1. The total length of a spring is 0.25 m. What it is unstretched and 0.30 m when a force of 17.82 N is applied to it. What will be the length when 26.72 N is applied to it?
2. A piller with a cross sectional area of 1.5 m^2 supports a portion of a building with a mass of 1.5 x 10^4 kg. What is the stress if the column is made from concrete?
3. The cross section of a rectangular block ABCD. The mass of the block is evenly distributed throughout the block. The block has a dimension of 10 cm x 40 cm x 40 cm.
a. Given that the density of the natural used to make the block is 500 kgm^3, what is the mass of the block in kg?
b. Calculate the density of 5 each block.
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1. To find the length of the spring when a force of 26.72 N is applied to it, we can use Hooke's Law. Hooke's Law states that the force applied on a spring is directly proportional to the extension or compression of the spring. Mathematically, it can be represented as F = k * x, where F is the force applied, k is the spring constant, and x is the extension or compression of the spring.
First, we need to find the spring constant (k) of the given spring. The spring constant can be determined by using the initial and final lengths of the spring. Let's use the given information to calculate k:
The initial length of the spring (unstretched) = 0.25 m
The final length of the spring (when 17.82 N force is applied) = 0.30 m
The extension of the spring (x) = final length - initial length = 0.30 m - 0.25 m = 0.05 m
Now, we can find the spring constant (k) using the formula F = k * x and the given force of 17.82 N:
17.82 N = k * 0.05 m
k = 17.82 N / 0.05 m
k = 356.4 N/m
Now that we have the spring constant (k), we can find the length of the spring when 26.72 N force is applied. Let's call this length "L":
26.72 N = 356.4 N/m * L
L = 26.72 N / 356.4 N/m
L = 0.075 m
Therefore, the length of the spring when 26.72 N force is applied will be 0.075 m.
2. To calculate the stress on the concrete column, we need to know the force applied and the cross-sectional area of the column. The stress (σ) can be calculated using the formula σ = F / A, where σ is the stress, F is the force applied, and A is the cross-sectional area.
Given:
Force applied (F) = weight of the portion of the building supported by the column = mass * acceleration due to gravity = 1.5 x 10^4 kg * 9.8 m/s^2
Cross-sectional area (A) = 1.5 m^2
Now, we can calculate the stress (σ):
σ = (1.5 x 10^4 kg * 9.8 m/s^2) / (1.5 m^2)
= 147,000 N / 1.5 m^2
= 98,000 Pa (Pascal)
Therefore, the stress on the concrete column is 98,000 Pascal.
3. a. To calculate the mass of the block, we need to know its volume and density. The volume can be determined by multiplying the dimensions of the block.
Given:
Dimension of the block: 10 cm x 40 cm x 40 cm
Density of the natural used to make the block: 500 kg/m^3
First, let's convert the dimensions to meters:
10 cm = 0.10 m
40 cm = 0.40 m
Volume = length x width x height = 0.10 m x 0.40 m x 0.40 m = 0.016 m^3
Now, we can calculate the mass using the formula mass = density x volume:
Mass = 500 kg/m^3 x 0.016 m^3 = 8 kg
Therefore, the mass of the block is 8 kg.
b. To calculate the density of 5 blocks, we need to know the total mass and total volume of the blocks.
Since we know the mass of one block is 8 kg, the total mass of 5 blocks would be:
Total mass = 8 kg/block * 5 blocks = 40 kg
And since we know the volume of one block is 0.016 m^3, the total volume of 5 blocks would be:
Total volume = 0.016 m^3/block * 5 blocks = 0.08 m^3
Now, we can calculate the density using the formula density = mass / volume:
Density = 40 kg / 0.08 m^3 = 500 kg/m^3
Therefore, the density of 5 blocks remains the same at 500 kg/m^3.