A 4.8-m-tall, 30-cm-diameter concrete column supports a 5.0×105 kg load. By how much is the column compressed?

compression distance = (column length)*strain

Strain = Stress/(Young's modulus)

Stress = (load)/(area) = M*g/[(pi/4)D^2]

Look up Young's modulus for concrete and do the numbers. The modulus might be dfferrnt if the concrete is reinforced with steel, as most is.

According to information online, use 26,000*10^6 Pascals for Young's modulus of concrete, whether reinforced or not.

To calculate the compression of the column, we need to determine the amount of stress on the column and then use Hooke's Law to find the compression.

Step 1: Calculate the cross-sectional area of the column.
The diameter of the column is given as 30 cm, which is equal to 0.3 m.
The cross-sectional area of a circle can be calculated using the formula: A = π * r^2, where r is the radius of the circle.
So, the radius of the column is 0.3 m / 2 = 0.15 m.
The cross-sectional area of the column is A = π * (0.15 m)^2.

Step 2: Calculate the stress on the column.
Stress is the force applied per unit area and can be calculated using the formula: Stress = Load / Area.
The load on the column is given as 5.0 × 10^5 kg.
The stress on the column is Stress = (5.0 × 10^5 kg) / A.

Step 3: Calculate the compression using Hooke's law.
Hooke's Law states that the compression of an object is directly proportional to the applied force and inversely proportional to the object's stiffness or spring constant.
Hooke's Law can be represented as: Compression = Stress / Elastic Modulus x Length, where Elastic Modulus is a constant representing the stiffness of the material and Length is the height of the column.

Step 4: Calculate the compression of the column.
Given that the height of the column is 4.8 m, Elastic Modulus for concrete is approximately 30 × 10^9 N/m^2.
Therefore, the compression of the column is Compression = Stress / Elastic Modulus x Length.

By substituting the values into the formula, we can calculate the compression of the column.

To determine how much the column is compressed, we need to consider the weight of the load and calculate the change in height.

First, let's convert the diameter of the column from centimeters to meters:
30 cm = 0.3 m

Next, we'll calculate the cross-sectional area of the column:
A = π * r²
A = π * (0.3/2)²
A ≈ 0.0707 m²

Now, we can calculate the force acting on the column due to the load:
F = m * g
F = 5.0 × 10^5 kg * 9.8 m/s²
F ≈ 4.9 × 10^6 N

We can then calculate the compressive stress on the column:
σ = F / A
σ ≈ 4.9 × 10^6 N / 0.0707 m²
σ ≈ 6.9 × 10^7 Pa

The stress applied to the column causes a compressive strain, which is the change in length per unit length. Since the column is assumed to be incompressible in the horizontal direction (negligible change in diameter), we can consider only the vertical compression.

To calculate the strain, we need to know the Young's modulus of the concrete. Let's assume it is 30 × 10^9 Pa.

Now we can use Hooke's law to calculate the change in height (Δh) of the column:
σ = E * ε
ε = σ / E
Δh = ε * h
where ε is the strain, E is the Young's modulus, and h is the original height of the column.

Substituting the values:
ε ≈ 6.9 × 10^7 Pa / 30 × 10^9 Pa
ε ≈ 2.3 × 10^(-3)

Δh ≈ 2.3 × 10^(-3) * 4.8 m
Δh ≈ 0.011 m

Therefore, the column is compressed by approximately 0.011 meters.