PHYS 17200 Exam Review: Momentum Principle, Forces, Energy and Thermal Physics

Terms in this set (30)

1. Momentum principleThe change in a system's momentum equals the net external force times the time interval: delta p = F_net * delta t. It is the general form of Newton's second law.
2. Relativistic momentump = gamma*m*v, where gamma = 1/sqrt(1 - v^2/c^2). For v much less than c, gamma is about 1 and p is about m*v.
3. Position update formula for a short time stepr_f = r_i + v_avg * delta t. In iterative computer models, v_avg is approximated by the velocity at the end of the step (p_f/m).
4. Steps of an iterative (numerical) motion predictionIn a loop: compute the net force from the current position, update momentum with p = p + F_net*dt, update position with r = r + (p/m)*dt, then advance time.
5. Newton's law of gravitation in vector formF on 2 by 1 = -G*m1*m2/|r|^2 * r-hat, where r points from object 1 to object 2. G = 6.7 x 10^-11 N*m^2/kg^2.
6. Near-Earth gravitational forceF = m*g, directed downward, with g = 9.8 N/kg. It is the approximation of universal gravitation near Earth's surface.
7. Coulomb's lawF = (1/(4*pi*epsilon0)) * q1*q2 / r^2, with 1/(4*pi*epsilon0) = 9 x 10^9 N*m^2/C^2. Like charges repel, unlike charges attract.
8. Spring force and the ball-and-spring model of a solidF = -ks*s, where s is the stretch from relaxed length. Solids are modeled as atoms connected by springs representing interatomic bonds.
9. Young's modulusY = (F/A) / (delta L/L), stress over strain. It is a macroscopic property related to the interatomic spring stiffness by Y = ks_i / d, where d is the interatomic spacing.
10. Conservation of momentum in a collisionIf the net external force on the system is negligible during the collision, the total momentum before equals the total momentum after.
11. Elastic vs inelastic collisionElastic: total kinetic energy is conserved. Inelastic: some kinetic energy becomes internal energy. Momentum is conserved in both if external forces are negligible.
12. Mini-problem: a 2 kg cart at 3 m/s sticks to an identical cart at rest. Final speed?Momentum: 2*3 = 4*v, so v = 1.5 m/s.
13. Period of a mass on a springT = 2*pi*sqrt(m/ks). It does not depend on amplitude.
14. Energy principledelta E_system = W + Q: the change in the system's energy equals the work done on it by surroundings plus energy transferred by heat.
15. Particle energy in relativityE = gamma*m*c^2. Rest energy is m*c^2, and kinetic energy K = (gamma - 1)*m*c^2, which is about (1/2)m*v^2 at low speed.
16. Work done by a constant forceW = F dot delta r = |F||delta r|cos(theta). Only the force component along the displacement does work.
17. Gravitational potential energy: general and near-Earth formsGeneral: U = -G*m1*m2 / r (zero at infinite separation). Near Earth: delta U = m*g*delta y.
18. Escape speed from a planet of mass M and radius Rv_esc = sqrt(2*G*M/R), from setting K + U = 0 at the surface.
19. Spring potential energyU = (1/2)*ks*s^2.
20. Mass-energy and binding energyA bound system has less mass than its separated parts. The binding energy is delta m * c^2, the energy needed to pull the parts apart.
21. Quantized energy levels in atomsElectrons in atoms have only certain discrete energies. A photon emitted or absorbed has energy equal to the difference between two levels: E_photon = E_upper - E_lower.
22. Energy levels of a quantum harmonic oscillatorE_N = N*h-bar*omega0 + E0, so levels are equally spaced by h-bar*omega0, where omega0 = sqrt(ks/m).
23. Torque and angular momentum principleTorque tau = r x F. The rate of change of angular momentum equals net torque: dL/dt = tau_net. If net torque is zero, L is conserved.
24. Moment of inertia and rotational kinetic energyI = sum of m*r_perp^2. Rotational kinetic energy K_rot = (1/2)*I*omega^2, and L_rot = I*omega.
25. Translational kinetic energy of the center of massK_trans = p^2/(2*M_total) = (1/2)*M*v_cm^2. Total K = K_trans + K_rel, where K_rel includes rotation and vibration.
26. Specific heat capacityQ = m*c*delta T for a temperature change without phase change. For water, c = 4.2 J/(g*K).
27. Entropy in terms of microstatesS = k_B * ln(Omega), where Omega is the number of microstates consistent with the macrostate. The second law: total entropy of an isolated system tends to increase.
28. Thermodynamic definition of temperature1/T = dS/dE: temperature measures how a system's entropy changes as energy is added. Energy flows from higher to lower temperature, increasing total entropy.
29. Average translational kinetic energy of an ideal gas moleculeK_avg = (3/2)*k_B*T, where k_B = 1.38 x 10^-23 J/K.
30. Ideal gas law in microscopic formP*V = N*k_B*T, where N is the number of molecules. Pressure comes from momentum transfer when molecules hit the walls.