A solid concrete block weighs 160 N and is resting on the ground. Its dimensions are 0.400 m x 0.240 m x 0.0950 m. A number of identical blocks are stacked on top of this one. What is the smallest number of whole bricks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the first block? (Hint: First decide which face of the brick is in contact with the ground.)

Question

A solid concrete block weighs 160 N and is resting on the ground. Its dimensions are 0.400 m x 0.240 m x 0.0950 m. A number of identical blocks are stacked on top of this one. What is the smallest number of whole bricks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the first block? (Hint: First decide which face of the brick is in contact with the ground.)

Answer 1

p = 2 atm = 202650 Pa

p₀ = mg/a•b = 160/0.4•0.24 =1667 Pa
N = p/p₀ =202650/1667=121.6 ≈122

Answer 2

The answer from Elena is almost correct. The question asks for the least number of bricks, so you would actually use the smallest side of the brick to stack them.

Po = 160 / (.24*.095) =~ 7018 Pa
N = 202650 / 7018 = 28.9 = 29 Bricks.

Answer 3

To solve this problem, we need to determine the pressure exerted by each block on the ground and then calculate the number of blocks required to reach a pressure of at least two atmospheres.

Step 1: Finding the pressure exerted by each block
The pressure exerted by an object is given by the formula:

Pressure = Force/Area

In this case, the force is the weight of each block, which is given as 160 N. The area of contact between the block and the ground depends on which face of the brick is in contact with the ground. Let's consider the bottom face of the block, which has dimensions 0.400 m x 0.240 m.

Area = Length x Width
Area = 0.400 m x 0.240 m

Now, we can calculate the pressure exerted by each block using the formula:

Pressure = Force/Area
Pressure = 160 N / (0.400 m x 0.240 m)

Step 2: Determining the number of blocks required
To reach a pressure of at least two atmospheres, we need to compare the pressure exerted by each block to the pressure exerted by one atmosphere (standard atmospheric pressure).

Standard atmospheric pressure is approximately 101,325 Pascals (Pa). To convert this to Newtons per square meter (N/m²), we multiply by the conversion factor 1 Pa = 1 N/m².

One atmosphere = 101,325 N/m²

Therefore, we need to calculate the number of blocks that exert a pressure of at least 2 atmospheres, which is:

Number of blocks = (2 x 101,325 N/m²) / Pressure of one block

By substituting the values, we can find the smallest number of whole bricks required to create a pressure of at least two atmospheres on the ground beneath the first block.