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
pressure= total weight/area
I will be happy to critique your thinking.
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 doesnt work
smallest number of bricks will mean the greatest pressure, or smallest area. The side of the brick giving the smallest area will be .0890 x .0570, wouldn't it? The weight on that face gives the greatest pressure.
oo ok cool thanks
To find the smallest number of whole bricks required to create a pressure of at least one atmosphere on the ground beneath the first brick, we need to calculate the force exerted by the weight of the bricks.
First, let's calculate the pressure exerted by one atmosphere. Given that 1 atm = 101,300 Pa, the pressure is 101,300 Newtons per square meter (N/m^2).
To determine which face of the brick is in contact with the ground, we need to look at its dimensions. The face with the largest area will be in contact with the ground. From the dimensions given, we see that the face with dimensions 0.203 m * 0.0890 m = 0.018127 m^2 has the largest area.
Next, we need to find the force exerted by the weight of the bricks on the ground. We can use the formula: force = mass * acceleration due to gravity.
The gravitational acceleration is approximately 9.8 m/s^2.
Given that 1 N = 1 kg * m/s^2, we can find the mass of the brick using the formula: weight = mass * gravitational acceleration.
Weight = 15.0 N
Mass = Weight / gravitational acceleration = 15.0 N / 9.8 m/s^2 ≈ 1.53 kg.
Now, let's calculate the force exerted on the ground by this single brick: force = mass * gravitational acceleration = 1.53 kg * 9.8 m/s^2 = 15.03 N.
To create a pressure of at least 101,300 N/m^2 (one atmosphere), we divide this force by the area of the contact face: pressure = force / area = 15.03 N / 0.018127 m^2 ≈ 827.64 N/m^2.
The pressure exerted by one brick alone is less than one atmosphere. So, we need to stack multiple bricks on top of each other to achieve the desired pressure.
To find the number of bricks required, we divide the desired pressure by the pressure exerted by one brick. Minimum number of bricks = desired pressure / pressure exerted by one brick = 101,300 N/m^2 / 827.64 N/m^2 ≈ 122 whole bricks (including the one on the ground).
Therefore, the smallest number of whole bricks that could be used to create a pressure of at least one atmosphere on the ground beneath the first brick would be 122.