At the bow of a ship on a stormy sea, a crew member conducts an experiment by standing on a bathroom scale.

Question

In calm waters, the scale reads 755  . During the storm, the crew member observer a maximum reading of 920  and a minimum reading of 555  .

A) Find the maximum upward acceleration experienced by the crew member.

B) Find the maximum downward acceleration experienced by the crew member.

Express your answer to three significant figures and include the appropriate units.

Answer 1

This is similar to the elevator problem. The normal force is the scale reading. His actual weight is the scale reading in the calm sea.

To have an upward acceleration, there must be a net upward force. As his actual weight doesn't change and acts downward, the normal force acts upward and must be greater than the weight, so ma = N- W = 920 -755 = 165. a = 165/m. The units of the scale reading weren't given, but I will take them as Newtons; therefore, his weight is 755 N, and his mass is 755N / 9.8 ms^-2 = 77.0 kg. The acceleration is 165N / 77.0kg = 2.14 ms^-2.

In the downward acceleration, the net force on the sailor is F = W - N. Follow the same procedure to calculate the downward acceleration. Use ma = 755 - 555.