Calculating Pressure from Stacked Bricks: Fluids Homework Solution

[koolkris623]

Homework Statement

A brick weighs 15.0 N and is resting on the ground. Its dimensions are 0.203 m 0.0890 m 0.0570 m. A number of the bricks are then stacked on top of this one. What is the smallest number of whole bricks (including the one on the ground) that could be used, so that their weight creates a pressure of at least one atmosphere on the ground beneath the first brick? (Hint: First decide which face of the brick is in contact with the ground.)

pressure = force / area
density = Mass / volume
1atm = 101300 Pa
Volume = l* w* h

The Attempt at a Solution

well what i did was i found the area of the face to be .203 * .0890..then i divided 15/ Area to get pressure then i did 101300 / pressure to get number of bricks..this doesn't work

 

[Shooting Star]

To get max pressure, the area should be the least. Do you think you have found that correctly?

After that, total weight/area = pressure on the ground.

 

[ogb p]

because i'm not considering the weight of the additional bricks stacked on top of the first one.

I would approach this problem by first identifying the variables involved and using the appropriate equations to solve for the unknown values. In this case, the variables are the weight of the brick, its dimensions, the number of bricks stacked on top, and the pressure on the ground beneath the first brick.

To calculate the pressure, we can use the formula: pressure = force / area. In this case, the force is the weight of the bricks, which is given as 15.0 N. The area in contact with the ground is the face of the brick, which has a dimension of 0.203 m x 0.0890 m = 0.0181 m^2. Therefore, the pressure on the ground beneath the first brick is 15.0 N / 0.0181 m^2 = 829.8 Pa.

Next, we need to determine the number of bricks required to create a pressure of at least 101300 Pa, which is equivalent to one atmosphere. To do this, we can use the equation: pressure = density * gravity * height, where density is the mass of the bricks divided by their volume, gravity is the acceleration due to gravity (9.8 m/s^2), and height is the total height of the stacked bricks.

Using the given dimensions of the brick, we can calculate its volume as 0.203 m x 0.0890 m x 0.0570 m = 0.000833 m^3. The mass of the brick can be found by multiplying its weight (15.0 N) by the acceleration due to gravity (9.8 m/s^2), giving us a mass of 1.47 kg. Therefore, the density of the bricks is 1.47 kg / 0.000833 m^3 = 1764 kg/m^3.

Now, we can rearrange the equation for pressure to solve for the height of the stacked bricks: height = pressure / (density * gravity). Plugging in the values, we get height = 101300 Pa / (1764 kg/m^3 * 9.8 m/s^2) = 5.76 m.

Since each brick has a height of 0.0570 m, we can divide the total height by the height of one