A diver descends from a salvage ship to the ocean floor at a depth of 35 m below the surface. The density of ocean water is 1.025x10^3 kg/m^3.
a) Calculate the guage pressure on the diver on the ocean floor.
b) Calculate the absolute pressure on the diver on the ocean floor.
The diver finda a rectangular aluminum plate having dimensions
1.0m x 2.0m x 0.03m. A hoisting cable is lowered from the ship and the diver connects it to the plate. The density of aluminum is 2.7x10^3 kg/m^3. Ignore the effects of viscosity.
c) Calculate the tension in the cable if it lifts the plate upward at a slow, constant velocity.
d) Will the tension in the hoisting cable increase, decrease, or remain the same if the plate accelerates upward at 0.05m/s^2? Justify your answer.
Bob
To solve these problems, we need to use the principles of fluid pressure and buoyancy.
a) To calculate the gauge pressure on the diver on the ocean floor, we can use the formula:
Gauge pressure = density of fluid x acceleration due to gravity x depth
In this case, the depth is 35 m, and the density of ocean water is given as 1.025x10^3 kg/m^3. The acceleration due to gravity is approximately 9.8 m/s^2.
Substituting the values into the formula:
Gauge pressure = (1.025x10^3 kg/m^3) x (9.8 m/s^2) x (35 m)
Gauge pressure = 351,787.5 Pa
Therefore, the gauge pressure on the diver on the ocean floor is 351,787.5 Pa.
b) The absolute pressure on the diver at the ocean floor is the sum of the atmospheric pressure and the gauge pressure. At the surface, the atmospheric pressure is typically around 101,325 Pa.
Absolute pressure = Gauge pressure + Atmospheric pressure
Absolute pressure = 351,787.5 Pa + 101,325 Pa
Absolute pressure = 453,112.5 Pa
Therefore, the absolute pressure on the diver on the ocean floor is 453,112.5 Pa.
c) To calculate the tension in the cable when the plate is lifted upward at a slow, constant velocity, we need to consider the forces acting on the plate.
The weight of the plate can be calculated using the formula:
Weight = mass x gravity
The mass of the plate can be found by multiplying its volume by its density:
Mass = volume x density
Mass = (1.0m x 2.0m x 0.03m) x (2.7x10^3 kg/m^3)
Mass = 0.162 kg
Substituting the values into the formula for weight:
Weight = (0.162 kg) x (9.8 m/s^2)
Weight = 1.5876 N
Since the plate is lifted upward at a slow, constant velocity, the tension in the cable is equal to the weight of the plate. Therefore, the tension in the cable is 1.5876 N.
d) If the plate accelerates upward at 0.05 m/s^2, the tension in the cable will increase. This is because the cable now has to provide an additional force to counteract the acceleration of the plate.
To calculate the new tension, we need to add the force due to the acceleration to the weight of the plate. The force due to acceleration can be calculated using the formula:
Force = mass x acceleration
Substituting the values into the formula:
Force = (0.162 kg) x (0.05 m/s^2)
Force = 0.0081 N
Adding the force due to acceleration to the weight of the plate:
New tension = Weight + Force
New tension = 1.5876 N + 0.0081 N
New tension = 1.5957 N
Therefore, the tension in the hoisting cable will increase to 1.5957 N if the plate accelerates upward at 0.05 m/s^2.