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

Answer 1

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