Two masses mi and m move under their mutual gravitational attraction in a uniform external gravita- tional field whose acceleration is g. choose as coordinates the cartesian coordinates x, y, z of the cen- ter ofmass vector r (taking z in the direction ofg) and the spherical coordinates r, θ and φ that define the relative vector r from mi and m2 (see hw problem set 1 for the definition of r). write down the lagrangian in terms of these 6 coordinates. calculate all 6 generalized momenta. which of these 6 momenta is conserved? write down the 6 euler-lagrange equations of motion.

If a negatively charged particle is placed at rest in an electric potential field that increases in the positive x-direction, what will the particle do? a. accelerate in the positive x-direction b. remain at rest c. accelerate in the negative x-direction

Which of the following is a characteristic shared by both electron and light microscopes? a. they both employ the use of objective lenses. b. both microscopes require an internal camera to visualize the specimen. c. both microscopes have a resolving power of 0.01 nm. d. they both utilize white light to magnify the specimen.

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.