A cubic block of side length d is in a water container as shown in the...

A cubic block of side length d is in a water container as shown in the figure. Only half of the block is immersed in water and the block is being held by a rope attached to the bottom of the container. The block is made of wood with density ρ0. A) Find the tension on the string. B) If the container is fill with water up to a height of 1.5 m, calculate the pressure at the bottom of the container

Expert Solution

The weight of the block W = mg = d3 g. The weight is in downward direction.

The volume of the block inside the water is half of total volume. Vinside = d3 / 2

The buoyant force acting on this block is B = Vinside x x g = d3 g / 2 and is in upwards.

The tension T in the string is acting in downward direction on the block.

The block is at rest. Hence the buoyant force is balanced by weight and tension.

d3 g / 2 = d3 g + T

T = ( /2 - ) d3 g

b) The hydrostatic pressure at a depth h from the surface of water is P = h g

P = 1.5 x 1000 x 9.8 = 14700 Pa (g=9.8 m/s2)

_____________

If the atmospheric pressure Po is included then the absolute pressure is PA = Po + P

PA = 1.01 x 105 + 0.147 x 105 = 1.157 x 105 Pa

genius_generous answered 2 years ago

A thin wall cubic container is half-filled with water. What is the vertical position of the...

A thin wall cubic container is half-filled with water. What is the vertical position of the center of gravity if the container is tipped over just to the point where is about to spill water? Consider the side of the cube d = 0.30 m. a. yCG = 0.14 m b. yCG = 0.21 m c. yCG = 0.23 m d. yCG = 0.25 m

In a thought experiment, a cubic box of side length 0.01 mm contains three particles. One...

In a thought experiment, a cubic box of side length 0.01 mm contains three particles. One particle moves just in the x-direction, colliding elastically with the left and right walls of the cube. The second atom moves just in the y-direction, colliding elastically with the front and back walls of the cube. The third atom moves just in the z-direction, colliding elastically with the top and bottom walls of the cube. All three atoms have speed 500 m/s and mass...

2. A spring whose coefficient is k is compressed by length d and a block of...

2. A spring whose coefficient is k is compressed by length d and a block of mass m is placed right next to the end of the spring. When the spring is released, the block acquires a velocity and keeps on moving along a horizontal smooth surface until it reaches an inclined plane whose angle is θ and whose coefficient of friction with the block is μ. It travels up the inclined plane for a while before reaching maximum height....

cylindrical container with circular hole at the bottom with diameter d , is filled with water...

cylindrical container with circular hole at the bottom with diameter d , is filled with water to height h . Which of the following statement is correct for the itime required to empty the container If d is constant , the time is inversely proportional to the height of water . If h is constant , the time is inversely proportional to the area of hole . If his constant , the time is directly proportional to the area of...

An electron is in a #D quantum box with each side having length a0. a) What...

An electron is in a #D quantum box with each side having length a0. a) What is the largest wavelength of light emitted when the electron in the box transitions between levels? Consider only between levels up to the second excited energy level and express your answer in terms of a0. b) What is the smallest wavelength of light emitted when considering every possible transition?

A rigid container is divided into two parts, the left side of the container contains 1.5...

A rigid container is divided into two parts, the left side of the container contains 1.5 kg of water vapor at 1200 kPa and 350 ° C, while the right side contains 3.5 kg of wet water vapor, at 500 kPa with 50 per quality percent. Then the division is removed, and the two sides are allowed to mix, after this the temperature inside the container is measured which is 135 ° C, the amount of heat transferred in this...

A container contains water at 100 kPa. The specific volume of the water inside the container...

A container contains water at 100 kPa. The specific volume of the water inside the container is 1.00 m3/kg. What is the quality (x) of the water in the container, as a percentage and what is the phase of the water in the container?

A rectangular storage container with an open top is to have a volume of 16 cubic...

A rectangular storage container with an open top is to have a volume of 16 cubic meters. The length of its base is twice the width. Material for the base costs 15 dollars per square meter. Material for the sides costs 6 dollars per square meter. Find the cost of materials for the cheapest such container.

A rectangular storage container with an open top is to have a volume of 14 cubic...

A rectangular storage container with an open top is to have a volume of 14 cubic meters. The length of its base is twice the width. Material for the base costs 14 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.

A rectangular storage container with an open top is to have a volume of 20 cubic...

A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its base is twice the width. Material for the base costs 14 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.

Question