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 235 lb and a minimum reading of 132 lb. Find the maximum upward acceleration experienced by the crewman. Find the maximum downward acceleration experienced by the crewman.
Upward acceleration increases the apparent weight, as measured by the scale. In this case, the maximum upward acceleration is (55/180)g.
The maximum downward acceleration is (48/180)g
To find the maximum upward and downward acceleration experienced by the crewman, we need to analyze the forces acting on him in both scenarios.
Let's start by calculating the maximum upward acceleration.
1. In calm waters, the crewman weighs 180 lb. We can convert this to mass using the conversion factor: 1 lb = 0.4536 kg.
Mass in calm waters = 180 lb * (0.4536 kg/1 lb) = 81.648 kg (approximately)
2. In stormy waters, when the crewman finds a maximum reading of 235 lb on the scale, it means there is an additional force acting on him due to the upward acceleration.
Additional force in upward direction = Maximum reading on the scale - Normal weight
Additional force = 235 lb - 180 lb
Additional force = 55 lb
3. We will now convert this additional force into newtons (N). Using the conversion factor: 1 lb = 4.448 N.
Additional force in newtons = 55 lb * (4.448 N/1 lb) ≈ 244.64 N (approximately)
4. To calculate the maximum upward acceleration (a), we can use Newton's second law of motion: F = ma, where F is the net force and m is the mass.
Maximum upward acceleration = Additional force / Mass
Maximum upward acceleration = 244.64 N / 81.648 kg ≈ 3.00 m/s² (approximately)
So, the maximum upward acceleration experienced by the crewman is approximately 3.00 m/s².
Next, let's calculate the maximum downward acceleration.
1. In stormy waters, when the crewman finds a minimum reading of 132 lb on the scale, it means there is an additional force acting on him due to the downward acceleration.
Additional force in downward direction = Normal weight - Minimum reading on the scale
Additional force = 180 lb - 132 lb
Additional force = 48 lb
2. Converting this additional force into newtons by using the conversion factor: 1 lb = 4.448 N.
Additional force in newtons = 48 lb * (4.448 N/1 lb) ≈ 213.5 N (approximately)
3. To calculate the maximum downward acceleration (a), we can use Newton's second law of motion: F = ma, where F is the net force and m is the mass.
Maximum downward acceleration = Additional force / Mass
Maximum downward acceleration = 213.5 N / 81.648 kg ≈ 2.61 m/s² (approximately)
So, the maximum downward acceleration experienced by the crewman is approximately 2.61 m/s².