University Physics Volume 1 — Mechanics · Problem 52

Units and Measurement — OpenStax

Physics — University · dimensional-analysis

Problem

Consider the physical quantities

m

s

v

a

, and

t

with dimensions

[m] = M

[s] = L

[v] = LT^{-1}

[a] = LT^{-2}

, and

[t] = T

. Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a)

F = ma

; (b)

K = 0.5mv^2

; (c)

p = mv

; (d)

W = mas

; (e)

L = mvr