drquanzae

[drquanzae]

A segment (dℒ) along the curve, take this to be the hypotenuse in a right angle triangle base dx=vₓdt and height dy=vᵧdt

dℒ²=dx²+dy²

dℒ²=(vₓdt)²+(vᵧdt)²

dℒ=√(vₓ²+vᵧ²)dt²

∫dℒ=∫|v| vector dt

Total distance by the particle

[drquanzae]

For an instant change of time the frictional driving force acting on the wheels of the 2.5g mars rover is F=600t²N where t=s. If the mats rover has a speed of 20km/h determine when t=0 and the stopping speed at t=5?

m=2.5Mg=2500kg

v₁=20(¹⁰⁰⁰⁄₃₆₀₀)=⁵⁄₁₈=5.556ᵐ⁄ₛ

m(v₂-v₁)=∫ₜ₁ᵗ²F dt

2500kg(v₂-5.556ᵐ⁄ₛ)=∫₀⁵ 600t² dt

¹⁄₂₅₀₀ ∫₀⁵ 600t² dt

(v₂-5.556ᵐ⁄ₛ)

v₂=¹⁄₂₅₀₀ ∫₀⁵ 600t² dt+5.556ᵐ⁄ₛ

v₂=⁶⁰⁰⁄₂₅₀₀|t³/3|₀⁵+5.556ᵐ⁄ₛ

v₂=⁶⁄₂₅(¹²⁵⁄₃)+5ᵐ⁄ₛ

v₂=10+5ᵐ⁄ₛ=15ᵐ⁄ₛ

v₂=15.556ᵐ⁄ₛ(³⁶⁰⁰⁄₁₀₀₀)

v₂=56km/h

[drquanzae]

Standard Model classification of particles

[drquanzae]

The pseudo rieman

geodesic manifold

dρ=√gᵤᵥ dxᵘdxᵛ

dρ=(λ₂ λ₁)∫√gᵤᵥ(dxᵘ/dλ dxᵛ/dλ) dλ

d/dx ∂(√gᵤᵥdxᵘdxᵛ)/∂xᵘ

d/dλ ∂L/∂xᵘ=∂L/∂xᵘ

d/dx ∂(√gᵤᵥdxᵘdxᵛ)/∂xᵘ

dρ=∂(√gᵤᵥdxᵘdxᵛ)/∂xᵘ

Δ²φ=0 ∂L≠0

[drquanzae]

Identify each of the following functions as even or odd: f(x)=|23x| Is even

g(p)=5p/p²+2 is odd

h(t)5-4t-2t³ is neither even or odd

[drquanzae]

The discovery in thermodynamics, of the Helmholtz free energy is a thermodynamic potential that measures the work obtainable from a closed entropic system at a constant temperature. The negative of the difference in the Helmholtz energy is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant and the volume is not held constant.

[drquanzae]

The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered this phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples. The samples, in the presence of an applied magnetic field, were cooled below their superconducting transition temperature.

[drquanzae]

[drquanzae]

What’s the volume of the riemann surface on the x-axis of the integral on the line when the cross sections are perpendicular to x=-1, x=1 connecting two parabolas of area y=x² and y=2-x²

A(s)=π(diameter)²/4

A(s)=π[(2-x²)-x²]²/4

π[2(1–x²)]²/4

A(x)=π(1-2x²+x⁴)

a=-1, b=1 gpa

ɪ=∫ₐᵇA(x) dx

ɪ=∫₋₁¹ π(1-2x²+x⁴) dx

ɪ=π[x-⅔x³+x³/5]¹₋₁

ɪ=2π(1-⅔+⅕)

A=16π/15

[drquanzae]

[drquanzae]

A 0.2kg golf ball is hit with a putter causing it to change its velocity from 10ᵐ⁄ₛ to the left and 15ᵐ⁄ₛ to the right determine the impulse imparted by the ball. Contact between the putter, and the golf ball was at 0.04s. Find the force exerted by the putter on the ball?

m=0.2kg v₀=10ᵐ⁄ₛ v= 15ᵐ⁄ₛ ɪ=?

ɪ=m(v-v₀)

ɪ=0.2(15+10)

ɪ=0.2(25)=5Ns

Impulse by the golf ball is 5Ns

ɪ=Ft, F=ɪ/t

F=5Ns/0.04s=125N

force exerted by the putter 125N onto the ball.

[drquanzae]

V=∫∫A∫ρ² sinφ dρdφdθ

V=∫(0,2π)∫(π/3,0)D∫(0,1) ρ² sinφ dρdφdθ

V=∫(0,2π)∫(π/3,0) [ρ²/3]¹₀ sinφ dφdθ

V=∫(0,2π)∫(π/3,0) ⅓ sinφ dφdθ

ɪ=∫(0,2π) [-⅓ cosφ]π/3,0 dθ

ɪ=∫(0,2π)(-⅙-⅓) dθ

ɪ=⅙(2π)

ɪ=π/3

[drquanzae]

dx/dy=1/√2y-1

d²x/dy²=1/2y-1

A=⅝¹∫2π√2y-1√1+1/2y-1 dy

2π ⅝¹∫√(2y-1)+1 dy

2π ⅝¹∫√2y^½ dy

(2π√2)|⅔y^³⁄₂|⅝ ¹

A=4π√2/3(1-5√5/8√8)

A=π/12(16√2-5√5)

[drquanzae]

A=10⁻⁶m² ρₑ=10⁻⁷ Ωm

r=⁷⁄₂₂m n=100 V=50V ɪ=?

ℓ=2πrN

ℓ=2 x ²²⁄₇ x ⁷⁄₂₂ x 100

ℓ=200m

R=ρₑℓ/A

R=10⁻⁷ Ωm x 200/10⁻⁶

R=20 Ω

ɪ=ᵛ⁄ᵣ= ⁵⁰⁄₂₀=2.5 Ampere

[drquanzae]

The best laser with which to do spectroscopy over a range of visible wavelengths is a Dye laser.

[drquanzae]

Here is Thomas Young’s double-slit experiment

written mathematically

S₂A=Xd/D is the path difference

Xd/D=mλ

m=0,1,2… the distance of mᵗʰ fringe from O

X=m Dλ/d maximum intensity

Dark fringes look like

Xd/D=(m-½)λ

X=(m-½)Dλ/d

The first black fringe is at m=1

Fringe width

W=Dλ/d

And the angular fringe width is

θ=λ/d

[drquanzae]

The greater the reduction potential, the stronger the oxidizing agent. The cell in which two electrodes are the same is referred to as the concentration cell. E=E_(cathode)-E_(anode)=0, E=0.059/n logA₂/A₁ because oxidation occurs at the anode and reduction occurs at the cathode.