Question 1

A right triangle is submerged vertically with one side at the surface in a liquid of density $\rho$. The triangle has a leg that is 5 m long located at the surface and a leg 5 m long straight down. Find the force exerted on the triangular surface, in terms of the density. Neglect the effect of the atmosphere above the liquid.

Accepted Answer

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Question 2

Answer true or false. If a square, flat surface is suspended vertically in water and its center is 64 m deep, the force on the bottom side of the object will triple if the object is relocated to a depth of 192 m. Neglect the effect of the atmosphere above the liquid.

Accepted Answer

The force exerted by a fluid in rest on an object submerged in it depends on the depth of the object, the area of the object, and the density of the fluid, according to the formula $P = \rho gh$, where $P$ is the pressure, $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity, and $h$ is the depth of the fluid. Although the pressure does increase with depth, it does not triple when the depth is tripled; it increases linearly with depth. Therefore, if the depth triples, the pressure (and thus the force, since $F = PA$, where $A$ is the area) also triples, assuming the area and the fluid density remain constant.

Question 3

Answer true or false. The force on a semicircular, vertical wall with top d is given by  . Neglect the effect of the atmosphere above the liquid and assume the liquid is at a depth equal to the height of the wall. (The letter  stands for the weight of the liquid.)

Accepted Answer

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Question 4

Find the force (in N) on the top of a submerged object if its surface is 6.6 m² and the pressure acting on it is 4.6 * 10⁴ Pa. Neglect the effect of the atmosphere above the liquid.

Accepted Answer

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Question 5

Liquid cement (weight density 250lbs/ft³) is poured into a form whose ends are 3 foot squares. Find the force on one end if the cement is 2 feet deep.

Accepted Answer

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Question 6

A flat plate, shaped in the form of a semicircle 10 meters in diameter is submerged in water (weight density 9810 N/m³) as shown. Find the force against the surface of the plate.

Accepted Answer

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Question 7

A flat triangular plate whose dimensions are 17, 17, and 30 feet is submerged in water (weight density 62.4 lbs/ft³) point up so that its longer side is below the surface and parallel to it and its vertex is 4 feet below the water. Find the force against the surface of the plate.

Accepted Answer

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Question 8

A semicircular wall 10 ft across the top forms one vertical end of a tank. What is the total force exerted on this wall by water if the tank is full of water? Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Accepted Answer

The answer of A semicircular wall 10 ft across the...

Question 9

Answer true or false. If a submerged rectangle is rotated 125° about an axis through its center and perpendicular to its surface, the force exerted on one side of it will be the same, provided the entire rectangle remains submerged.

Accepted Answer

When a submerged rectangle is rotated about an axis through its center and perpendicular to its surface, it experiences a rotational force. However, this force is distributed evenly across the entire submerged surface, and therefore the force exerted on one side of the rectangle remains the same.

Question 10

A flat rectangular plate is submerged horizontally in water to a depth of 3.2 ft. If the top surface of the plate has an area of 50 ft², and the liquid in which it is submerged is water, find the force on the top of the plate. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.6 lb/ft³.)

Accepted Answer

The answer of A flat rectangular plate is submerged horizontally...

Question 11

Answer true or false. The force exerted by water on a surface of a square, vertical plate (suspended vertically) with edges of 4 ft if it is suspended with its top 4 ft below the surface is 5,990.4 lb. (The density of water is 62.4 lb/ft³.)

Accepted Answer

The force exerted by water on a surface of a square, vertical plate (suspended vertically) with edges of 4 ft if it is suspended with its top 4 ft below the surface is 5,990.4 lb. (The density of water is 62.4 lb/ft³.)

Question 12

A right triangle is submerged vertically with one side parallel to the surface in a liquid of density$\rho$. The triangle has a leg that is 16 m long located at the surface and a leg 16 m long straight down. Find the force exerted on the triangular surface, in terms of the density. Neglect the effect of the atmosphere above the liquid.

Accepted Answer

The answer of A right triangle is submerged vertically with...

Question 13

Answer true or false. A 106 ft² flat sheet of material is submerged vertically in water. The force acting on each side must be the same.

Accepted Answer

This is due to Pascal's law, which states that pressure applied to a fluid in a closed container is transmitted equally to every point in the fluid and to the walls of the container. Since water is a fluid, the pressure on each side of the sheet at the same depth will be equal, resulting in equal forces acting on each side.

Question 14

A flat rectangular plate, 5 feet long and 6 feet wide is submerged in water (weight density 62.4 lbs/ft³) with the 5 foot edge parallel to and 3 feet below the surface. Find the force against the surface of the plate.

Accepted Answer

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Question 15

Find the force on a 30-ft wide by 4-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft³.)

Accepted Answer

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Question 16

A horizontal cylindrical tank of diameter 12 feet is half full of a chemical (weight density 55 lbs/ft³). Calculate the force against one end.

Accepted Answer

The answer of A horizontal cylindrical tank of diameter 12...

Question 17

What is the force exerted by water on a surface of a square, vertical plate with edges of 3 ft if it is suspended with its top 3 ft below the surface? (The density of water is 62.4 lb/ft³.)

Accepted Answer

The answer of What is the force exerted by water...

Question 18

Answer true or false. If a submerged horizontal object is elevated to twice its original depth, the force exerted on the top of the object will be twice the force originally exerted on the object. Assume there is a vacuum above the liquid surface.

Accepted Answer

This statement is known as Pascal's Law, which states that the pressure applied to an enclosed fluid is transmitted uniformly throughout the fluid. In this case, since the depth of the object has doubled, the pressure exerted on it at the bottom (due to the weight of the liquid above it) has also doubled. This increased pressure is transmitted uniformly throughout the fluid, resulting in a doubling of the force exerted on the top of the object.

Question 19

Find the force on a 60 ft² horizontal surface 48 ft deep in water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft³.)

Accepted Answer

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Question 20

A flat triangular plate whose dimensions are 13, 13, and 10 feet is submerged in water (weight density 62.4 lbs/ft³) so that its longer side is at the surface and parallel to it. Find the force against the surface of the plate.

Accepted Answer

The answer of A flat triangular plate whose dimensions are...

Quiz 6: Applications of the Definite Integral in Geometry, Science and Engineering

Answer true or false. If a square, flat surface is suspended vertically in water and its center is 64 m deep, the force on the bottom side of the object will triple if the object is relocated to a depth of 192 m. Neglect the effect of the atmosphere above the liquid.

Answer true or false. The force on a semicircular, vertical wall with top d is given by . Neglect the effect of the atmosphere above the liquid and assume the liquid is at a depth equal to the height of the wall. (The letter stands for the weight of the liquid.)

Find the force (in N) on the top of a submerged object if its surface is 6.6 m2 and the pressure acting on it is 4.6 * 104 Pa. Neglect the effect of the atmosphere above the liquid.

Liquid cement (weight density 250lbs/ft3) is poured into a form whose ends are 3 foot squares. Find the force on one end if the cement is 2 feet deep.

A flat plate, shaped in the form of a semicircle 10 meters in diameter is submerged in water (weight density 9810 N/m3) as shown. Find the force against the surface of the plate.

A flat triangular plate whose dimensions are 17, 17, and 30 feet is submerged in water (weight density 62.4 lbs/ft3) point up so that its longer side is below the surface and parallel to it and its vertex is 4 feet below the water. Find the force against the surface of the plate.

A semicircular wall 10 ft across the top forms one vertical end of a tank. What is the total force exerted on this wall by water if the tank is full of water? Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft3.)

Answer true or false. If a submerged rectangle is rotated 125° about an axis through its center and perpendicular to its surface, the force exerted on one side of it will be the same, provided the entire rectangle remains submerged.

Answer true or false. The force exerted by water on a surface of a square, vertical plate (suspended vertically) with edges of 4 ft if it is suspended with its top 4 ft below the surface is 5,990.4 lb. (The density of water is 62.4 lb/ft3.)

Answer true or false. A 106 ft2 flat sheet of material is submerged vertically in water. The force acting on each side must be the same.

A flat rectangular plate, 5 feet long and 6 feet wide is submerged in water (weight density 62.4 lbs/ft3) with the 5 foot edge parallel to and 3 feet below the surface. Find the force against the surface of the plate.

Find the force on a 30-ft wide by 4-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft3.)

A horizontal cylindrical tank of diameter 12 feet is half full of a chemical (weight density 55 lbs/ft3). Calculate the force against one end.

What is the force exerted by water on a surface of a square, vertical plate with edges of 3 ft if it is suspended with its top 3 ft below the surface? (The density of water is 62.4 lb/ft3.)