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.
To get the pressure from the water weight, take a 1m^2 column of water of height given (35m). That gives you a volume of water, which can be converted to mass with the density.
Weight of the water= mass*g
Pressure on bottom of column is weight/1m^2
That is guage pressure. Now, absolute will add the atmospheric pressure at the top.
c. the tension on the cable will be weight of the aluminum minus bouyancy. Bouyancy will be the weight of water of the same volume as the aluminum.
d. Tension = weight-bouyancy + massaluminum*acceleration. Think about that.
would u know what formula i should use to get started on this?? and the fromulas for the problem
Yes, I do. I gave them in verbal form. Read what I wrote. I will be happy to critique your thinking.
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??
P = Po + egh
P=(1.025x10^3)(10)(35)
density right, height right. What is the 10? Shouldnt it be 9.8? That gives the weight of the column of 1m^2, and dividing it by the area (1m^2) gives pressure in Pascals, normally, we write in kilopascals. Here is a rule of thumb to memorize: 33 feet (10 meters of water) equals barometric pressure, so 35 meters is about three times barometric pressure, which is just about what you have (baro pressure= 101kpa)
Good work.
yea my teacher makes us use 10 instead of 9.81 but for b) i just did
P = Po + egh
P = 1atm + 358750atm
so Pabs = 358751 atm ?????
and i am completely lost on c.. I know that tension = mg but i don't no how to find the mass of the aluminum.. they give me the volume right?
No. THe egh....and you need to do the units, is in Pascals. You cannot add pascals and atmospheres without changing one or the other. Practice putting units in your quantities, to see what comes out. Otherwise, you are blind to the units.
You may point out to your teacher, nicely, that nowhere on Earth is the acceleration due to gravity 10m/s^2.
Mass of aluminum is equalt to volume*density.
ok so my a is right but my b si wrong??
guage pressure is in pascals??
so what would my Patm be if I have
Patm = Po + 358750atm????
IM lost.. also for c i got the tension = 1620 and it increases for d.. it that right?
You may write pressure in any units you want, but you cannot add 1atm + xxxxpascals. the units have to be the same.
atmospheric pressure= 1atm= 101.3kPa
dont forget to include the boeyant force in your calculation for tension
dont forget to include the boeyant force in your calculation for tension
Yes, you need to include the buoyant force. The buoyant force is equal to the weight of the water displaced by the aluminum plate.
For part a) and b):
a) The gauge pressure on the diver on the ocean floor can be calculated as follows:
P_gauge = density * gravity * depth
P_gauge = (1.025x10^3 kg/m^3) * (9.8 m/s^2) * 35 m
P_gauge = 352387.5 Pa
b) The absolute pressure on the diver on the ocean floor is the sum of the gauge pressure and the atmospheric pressure:
P_abs = P_gauge + P_atm
P_abs = 352387.5 Pa + 101325 Pa
P_abs = 453712.5 Pa
For part c):
The tension in the cable can be calculated as follows:
Tension = weight of the aluminum - buoyancy force
Weight of the aluminum = volume * density * gravity
Weight of the aluminum = (1.0 m * 2.0 m * 0.03 m) * (2.7x10^3 kg/m^3) * (9.8 m/s^2)
Weight of the aluminum = 158.76 kg * 9.8 m/s^2
Weight of the aluminum = 1554.648 N
Buoyancy force = weight of water displaced by the aluminum
Buoyancy force = volume * density of water * gravity
Buoyancy force = (1.0 m * 2.0 m * 0.03 m) * (1.025x10^3 kg/m^3) * (9.8 m/s^2)
Buoyancy force = 60.9 N
Tension = 1554.648 N - 60.9 N
Tension = 1493.748 N
For part d):
If the plate accelerates upward at 0.05 m/s^2, the tension in the hoisting cable will increase. The new tension can be calculated using the equation:
Tension = weight of the aluminum - buoyancy force + mass of the aluminum * acceleration
Since the plate is accelerating upward, the tension has to provide an additional force to overcome the acceleration.
For part b, to find the absolute pressure, you need to add the atmospheric pressure (101.3 kPa) to the gauge pressure you calculated in part a. So the correct equation would be:
P_abs = P_gauge + P_atm
P_abs = 358750 Pa + 101300 Pa
P_abs = 460050 Pa
So the absolute pressure on the diver at the ocean floor is 460050 Pa.
For part c, you are correct that the tension in the cable is equal to the weight of the aluminum minus the buoyancy force. The weight of the aluminum can be calculated using the formula:
Weight = mass * gravity
To find the mass of the aluminum, you need to multiply its volume by its density. The volume of the aluminum plate is given as 1.0 m x 2.0 m x 0.03 m. So the equation for the mass of the aluminum would be:
Mass_aluminum = volume * density
Mass_aluminum = (1.0 m)(2.0 m)(0.03 m) * 2.7x10^3 kg/m^3
Now, the buoyancy force is equal to the weight of the water displaced by the aluminum plate. Since the plate is fully submerged, the volume of water displaced is equal to the volume of the aluminum plate. So the equation for the buoyancy force would be:
Buoyancy = volume * density_water * gravity
Buoyancy = (1.0 m)(2.0 m)(0.03 m) * 1.025x10^3 kg/m^3 * 9.8 m/s^2
Finally, the tension in the cable would be:
Tension = Weight_aluminum - Buoyancy
Tension = Mass_aluminum * gravity - Buoyancy
You can substitute the calculated values to find the tension.
For part d, if the plate accelerates upward at 0.05 m/s^2, you need to consider the additional force due to acceleration. The tension in the cable would be:
Tension = Weight_aluminum - Buoyancy + Mass_aluminum * acceleration
Since the acceleration is in the upward direction, the tension in the cable will increase.