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)
Question
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:
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]