A 600,000 kg subway train is brought to a stop from a speed of 0.5 m/s by a large spring bumper at the end of
its track which compresses 0.4 m. This transfer of
energy has been loaded onto the spring. What is the
spring constant of the bumper?

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Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. the wave is incident on a conductor which is placed at z > 0 region of the space. the conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) find the characteristic time for the free charge density which dissipates at the conductor. (b) write the maxwell equations and derive the wave equation for a plane wave propagating in a conductor. (c) find the attenuation distance at which the incident amplitude reduces to e ^−1 of its initial value. (d) find the electric and magnetic fields inside the conductor. 8 (e) find the power loss per area of the incident electromagnetic wave at the surface of conductor.

Two point charges are on the y axis. a 3.90-µc charge is located at y = 1.25 cm, and a -2.4-µc charge is located at y = −1.80 cm. (a) find the total electric potential at the origin. v (b) find the total electric potential at the point whose coordinates are (1.50 cm, 0). v

If you wanted to move an electron from the positive to the negative terminal of the battery, how much work w would you need to do on the electron? enter your answer numerically in joules.