An object becomes charged due to an excess or deficiency (shortage) of electrons. Knowing the exact number of excess or deficient electrons in an object allows one to determine the object's charge. The charge of one electron is 1.6 x 10⁻¹⁹ C. Use this to determine the charge of the following objects.
A. 1.0 x 10³ excess electrons
B. 1.0 x 10⁶ deficient electrons
C. 2.0 x 10⁹ excess electrons
D. 2.5 x 10⁸ deficient electrons
E. 6.82 x 10¹² excess electrons

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.