The lens material is cr-39 monomer, with an index of refraction of 1.499. calculate r, the radius of curvature of the inner surface of the lens. note: diopter is a measure of the refractive power of a lens, and equals the reciprocal of the focal length in meters. example: for +3 diopters, f=0.333 meters.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

Place several e-field sensors at a few points on different equipotential lines, and look at the relationship between the electric field and the equipotential lines. which statement is true? 1-at any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of higher voltages. 2-at any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages. 3-at any point, the electric field is parallel to the equipotential line at that point.

The electric field inside a cell membrane is 8.0mn/c. what's the force on a singly charged ion in this field?