Analysis dimensionalis – problemata et solutiones
1. Secundum analysin dimensionalem, dimensiones physicas sequentes quae easdem dimensiones habent determina.
A. opus et potestatem
B. potentia et pressio
C. vis et impetus
D. labor et calor
Notum:
Dimension of length = dimension of width = dimension of displacement = L
Dimension of time = T
Dimension of mass = M
solution:
Dimension of area = dimension of length x dimension of width = [L][L] = [L]2
Dimension of velocity = dimension of obsessio / dimension of time = [L] / [T] = [L][T]-1
Dimension of acceleration = dimension of velocity / dimension of time = [L][T]-1 / [T] = [L][T]-1[T]-1 = [L][T]-2
Dimension of force = dimension of mass x dimension of acceleration = [M][L][T]-2
Dimension of work = dimension of force x dimension of displacement = [M][L][T]-2 [L] = [M][L]2[T]-2
Dimension of power = dimension of work / dimension of time = [M][L]2[T]-2 / [T] = [M][L]2[T]-2[T]-1 = [M][L]2[T]-3
Dimension of Curabitur = dimension of force / dimension of area = [M][L][T]-2 / [L]2 = [M][L][T]-2 [E]-2 = [M] [E]-1[T]-2
ratio of momentum = dimension of mass x dimension of velocity = [M][L][T]-1
Dimension of heat = dimension of energy = dimension of work = [M][L]2[T]-2
Rectam responsum est D.
Note:
Calor is energy that moves due to the temperature difference.
Work is the process of energy transfer through the displacement of objects.
So, the dimension of heat = the dimension of energy = the dimension of work.
2. Two quantities that have the same quantity but have a different physical concept…
A. Force and momentum
B. Energy and force
C. Potential energy and kinetic energy
D. Energy and momentum
solution:
Unit of potential energy = unit of Hanc in motu navitas = unit of energy = unit of work.
Although it has the same unit, but the potential energy and the kinetic energy are different types of energy.
Responsum rectum est C.
3. The following quantities that have the same units are…
A. Force and emf
B. Velocity and acceleration
C. Labor et energia
D. Work and power
solution:
Work is the process of energy transfer through the displacement of objects.
Energy is the ability to do work.
Work and energy are two quantities of physics that have the same unit.
Responsum rectum est C.
