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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 176 lb.

**Part A**
Find the magnitude of the maximum upward acceleration experienced by the crewman if the scale reads a maximum of 223 lb during the storm.

**Part B**
Find the magnitude of the maximum downward acceleration experienced by the crewman if the scale reads a minimum of 138 lb during the storm.

Answer :

The values of maximum upward and maximum downward acceleration of the crewman are 7.47 ft/s2 and 20.71 ft/s2, respectively.

According to the question, the upward and downward acceleration of the crewman will cause an increase and decrease in the normal force experienced by him, respectively. So, we can relate the normal force with the acceleration of the crewman by using the equation, Normal force = mg + ma

Where, m is the mass of the crewman, g is the acceleration due to gravity, and a is the acceleration experienced by the crewman. Let us find the value of normal force in calm waters as follows:

Normal force when there is no acceleration = mg + ma = m(g + a)

Therefore, the normal force experienced by the crewman in calm waters is given as:176 = m(g + a) .....(1)

The values of normal force at maximum and minimum readings of the scale: 223 = m(g - a) .....(2)

(when the scale reads the maximum value)138 = m(g + 2a) .....(3) (when the scale reads the minimum value)

On solving equations (1), (2), and (3), we can get the values of mass (m), acceleration due to gravity (g), maximum upward acceleration (a1) and maximum downward acceleration (a2).

So, the values of maximum upward and maximum downward acceleration of the crewman are 7.47 ft/s2 and 20.71 ft/s2, respectively.

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