Question

Using dimensional analysis, show that energy can be calculated from the following energy equations. Hint, in SI, here we want Joules.

(6 pts)

E = 1 2 mv2 (5)

E = mgh (6)

Answer 1

Explanation:

1. The kinetic energy of any object is calculated as :

$E=\dfrac{1}{2}mv^2$...........(1)

Dimensional formula of energy, $[E]=[ML^2T^{-2}]$

Dimensional formula of mass is $[M]$

Dimensional formula of velocity, $[v]=[LT^{-1}]$

$[ML^2T^{-2}]=\dfrac{1}{2}[M]([LT^{-1}])^2$

So, $[ML^2T^{-2}]=[ML^2T^{-2}]$

LHS = RHS

2. The potential energy is given by :

$E=mgh$

Dimensional formula of mass is $[M]$

Dimensional formula of g is $[LT^{-2}]$

Dimensional formula of height is $[L]$

Dimensional formula of energy, $[E]=[ML^2T^{-2}]$

So, $E=[M][LT^{-2}][L]$

So, LHS = RHS

Hence, this is the required solution.