

Hope this helps



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