For the following questions, use the equation below for the water pressure as a

Question

For the following questions, use the equation below for the water pressure as a function of depth:

P = (9800 Pa/m)*d + 101,300 Pa

PART A:
A cube of plastic that has dimensions of 2.3 m x 2.3 m x 2.3 m, is submerged in a tank of water such that the top surface of the cube is 2.2 m below the surface of the water. First, let's determine the water pressure acting on the top and bottom of the cube.

(i) What is the depth of the top surface of the cube?
m


(ii) What is the magnitude and direction of the water pressure acting on the top surface of the plastic cube?
Magnitude =  Pa and the direction is  Choose a direction. up down right left


(iii) What is the depth of the bottom surface of the cube?
m


(vi) What is the magnitude and direction of the water pressure acting on the bottom surface of the plastic cube?
Magnitude =  Pa and the direction is  Choose a direction. up down right left

Now, let's determine the forces caused by the water pressure acting on the top and bottom of the cube.

(v) What is the magnitude and direction of the force caused by the water pressure acting on the top surface of the cube?
Magnitude =  N, and the direction is  Choose a direction. up down right left .

(vi) What is the magnitude and direction of the force caused by the water pressure acting on the bottom surface of the cube?
Magnitude =  N, and the direction is  Choose a direction. up down right left .

Given the forces caused by the water pressure acting on the top and bottom of the cube, what is the magnitude and direction of the overall buoyant force that the water exerts on the cube?
Magnitude:  N and the direction is  Choose a direction. up down right left


PART B:
Now, imagine that you move the cube from PART A deeper in the water so that the top surface of the cube is 29 m below the surface of the water.

(i) What is the depth of the top surface of the cube?
m
(ii) What is the magnitude and direction of the water pressure acting on the top surface of the plastic cube?
Magnitude =  Pa and the direction is  Choose a direction. up down right left
(iii) What is the depth of the bottom surface of the cube?
m
(vi) What is the magnitude and direction of the water pressure acting on the bottom surface of the plastic cube?
Magnitude =  Pa and the direction is  Choose a direction. up down right left

Now, let's determine the forces caused by the water pressure acting on the top and bottom of the cube.

(v) What is the magnitude and direction of the force caused by the water pressure acting on the top surface of the cube?
Magnitude =  N, and the direction is  Choose a direction. up down right left .

(vi) What is the magnitude and direction of the force caused by the water pressure acting on the bottom surface of the cube?
Magnitude =  N, and the direction is  Choose a direction. up down right left .

Given the forces caused by the water pressure acting on the top and bottom of the cube, what is the magnitude and direction of the overall buoyant force that the water exerts on the cube?
Magnitude:  N and the direction is  Choose a direction. up down right left

PART C:
Notice that the buoyant force acting on the cube when it is at the greater depth in PART B is exactly the same as the buoyant force acting on the cube when it was at the more shallow depth in PART A. Which one of the following statements is an explanation for why the buoyant force remains the same at a greater depth?

When the cube is taken from the shallow depth of PART A, to the greater depth of PART B

A. the pressure acting downward on the top of the cube and the pressure acting upward on the bottom of the cube both increase by the same amount so that the buoyant force remains the same.

B. the pressure acting downward on the top of the cube and the pressure acting upward on the bottom of the cube both remain the same so that the buoyant force also remains the same.   

C. the pressure acting downward on the top of the cube increases, but the pressure acting upward on the bottom of the cube increases by a lesser amount so that the buoyant force remains the same.

D. the pressure acting downward on the top of the cube increases, but the pressure acting upward on the bottom of the cube increases by a greater amount so that the buoyant force remains the same.

Explanation / Answer

(1) depth of top surface of cube = 2.2 m

(2) pressure = 9800*2.2 + 101300 = 122860 pa downward

(3) depth of bottom surface = 2.2 + 2.3 = 4.5 m

(4) pressure on bottom surface = 9800*4.5 + 101300 = 145400 pa

Area of surface = 2.3 × 2.3 = 5.29 m^2

(5) Force on top surface = 122860 * 5.29 = 649929.4 N

(6) Force on bottom surface = 145400 * 5.29 = 769166 N

PART B

(1) Depth of top surface = 29 m

(2) pressure on top surface = 9800*29 + 101300 = 385500 pa

(3) depth of bottom surface = 29+2.3 = 31.3 m

(4) pressure on bottom surface = 9800*31.3 + 101300 = 408040 pa

(5) force on top surface = 5.29 * 385500 = 2039295 N

(6) force on bottom surface = 5.29 *408040 = 2158531.6N

PART C

A pressure and force increase on both surface but net force remain same

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