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 1.8 m x 1.8 m x 1.8 m, is submerged in a tank of water such that the top surface of the cube is 1.8 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 15 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

-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

-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.    

-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.

-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.

Answer 1

A i) The depth of the top face of the cube =(1.8m) ii) The magnitude of pressure Using P = 9800* d +101300 Pa , d=1-8m P= 9800X1.8+ 101300 =1118940 Pa direction = down as water above the surface is pushing it down. lii) The depth of the bottom surface = 1-8 +18 = 3.6m iv) The magnitude of the pressure - 9800X 3-67 101300 -136580 Pal in op direction v) The force on the top Proo* area of the top Ftop = !8940 * (1-8X1.8) / Area of / any surface Ftop = 385365-6N) inders in 385365 6N1 in/down of the cube of direction. vi) The force on the bottom a Poottom – Area = 136580 x1=g2 O Fbottom = 442519-2N) in Cup direction) 1. The buoyant force = Fbotton- Ftop = 442519-2-385365-6 = 5115 3-6 N) inful. Bi) The depth of the top face = [15 m) j) The pressure ftop = 9800x15 + 101300 = 2483 00 Pallowers ii) the depth of the bottom face = 15+18= (16-8 m) iv) The pressure Phottom = 9800x 16-8 + 10!300 =1265940) in v) The force on the top = Froo= 248300x1-82=804492 Ny in down direction = 1-8X1-8 m2

vi) The force on the bottom = 265940 X1.82 861645.6 Nyinlup. The buoyant force F = 86164506 - 804492 = 57153-6N , up] c) The buoyant force is the same because the pressure acting downward on the top and the pressure acting upward on the bottom increase by the same amount LIVORNOST