Walking across campus on a windy day, floyd fluids speculates about using an umbrella to ‘sail’ his bicycle across campus. the frontal area of the bike and rider is 0.3 m2 and they have a drag coefficient of about 1.2. assume the rolling friction coefficient is 0.05 and the combined mass of bike and rider is 85 kg. floyd’s umbrella is 1.22 m in diameter, and the wind is blowing at 24 km/hr.

Industrial processes often require the damping of vibrations. consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of 47500 n/m. this workbench is used when creating products that involve highly unstable chemicals. according to specifications, the acceleration of the manufacturing equipment must be held to less than 22.3 m/s2 for the manufacturing process to proceed safely. the amplitude of vibrations are expected to remain under 0.622 mm throughout. given that the workbench and maufacturing equipment combine to 6.05 kg, find the maximum acceleration expected of the equipment and workbench. (ignore the mass of the springs.)