* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PHY 303k Test 2 Formula Sheet 1. Values of
Survey
Document related concepts
Transcript
PHY 303k Test 2 Formula Sheet 1. Values of√ Trigonometric Functions √ (angle in degrees): cos(0) = sin(90) = 1, cos(30) = sin(60) = 3/2, cos(45) = sin(45) = 2/2, cos(60) = sin(30) = 1/2, and cos(90) = sin(0) = 0. 2. Momentum Principle: F~net = d~p/dt = m~a. If F~net is constant, F~net = ∆~p/∆t. (Remember, d~p/dt, or equivalently m~a, describes the response of the system to the net force acting on it.) 3. Energy Principle (without heat exchanges): ∆E = Wsurr . 4. Kinematics (constant ~a or constant α): • ~r = ~r0 + ~v0 t + 1/2~at2 and ~v = ~v0 + ~at. • θ = θ0 + ω0 t + 1/2αt2 and ω = ω0 + αt. q 5. Relativistic Factor: γ ≡ 1−(|~v1|/c)2 6. Momentum: • Relativistic: p~ = γ m~v • Non-Relativistic: p~ = m~v 7. Energy for a Single Particle: • Relativistic: E = γ mc2 = mc2 + K where mc2 is the rest energy and K is the kinetic energy. • Non-Relativistic: E = K = 1/2mv 2 where K is the kinetic energy. 8. Forces: • Gravitational: F~grav = − Gm|~r1|2m2 r̂. • Spring Force: The force an ideal spring exerts on a mass is Fs = −ks sL̂ where ks is the force ~ − L0 , L0 is the equilibrium length of the spring and L ~ is the constant for the spring, s = |L| position of the mass relative to the point where the spring is anchored. • Frictional Force: is directed opposite the motion that would occur if friction were not present. – Kinetic Friction: |fk | = µk FN where µk is the coefficient of kinetic friction and FN is the force normal to the surface. – Static Friction: |fs | ≤ µs FN where µs is the coefficient of static friction and FN is the force normal to the surface. 9. Circular Motion: • Fnet,radial = maradial = mv 2 /r towards the center of rotation. • s = rθ where s is arclength so v = rω where v is tangential speed and ω is the angular speed. • If v is constant ω = 2π/T and T = 2πr/v where T is the period. ~·B ~ = Ax Bx + Ay By + Az Bz = |A|| ~ B| ~ cos θ, where θ is the angle b/w the vectors. 10. Dot Product: A R 11. Work (mechanical energy transfer): W = F~ · d~r. If F~ is constant, W = F~ · ∆~r 12. Work and Potential Energy: ∆UF = −WF where WF is the work done by force F~ and ∆UF is the change in the potential energy function associated with the force F~ . • Spring Potential Energy: Us = (1/2)kx2 where x is displacement relative the spring’s relaxed length. (F/A) 13. Young’s Modulus: Y = (∆L/L) = kdi where F/A is the applied force per area, (∆L/L) is the fractional change in length, ki is the interactomic spring constant, and d is the interatomic spacing. 14. Simple Harmonic Oscillator: The equation m(d2 x/dt2 ) = −kx p has the solution x = A cos(ωt + φ) or equivalently x = A sin(ωt + θ) where A is the amplitude, ω = (k/m) is the angular frequency, and φ or θ is the phase angle.