At the bow of a ship on a stormy sea, a crewman conducts an experiment by standing on a bathroom scale. In calm waters, the scale reads 180 lb. During the storm, the crewman finds a maximum reading of 220 lb and a minimum reading of 139 lb.

Calculate the maximum upward acceleration experienced by the crewman.

The maximum upward acceleration experienced by the crewman, calculated by analyzing the maximum force exerted on him during the storm and subtracting the acceleration due to gravity, is 2.19 m/s².

Explanation:

The scale reads variations in weight due to changes in acceleration. When at rest or in calm waters, the weight read by the scale equals the crewman’s actual weight due to gravity alone. During the storm, the maximum reading on the scale occurs when the upward acceleration is greatest.

First, we calculate the force exerted on the crewman at the maximum scale reading using the formula F = ma, where m is the mass and a is the acceleration due to gravity (9.8 m/s²). Given the crewman's weight in calm waters is 180 lb (which equals the force due to gravity), we can find his mass: 180 lb = m * 9.8 m/s², thus m = 81.63 kg.

During the storm, the maximum force exerted on the crewman (as read by the scale) is 220 lb. To find the maximum acceleration, we rearrange the F = ma equation: a = F/m. Converting 220 lb to Newtons (1 lb = 4.44822 N), we get 978.6044 N. Therefore, a = 978.6044 N / 81.63 kg = 11.99 m/s². However, this includes gravity, so the net acceleration experienced by the crewman is a - g = 11.99 m/s² - 9.8 m/s² = 2.19 m/s².