Formula Sheet For Sph4u (2).pdf

FORMULA SHEET FOR SPH4U Kinematics

Work and Energy 𝑣=

𝛥𝑑 𝛥𝑡

𝑎=

𝛥𝑣 𝛥𝑡

Work

𝑉 = - 𝐺

𝑊 = 𝐹 ∙ 𝛥𝑑 = 𝐹𝛥𝑑 cos 𝜃 Work-Energy Principle:

Five Kinematics Equations 1 𝛥𝑑 = 𝑣) + 𝑣, 𝛥𝑡 2

𝑊 = 𝛥𝐸

1 𝐸H = 𝑚𝑣 2 1 𝛥𝐸H = 𝑚(𝑣,- -𝑣)- ) 2 Gravitational Potential Energy

𝑣, = 𝑣) + 𝑎𝛥𝑡 𝑣,-

=

𝑣)-

𝐸K = 𝑚𝑔ℎ

+ 2 𝑎 ∙ 𝛥𝑑

Dynamics

Coulomb’s Law 𝑄𝑞 𝑟 𝑟Nm𝑘 = 9 ∙ 10h 𝐶 Field Strength (Intensity) ℰ =

𝐹2 𝑄 = 𝑘 - 𝑟 𝑞 𝑟

Electrical Potential

𝛥𝐸K = 𝑚𝑔(ℎ, -ℎ) )

𝑉 = - 𝑘

𝐹) = 0 )

𝐸 = 𝐸H + 𝐸K

𝐹123 = 𝑚𝑎 Newton’s Third Law: 𝐹:; = - 𝐹;: Gravity and Friction 𝐹= = 𝑚𝑔 𝐹,? = 𝜇𝑁

Magnetic Force on a moving charge

Power

𝑣 = 𝑐𝑜𝑛𝑠𝑡

Newton’s Second Law:

𝑄 𝑟

Magnetic Field

Newton’s First Law:

and

Electric Field

Mechanical Energy

𝐹123 =

𝑀 𝑟

𝐹2 = 𝑘

Kinetic Energy

1 𝛥𝑑 = 𝑣) 𝛥𝑡 + 𝑎𝛥𝑡 2 1 𝛥𝑑 = 𝑣, 𝛥𝑡 − 𝑎𝛥𝑡 2

Gravitational Potential

𝛥𝑃 =

𝛥𝐸 𝑊 = 𝛥𝑡 𝛥𝑡

Gravitational Fields Newton’s Law of Gravity 𝑀𝑚 𝐹= = 𝐺 - 𝑟 𝑟 Field Strength (Intensity) 𝒢 =

𝐹= 𝑀 = 𝐺 - 𝑟 𝑚 𝑟

(= 𝑔 at the surface of the Earth) ]^^

𝐺 = 6.67 ∙ 10

Nmkg -

𝐹k = 𝑞 𝑣 ×𝐵 𝐹k = 𝑞𝑣𝐵 sin 𝜃 on a current 𝐹k = 𝐼 𝑙 ×𝐵 𝐹k = 𝐼𝑙𝐵 sin 𝜃 Magnetic Field of a Wire with Current 𝜇r 𝐼 𝐵= 2𝜋 𝑟 Magnetic Field of a Solenoid 𝑁 𝐵 = 𝜇r 𝐼 𝑙

Wave Nature of Light

Interference

𝑐 =𝑓∙𝜆 𝑐 = 3.0 ∙ 10w m/s 𝑐=

𝜀r 𝜇r

𝜀r = 8.854 ∙ 10

𝜇r = 4 𝜋 ∙ 10]~

For distance d between the sources and the nth nodal line, sin 𝜃‚ = 𝑛 −

1

]^-

Special Theory of Relativity

1 𝜆 ∙ 2 𝑑

For light waves CN ∙ mN A-

Wave equation 𝑣 =𝑓∙𝜆

𝑥‚ 1 𝜆 = 𝑛 − ∙ 𝐿 2 𝑑 Young’s Interference

𝑣^ 𝜆^ = 𝑣- 𝜆Refraction 𝜆^ sin 𝜃^ 𝑣^ = = 𝜆- sin 𝜃- 𝑣-

𝜆 sin 𝜃k = 𝑚 ∙ , 𝑚 = 0, 1, 2, … 𝑑

sin 𝜃‚ = 𝑛 −

1 𝜆 ∙ , 𝑛 = 0, 1, 2, … 2 𝑑

Thin Film Interference Reflected rays Constructive

𝜆 𝑡 = 2𝑛 − 1 4

Destructive

Snell’s Law

𝑡=𝑛

𝑛^ sin 𝜃^ = 𝑛^ sin 𝜃-

𝜆 ≥1 𝑤 𝜆 is wavelength 𝑤 is width of the opening or size of the obstacle

𝜆 2

𝑛 = 0, 1, 2, …

Observable diffraction condition

Transmitted rays Constructive 𝑡=𝑛 Destructive

1− Time dilation

𝑣𝑐-

Δ𝑡k = 𝛾 Δ𝑡‰ Length contraction 𝐿‰ 𝐿k = 𝛾 Relativistic Mass 𝑚k = 𝛾 𝑚‰ Relativistic Momentum 𝑝 = 𝛾 𝑚𝑣

Bright fringes

Dark fringes

Transmission

1

𝛾=

𝜆 2

𝜆 𝑡 = 2𝑛 − 1 4 𝑛 = 0, 1, 2, …

Rest Energy 𝐸?2‰3 = 𝑚?2‰3 𝑐 Total energy 𝐸?2‰3 = 𝛾 𝑚?2‰3 𝑐 Quantum Mechanics Planck’s Constant ℎ = 6.626 ∙ 10]‹Œ J ∙ s, or ℎ = 4.136 ∙ 10]^Ž eV ∙ s Quantized energy 𝐸 = 𝑛ℎ𝑓, 𝑛 = 1, 2, 3, … De Broglie Wavelength ℎ ℎ 𝑝=𝜆= = 𝑝 𝑚𝑣 Heisenberg Uncertainty Principle 1 Δ𝑥 ∙ Δ𝑝 ≥ ℏ 2 ℎ ℏ= 2𝜋