Two hypothetical planets of masses m1 and m2 and radii r1 and r2, respectively, are nearly at rest when they are an infinite distance apart. Because of their gravitational attraction, they head toward each other on a collision course. (a) When their center-to-center separation is d, find expressions for the speed of each planet and for their relative speed. (b) Find the kinetic energy of each planet just before they collide, taking m1 5 2.00 3 1024 kg, m2 5 8.00 3 1024 kg, r1 5 3.00 3 106 m, and r2 5 5.00 3 106 m. Note: Both the energy and momentum of the isolated two-planet system are constant.
Physics 2 for Engineering Week 3 September 18 24 th th Metal sphere = conductor Charge comes to the surface Surface charge σ = Q / A Insulator Charge distributed over the volume ρ = Q / V Gauss’s Law Charges inside closed surfaces (Q = enclosed charge) ϕ is electric flux (electric field and area product with units N*m /C) 2 ϕ = E * A = Q / Ɛ 0 Gaussian surface must be symmetric For point or sphere charges, Gaussian surface has a spherical distribution For linear or sheet charges, Gaussian surface has a cylindrical distribution For a conducting sphere on the circumference E = q / (4πƐ R ) 0 2 Eon the inside of a conducting sphere =
