A cyclist intends to cycle up an 8 degrees hill whose vertical height is 150 m, with constant speed. If each complete revolution of the pedals moves the bike 6 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter D = 30 cm. The total mass of the cyclist and his bike is 150 kg.

The consumption of fossil fuels could be

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.

Identify the theory that can be used to explain each phenomenon. answers diffraction: wave theory interference: wave theory reflection: both particle and wave theories refraction: both particle and wave theories