Pressureee?

Question

A solid concrete block weighs 174 N and is resting on the ground. Its dimensions are 0.400 m 0.200 m 0.100 m. A number of identical blocks are then stacked on top of this one. What is the smallest number of whole blocks (including the one on the ground) that can be stacked, so that their weight creates a pressure of at least one atmosphere on the ground beneath the first block? (Hint: First decide which face of the brick is in contact with the ground.)

A solid concrete block weighs 174 N and is resting on the ground. Its dimensions are 0.400x m x 0.200 m x 0.100 m. A number of identical blocks are then stacked on top of this one. What is the smallest number of whole blocks (including the one on the ground) that can be stacked, so that their weight creates a pressure of at least one atmosphere on the ground beneath the first block? (Hint: First decide which face of the brick is in contact with the ground.)

Answer 1

Nice hint :) Since Pressure = Force / Area and you want to maximize pressure, you want to minimize area. This means you set the first block up such that the smallest face is in contact with the ground. Now stack up enough blocks such that their total weight (mg) divided by that area is one atmosphere.

1 atmosphere = about 1.01 x 10^5 N / m²

Answer 2

Face with smallest area, i.e., 0.200 m x 0.100 m is in contact with the ground.
Let n = minimum number of blocks needed.
Then 174n/[(0.2)(0.1)] ≥ 1.01 x 10^5
=> n ≥ [1.01 x 10^5 ] x (0.02) / [174 ]
=> n ≥ 11.6
n = 12.