Question

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 182lbs. During the storm, the crewman finds a max reading of 225lbs and a minimum reading of 138lbs A. find the max upward acceleration B. find the max downward acceleration

please use apparent weight formulas please...

Answer 1

The weight is just the apparent force acting on the crewman. During the upward acceleration, the apparent force is F_a = mg + ma. The ratio of this apparent force to his force at rest is the ratio of the above force to the force due to gravity alone. This will be equal to the ratio of the two weights:
\[\frac{ 225 lbs}{182 lbs} = \frac{ma+mg}{mg}\]
Cancelling m on the right hand side, we obtain:
\[\frac{a+g}{g}=\frac{225}{182}\]
Rearranging, and isolating g, we obtain:
\[a = g \big(\frac{225}{182}-1 \big) \]
\[=0.236g\]
\[=2.315 m/s^2\]

I'll leave it for you to find the maximum downward acceleration.

Answer 2

thanks totally figured it out later that night! but this helps with the clarification.