During friction welding, one solid is held stationary, while the other is rapidly vibrated sinusoidally at a frequency of 250 Hz. It oscillates between positive and negative positions of 2.5 mm. The coefficient of friction between the two surfaces is 0.3. Determine the compressive force (in Newtons and lbf) that must be applied to heat the metal to the melting point 1 mm below interface within 3 s. Because the vibrations occur so quickly, it's reasonable to assume that the heat flux is some average value that does not vary over time. Make the calculation first for titanium and then for carbon steel. The surfaces have a length of 100 mm in the direction of vibration and 50 mm in the other direction. Is the required normal force greater for one metal than the other