Physical Quantities (Theory)

Question 1

Solve: P = ab^n

Answer 1

ln P = ln a + ln b^n
ln P = ln a + n ln b

ln p = n ln b + ln a
This has the same structure as
y = mx + c

Question 2

Solve: P = ca^b

Answer 2

ln P = ln c + ln a^b
ln P = ln c + b ln a

ln p = b ln a + ln c
This has the same structure as
y = mx + c

Question 3

Solve:
F = K α ρ V
K = 6π

α = Length
ρ = Density
V = Speed

Answer 3

Force = mass • acceleration
Force = kgms^-2
Force = MLT^-2

α = L
ρ = ML⁻³
V = LT⁻¹

F = k αˣ ρʸ vᶻ

M¹ L¹ T⁻² = k Lˣ (ML⁻³)ʸ (LT⁻¹)ᶻ
M¹ L¹ T⁻² = Lˣ Mʸ L⁻³ʸ Lᶻ T ⁻ᶻ

M¹ L¹ T⁻² = Mʸ Lˣ ⁺ ⁻³ʸ ⁺ ᶻ T ⁻ᶻ

Y = 1
-z = -2 > divide (-) on both sides > z = 2
1 = x + (-3y) + z
1 = x + (-3(1)) + (2)
1 = x - 3 + 2
1 = x -1 > add one on both sides
2 = x

Since x = 2, y = 1, and z = 2

F = k αˣ ρʸ vᶻ

Then:
F = k α² ρ v²
F = 6π α² ρ v²