Question

If E=1/2Av^2+Bmx find the dimensions of A and B(Where E is energy,v,m and x are velocity,mass and distance respectively)

Answer 1

Answer:

A = [kg]

B = [m/s²]

Explanation:

E = ½ Av² + Bmx

Substitute the units:

[J] = ½ A [m/s]² + B [kg] [m]

A Joule written in base units is:

1 J = 1 Nm = 1 kg m²/s²

Each term must have the same units.

[kg m²/s²] = A [m/s]²

[kg m²/s²] = A [m²/s²]

A = [kg]

[kg m²/s²] = B [kg] [m]

B = [m/s²]