Respuesta :
Dimentional analysis is very important in physics, because it allows finding errors in equations. We find that the following true equations
a) F= m a
b) x = 2 a t²
c) E = [tex]\frac{1}{2} }\ m \ a \ x[/tex]
d) E = m a x
The fundamental units in mechanics are;
the length [L] whose unit is the meter
The time [T] that has the second as a unit
The mass [M] with fundamental unit the kilogram (kg)
all other quantities are derived from these three fundamental units, for example velocity is
v = x / t
we replace the units
[v] = [L] / [T]
so the units of velocity are the distance between time.
This exercise uses the units of various quantities and asks to find if the equations are dimensionally correct.
Let's substitute the units in each expression
a) F = m a
[M] [L] / [[T] ² = [M] [L] / [T] ²
the two sides of the expression are equal therefore the equation is correct
b) x = 2 a t²
scalar quantities have no units
[L] = [L] / [T] ² [T] ²
[L] = [L]
the two sides are equal, therefore the equation is correct
c) E = ½ m a x
[M] [L] ² [T] ² = [M] [L] [T] ² [L]
[M] [L] ² [T] ² = [M] [L] ² [T] ²
the two sides are equal the equation is correct
d) E = m a x
since scalar quantities have no units, this expression is equivalent to the expression in part c, therefore it is correct
e) F = F x / m
[M] [L] / [T] ² = [M] [L] / [T] ² [L] / [M]
[M] [L] / [T] ² = [L] ² / [T] ²
the two sides are different so the equation is false
In the dimensional analysis we find that expressions are true a, b, c, d and we see that the expression e is false
learn more about dimentional analysis here: https://brainly.com/question/15631494
