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.
ok for a im going to let e = roh...
so P = Po + egh
P=(1.025x10^3)(10)(35)
so my answer to a wiill be 358750??
yes, see below. The units are in pascals.
To calculate the gauge pressure on the diver on the ocean floor, you can use the equation P = P₀ + egh, where P₀ is the atmospheric pressure, e is the density of the fluid, g is the acceleration due to gravity, and h is the depth.
In this case, the density of ocean water is given as 1.025x10^3 kg/m^3, the depth is 35 m, and the gauge pressure is the pressure relative to atmospheric pressure. Assuming atmospheric pressure is 0, we can calculate the gauge pressure as follows:
P = (1.025x10^3 kg/m^3) * (10 m/s^2) * (35 m) = 358750 N/m^2 or 358750 Pa
So the gauge pressure on the diver on the ocean floor is 358750 Pa.
To calculate the absolute pressure on the diver on the ocean floor, we need to add the atmospheric pressure to the gauge pressure. Assuming the atmospheric pressure is 101325 Pa, the absolute pressure is:
Absolute pressure = Gauge pressure + Atmospheric pressure = 358750 Pa + 101325 Pa = 460075 Pa
So the absolute pressure on the diver on the ocean floor is 460075 Pa.
Now, let's move on to the next set of questions regarding the aluminum plate and the hoisting cable.
To calculate the tension in the cable if it lifts the plate upward at a slow, constant velocity, we need to consider the forces acting on the plate. The tension in the cable will be equal to the weight of the plate.
The weight of an object is given by the equation W = mg, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The density of aluminum is given as 2.7x10^3 kg/m^3, and the dimensions of the plate are 1.0 m x 2.0 m x 0.03 m.
First, we need to calculate the mass of the plate:
Volume of the plate = length x width x height = (1.0 m) x (2.0 m) x (0.03 m) = 0.06 m^3
Mass of the plate = density x volume = (2.7x10^3 kg/m^3) x (0.06 m^3) = 162 kg
Now, we can calculate the tension in the cable:
Tension in the cable = Weight of the plate = m x g = (162 kg) x (9.8 m/s^2) = 1587.6 N
So the tension in the cable if it lifts the plate upward at a slow, constant velocity is 1587.6 N.
Finally, let's address the last question.
If the plate accelerates upward at 0.05 m/s^2, the tension in the hoisting cable will increase. This is because there will be an additional force acting on the plate due to its acceleration. The tension in the cable needs to counteract this additional force to maintain the plate's upward acceleration.
To justify this, we can use Newton's second law of motion: F = m × a, where F is the net force acting on an object, m is its mass, and a is its acceleration.
In this scenario, the force due to the tension in the cable is F = Tension in the cable, and the force due to the plate's weight is F = Weight of the plate = m × g.
If the plate accelerates upward, there will be an additional force acting on the plate in the opposite direction to its motion. This force is given by F = m × a. So, the net force acting on the plate is:
Net force = F due to tension in the cable - F due to weight of the plate + F due to plate's acceleration
If the plate is accelerating upward at 0.05 m/s^2, the net force acting on the plate will be greater than just the force required to counteract the weight of the plate. Therefore, the tension in the hoisting cable will need to increase to provide the necessary additional force.
In summary, the tension in the hoisting cable will increase if the plate accelerates upward at 0.05 m/s^2.