Three electrons are located at the vertices of an equilateral triangle with side lengths of d. The electrons at the base of the triangle are stuck in place but the electron at the top is free to move. The mass of an electron is 9.109 *10-31 kg. a) Find the distance d such that the electron located at the top or apex of the triangle is balanced by the repulsive forces of the electrons below it and the gravitational force pulling it down.

In Chapter 3 we saw that the electric forces acting between neighboring atoms behave very much like springs, with the spring stiffness being in the range of up to a few tens of Newtons per meter. Consider a molecule made up of two atoms of the same kind, each atom having a mass of 6.5 x 10-27 kg. Suppose that the center of the spring does not move, in which case you can model the motion of one of the atoms as that of a single atom connected to a half-length spring. If we should observe that a gas of these molecules emits photons whose energies are integer multiples of 2.4 x 10-2 eV, what would be the stiffness of the half-length "spring"? half-length k, = i N/m

An electron has an initial velocity of 3.6x104 m/s to the right.  It then travels through a potential difference, which speeds the electron up to a velocity of 8.1x104 m/s to the right. a) Since the particle was traveling to the right, and sped up, what was the direction of the acceleration of the electron, left or right? b) What then must have been the direction of the force on the electron? c) And then what must have been the direction of the electric field in that area? d) Given that you know the electric field has to point from high potential to low potential, is the electron traveling from a low to a high potential, or is it traveling from a high to a low potential? e) Does that make the potential difference (the change in potential) positive, or negative?

The IKAROS spacecraft, launched in 2010, was designed to test the feasibility of solar sails for spacecraft propulsion. These large, ultralight sails are pushed on by the force of light from the sun, so the spacecraft doesn’t need to carry any fuel. The force on IKAROS’s sails was measured to be 1.12 mN. If this were the only force acting on the 290 kg spacecraft, by how much would its speed increase after 6 months of flight?