(Solved): A section of a high speed test track is circular with a radius of curvature \( \mathrm{R}= \) \( 1 ...

A section of a high speed test track is circular with a radius of curvature \( \mathrm{R}= \) \( 1700 \mathrm{~m} \). At what angle of \( \theta \) should the track be inclined so that a car traveling at \( 67.0 \) \( \mathrm{m} / \mathrm{s} \) ( \( 150 \mathrm{mph} \) ) would keep moving in a circle if there is oil on that section of the track, i.e., it would not slip sideways even with zero friction on that section. (Hint: The car's vertical acceleration is zero.) \( M_{1} \) and \( M_{2} \) are two masses connected as shown. The pulley is light and frictionless. Find the mass \( M_{1} \), given that \( M_{2}(6.00 \) \( \mathrm{kg}) \) is moving downwards and accelerates downwards at \( 3.39 \mathrm{~m} / \mathrm{s}^{2} \), that \( \theta \) is \( 30.0^{\circ} \), and that \( \mu_{k} \) is \( 0.410 \).