Διαστατική ανάλυση – προβλήματα και λύσεις
1. Με βάση την ανάλυση διαστάσεων, προσδιορίστε τις ακόλουθες διαστάσεις φυσικής που έχουν τις ίδιες διαστάσεις.
Β. δύναμη και πίεση
Γ. δύναμη και ορμή
Δ. έργο και θερμότητα
Γνωστό:
Dimension of length = dimension of width = dimension of displacement = L
Dimension of time = T
Dimension of mass = M
Λύση:
Dimension of area = διάσταση μήκους x dimension of width = [L][L] = [L]2
Dimension of velocity = διάσταση του εκτόπισμα / dimension of time = [L] / [T] = [L][T]-1
Dimension of acceleration = dimension of velocity / dimension of time = [L][T]-1 / [Τ] = [Λ][Τ]-1[Τ]-1 = [L][T]-2
Dimension of force = dimension of mass x dimension of acceleration = [Μ][Λ][Τ]-2
Dimension of work = dimension of force x dimension of displacement = [Μ][Λ][Τ]-2 [L] = [M][L]2[Τ]-2
Dimension of power = dimension of work / dimension of time = [Μ][Λ]2[Τ]-2 / [Τ] = [Μ][Λ]2[Τ]-2[Τ]-1 = [Μ][Λ]2[Τ]-3
διάσταση της χυτρα = dimension of force / dimension of area = [Μ][Λ][Τ]-2 / [Λ]2 = [Μ][Λ][Τ]-2 [ΜΕΓΑΛΟ]-2 = [M] [ΜΕΓΑΛΟ]-1[Τ]-2
Διάσταση of momentum = dimension of mass x dimension of velocity = [Μ][Λ][Τ]-1
Dimension of heat = dimension of energy = dimension of work = [Μ][Λ]2[Τ]-2
Η σωστή απάντηση είναι D.
Σημείωση:
θερμότητα 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
Λύση:
Unit of potential energy = unit of κινητική ενέργεια = 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.
Η σωστή απάντηση είναι Γ.
3. The following quantities that have the same units are…
A. Force and emf
B. Velocity and acceleration
C. Δουλειά και ενέργεια
D. Work and power
Λύση:
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.
Η σωστή απάντηση είναι Γ.
